Post-processing Routes for Design of Giant Magnetoimpedance Response and Domain Wall Dynamics Control in Glass-coated Magnetic Microwires

Post-processing Routes for Design of Giant Magnetoimpedance Response and Domain Wall Dynamics Control in Glass-coated Magnetic Microwires by Paula Corte-León Supervisors Prof. Dr. Arkady Zhukov Egorova Prof. Dr. Julián María González Estévez Departamento de Polímeros y Materiales Avanzados: Física, Química y Tecnología Facultad de Ciencias Químicas San Sebastián, 2022 (cc) 2022 Paula Corte-León (cc by-nc 4.0) Abstract The principal objective of this thesis is to investigate the post-processing routes for the optimization of the magnetic properties of cobalt and iron based glass-coated microwires according to their applications. For this purpose several series of microwires were prepared and characterized paying attention on the effect of postprocessing conditions allowing maximizing magnetic softness, Giant Magnetoimpedance (GMI) effect and/or fast domain wall (DW) dynamics control. The work attempts to give an overview of the tuning possibilities of glasscoated microwires, which is one of the characteristics, in addition to their simple fabrication method and inexpensiveness that make them quite attractive and suitable for an enormous range of applications. We have worked with nearly-zero magnetostriction amorphous Co-rich glasscoated microwires, of CoFeBSiC composition with small additions of Ni, Mo and C or Cr and different diameters, which present magnetic softness in as-prepared state. The results show that appropriate post-processing allows further improvement of magnetic softness and GMI effect. It is noteworthy the remarkable GMI ratio enhancement (up to 650%) achieved by Joule heating at optimal conditions of CoFeNiBSiMoC amorphous glass-coated microwires. For Fe and Fe-Ni based glass-coated microwires, with rectangular hysteresis loops and hence, single DW propagation in as-prepared state, DW dynamics is further improved by furnace annealing owing to the internal stresses relaxation. On the other hand, low GMI ratio is enhanced more than an order of magnitude after stressannealing, Joule heating or combined stress-annealed followed by conventional furnace annealing. Induced anisotropy depends on the post-processing conditions. Annealing was demonstrated as an effective tool for optimizing magnetic softness and GMI effect of FeSiBNbCu devitrified microwires, but deterioration and poor mechanical properties lead to focus on post-processing that allows maintaining the amorphous structure. Unique combination of GMI effect and fast single DW propagation is obtained for FeBSiC amorphous glass-coated microwires with moderate stress-annealing induced anisotropy. Such stress-annealing induced anisotropy is found to possess a partially reversible character. Subsequent annealing of stress-annealed samples allowed reversing part of the anisotropy induced by the stress-annealing. As a rule, Co- & Fe-based microwires present amorphous structure if their diameters are below 30 µm. Furthermore, Fe-rich glass coated microwires of FeBSiNbNi composition of about 100  m of metallic nucleus, considered as “thick” microwires, are successfully obtained by modified Taylor Ulitovsky technique. “Thick” microwires are highly demanded for certain applications and few documented. After proper annealing desirable combination of high GMI effect and single DW propagation is exhibited. Likewise, for samples of both groups of microwires a simple route to achieve graded magnetic anisotropy along the sample length is proposed. Graded magnetic anisotropy is satisfactorily achieved after stress-annealing under temperature gradient. Finally, among the many possibilities, a novel sensing technology is proposed and explored in order to illustrate the possibility of implementing the use of glasscoating microwires in sensing technologies. With this aim, as-prepared Co-based microwires and stress-annealed Fe-based microwires were used for non-destructive and non-contact monitoring of a composite material with microwire inclusions. Sensitivity of such microwires to tensile stress and temperature allows monitoring matrix polymerization process of the composite through the changes in the hysteresis loops of the microwires. The sensitivity of Fe-rich microwires to tensile stress can be improved by the stress-annealing induced anisotropy. Composite polymerization effect is observed to be opposite to the effect of applied tensile stress on the hysteresis loops of the microwire inclusions. Therefore, allows assuming compressive character of stresses acting upon the microwires during the polymerization process. Additionally, upon polymerization considerable variation of the transmission and reflection parameters (in the range of 4-7 GHz) of the composite with microwire inclusions is also observed by means of free space technique. Resumen (Spanish) El principal objetivo de esta tesis es investigar las rutas de posprocesamiento para la optimización de las propiedades magnéticas de microhilos recubiertos de vidrio basados en cobalto y hierro de acuerdo con sus aplicaciones. Para ello, se prepararon y caracterizaron varias series de microhilos prestando atención al efecto de las condiciones de posprocesado que permitieran maximizar el comportamiento magnético blando, el efecto de magnetoimpedancia gigante (GMI) y/o el control de la dinámica de paredes de dominio. El trabajo intenta dar una visión general de las posibilidades de ajuste de las propiedades de los microhilos recubiertos de vidrio, que es una de las características, además de su sencillo método de fabricación y bajo costo, que los hacen bastante atractivos y aptos para una enorme gama de aplicaciones. Se ha trabajado con microhilos amorfos recubiertos de vidrio ricos en Co de magnetostricción casi nula, de composición CoFeBSiC con pequeñas adiciones de Ni, Mo y C ó Cr y de diferentes diámetros, que presentan comportamiento magnético blando sin necesidad de posprocesado. Los resultados muestran que el procesamiento posterior adecuado permite una mejora de la suavidad magnética y el efecto GMI. Cabe destacar la notable mejora del efecto GMI (hasta un 650 %) lograda optimizando las condiciones de calentamiento por efecto Joule en microhilos amorfos recubiertos de vidrio de composición CoFeNiBSiMoC. Para los microhilos recubiertos de vidrio basados en Fe y Fe-Ni, con ciclos de histéresis rectangulares y, que por lo tanto, presentan propagación de una única pared de dominio sin necesidad de tratamiento de posprocesado, la dinámica de paredes de dominio se mejora aún más mediante el recocido en horno debido a la relajación de las tensiones internas. Por otro lado, el bajo ratio GMI mejora más de un orden de magnitud después del recocido bajo tensión, el calentamiento Joule o el recocido bajo tensión combinado seguidamente de recocido en horno convencional. La anisotropía inducida depende de las condiciones de posprocesamiento. Se demostró que el recocido es una herramienta eficaz para optimizar la suavidad magnética y el efecto GMI en microhilos desvitrificados de FeSiBNbCu, pero el deterioro de las propiedades mecánicas llevan a centrarse en posprocesado que permita mantener la estructura amorfa. Se obtiene una combinación única de efecto GMI y propagación rápida de una única pared de dominio para microhilos amorfos recubiertos de vidrio FeBSiC con anisotropía inducida por recocido bajo tensión moderada aplicada. Se encuentra que tal anisotropía inducida por recocido bajo tensión posee un carácter parcialmente reversible. El recocido posterior de muestras recocidas bajo tensión permitió revertir parte de la anisotropía inducida por el recocido bajo tensión. Generalmente, los microhilos basados en Fe y Co presentan estructura amorfa cuando sus diámetros están por debajo de 30 µm. Se han obtenido con éxito mediante la técnica modificada de Taylor Ulitovsky microhilos recubiertos de vidrio ricos en Fe de composición FeBSiNbNi de aproximadamente 100  m de núcleo metálico, considerados como microhilos "gruesos". Los microhilos “gruesos” son muy demandados para ciertas aplicaciones y están poco documentados. Después de un recocido adecuado, exhiben una combinación deseable de alto efecto GMI y propagación de una única pared de dominio. Asimismo, para muestras de ambos grupos de microhilos se propone una ruta sencilla para lograr una anisotropía magnética graduada a lo largo de la longitud de la muestra. La anisotropía magnética graduada se logra satisfactoriamente después del recocido bajo tensión bajo un gradiente de temperatura. Finalmente, entre las muchas posibilidades, se propone y explora una nueva tecnología de detección para ilustrar la posibilidad de implementar el uso de microhilos recubiertos de vidrio en tecnologías de detección. Con este objetivo, se utilizaron microhilos a base de Co sin posprocesar y microhilos a base de Fe recocidos bajo tensión para el control no destructivo y sin contacto de un material compuesto con inclusiones de microhilos. La sensibilidad de tales microhilos a la tensión de tracción y la temperatura permite monitorear el proceso de polimerización de la matriz del material compuesto a través de los cambios en los ciclos de histéresis de los microhilos. La sensibilidad de los microhilos ricos en Fe a la tensión de tracción puede mejorarse mediante la anisotropía inducida por recocido de tensión. A través de los ciclos de histéresis, se observa que la polimerización de la matriz del material compuesto tiene un efecto sobre las inclusiones de microhilo de carácter opuesto a la aplicación de tensión de tracción sobre los microhilos. Por lo tanto, permite asumir el carácter compresivo de las tensiones que actúan sobre los microhilos durante el proceso de polimerización. Además, tras la polimerización también se observa una variación considerable de los parámetros de transmisión y reflexión (en el rango de 4-7 GHz) del compuesto con inclusiones de microhilos. Acknowledgments First of all, I want to mention Prof. Ignacio Guerra, for being so much more than a friend over the years and our first guide in the research world. I would be grateful for life to Prof. Blanca Hernando for giving me the opportunity and the encouragement to take this path, how not to do it keeping in mind her enthusiasm. Also Prof. Víctor de la Prida and all the Magnetic Materials and Nanomaterials research group at the University of Oviedo. All my gratitude to my Supervisors Prof. Julián González Estévez and Prof. Arkady Zhukov for the support, guidance and continuous help received from them and especially from Prof. Valentina Zhukova, I admire her in many aspects, the most important her human quality, and I will be always grateful for their tireless help, also she introduce me to the use of the equipments needed and made me familiar in working on microwires. I deeply appreciate the time and efforts they made for me. This work has been accomplished thanks to them. Many sincere thanks to our entire group, Juan María Blanco, Alexander Chizhik and especially Mihail Ipatov for helping me in uncountable occasions, I honestly appreciate them, their friendship and the things they made for me. Working with them was gratifying and a great pleasure. I am very glad for the place they gave me in their group making me feel part of it since the first day, and making easy my day to day, I am very thankful to them for their help in all aspects that could continue saying so much more. I want to give a huge thank you to all of them. I want to give special thanks to Prof. Carlos García, for the acceptance of my stay at his laboratory in the Department of Physics of the Universidad Técnica Federico Santa María in Valparaíso, Chile, for his kind welcome, his help, friendship and support and the rest of the group, especially Dra. Marián Abellán, for making the time spent there a valuable and unforgettable experience. I greatly thank Prof. Ivan Škorvánek, Head of Department of Applied Magnetism and Nanomaterials at the Institute of Experimental Physics of the Slovak Academy of Sciences in Košice, Slovakia for the acceptance of my virtual stay, the fruitful collaboration carried out, his invaluable discussions and his kindness and efficiency and Dr. František Andrejka for his crucial and extremely useful assistance and help. Special thanks to Alexander Torcunov and Victor Muhortov for letting me introduce in the microwires fabrication procedure, sharing their priceless experience and also unforgettable anecdotes. I would also like to give special thanks to Dra. Lorena González-Legarreta and Dra. Andrea Džubinská, co-workers for short time, but their great help and friendship has been essential, and Ahmed Talaat, doing the same path before me, for his kindness and support. Many thanks to PhD colleagues Alfonso García and Álvaro González who came to bring freshness to the group and also Dr. Mohamed Salaheldeen for his significant help and support in the final strech. I would like to thank Dr. Koldo Gondra and Dra. Sandra Allue, our collaboration established in the framework of ELKARTEK project, allowed me introduce myself in the field of smart composite materials with the help of their expertise. I am truly grateful to my friends, especially Coral, Alba, Cristina and Bea, for always being there for me. I must express my gratitude to Touseef, my husband, for been by my side, I want to promise him that all our efforts will be worth it. My children, Hakim and Ayra, born at the same time that this thesis bringing the biggest joy to my life, for them everything makes sense. For my parents I will never have enough words of gratitude for their efforts in helping me, to them belongs the greatest merit of this work. To my brother for been always the best companion and counselor. I would like to acknowledge for the technical and human support provided by SGiker of UPV/EHU (Medidas Magnéticas Gipúzcoa) and the Government of the Basque Country in the framework of HAZITEK and ELKARTEK projects and under the scheme of “Ayuda a Grupos Consolidados” and Spanish MINECO for the financial support of the group. Finally, I thank the following grant for financial support: NEOHIRE-NEOdymium-IronBoron base materials, fabrication techniques and recycling solutions to HIghly REduce the consumption of Rare Earths in Permanent Magnets for Wind Energy Application, H2020NMBP-720838, European Comission (Horizon 2020). This thesis is also devoted to those who are no longer but made us being here. Thanks to everyone who has contributed to this work. Contents Part I: Fundamentals ………………….……………………….…………………………………………………………………………. 1-52 1. Introduction ……….…………………………………………………….……………………………………………………..…….. 1 1.1. Metallic glasses ……..……………………………………….……………………………………………………..………….. 2 1.2. Soft magnetic materials …………………………………………………………………….………………………..…….. 3 1.3. Amorphous glass coated microwires ……………………………………………………………………….....…….. 4 1.3.1. Fabrication method …………………………………………………………………….……………................ 4 1.3.2. Effect of composition on magnetic properties ………….…………………………..…….............. 6 1.3.3. Hysteresis loops and domain structure ………………………………………………..….……............ 7 1.3.4. Induced anisotropies ………………………………………………….………………………..……..…………. 9 1.3.5. Nanocrystalline glass-coated microwires ……………………………………………..…………….…… 11 1.4. Giant magnetoimpedance (GMI) effect …………………………………………………..…………..……………. 11 1.5. Magnetic bistability and Fast domain wall (DW) propagation ………….………………………………… 13 1.6. Technological applications of magnetic glass-coated microwires …………………………..………….. 15 1.7. Research structure ………………………………..…………………………………………………………….……………. 18 1.8. References ………………………………………………………………………………………………………………………… 19 2. Experimental techniques …………………………………………………………………………………………….…………. 25 2.1. Glass-coated microwires fabrication: Taylor Ulitovsky method ………….…………..…….….……….. 25 2.2. Post-processing techniques: Annealing procedures ……………………..…………....………….…………. 27 2.2.1. Conventional furnace annealing …………………………………………………………………………….. 27 2.2.2. Stress annealing ……………………………………………………………………………………………………… 27 2.2.3. Current annealing …………………………………………………………………………………………………… 28 2.3. Magnetic characterization techniques …………………………………………………………..………………….. 29 2.3.1. Hysteresis in ferromagnetic materials ……..……………………….………………………….…………. 29 2.3.2. Flux-metric method for hysteresis loops measurements ……...……………….………………... 30 2.3.3. PPMS Magnetometer ……………………………..………………………….……….…………….…………….. 33 2.3.4. Giant Magneto-Impedance (GMI) effect measurements …………………..………..………….. 34 2.3.5. Free space electromagnetic parameters measurement system ……..…………….…………. 37 2.3.6. Domain wall (DW) propagation measurements ……………….…..……………..………………….. 39 2.3.7. Small angle magnetization rotation (SAMR) technique for magnetostriction measurements ………………………………………………………………………………………………………… 40 2.4. Microstructural characterization techniques …………………………………………………..….……….….… 43 2.4.1. Powder X-ray diffraction (XRD) …………………………………….…………………………………….….. 43 2.4.2. Optical microscopy (OM) ………………………………………..…………….……………………………….. 45 2.4.3. Scanning Electron Microscopy (SEM) ……………………………………….………………………………. 46 2.4.4. Differential Scanning Calorimetry (DSC) ………….………………………….…………………………. 47 2.5. References ………………………..…………………………………….………………………………..……………...……... 51 Part II: Results and discussion …….…………..………………………………..……………………..…………………………..54-187 3. Engineering of magnetic properties of Co-rich microwires ………………….………………………….... 54 3.1. As-prepared Co-rich microwires …….………………….…………………………..…………..….…….…………… 55 Introduction 5 mechanical properties aforementioned wire properties, the glass coating adds anticorrosive properties and biocompatibility [18]. Figure 1.1. Glass-coated microwires casting at TAMAG Iberica, S.L., Spain (a). SEM (b) and optical (c) images of glass-coated microwire samples (the glass coating has been cut and the metallic core is exposed) and sample of a microwire bobbin produced (d). Among the rapid melt quenching methods to produce glass-coated microwires, the process used in this thesis consists on the modified TaylorUlitovsky technique, based on rapid cooling of the molten alloy. The main reasons are: because of the dimensionality reduction that it allows, with the production of the thinnest amorphous glass-coated metal microwires (typically with 1 - 30 µm in diameter) [19,20]; It is well known, being known since the ‘60s [18], and including magnetic materials since the ‘70s [21]; because it allows a controlled manufacture of continuous and homogeneous metallic microwires Fundamentals: Chapter I 6 (Figure 1d) (up to a few kilometres) [22]; and it is suitable for fabrication of magnetic microwires with either amorphous or nanocrystalline structure [2223]. As compared with crystalline microwires, amorphous microwires present high tensile strength values that are observed to decrease with the increase in the metallic core diameters. This tendency is explained by higher cooling rates with decreasing metallic core diameters [24,25]. Now, while the tensile strength in amorphous state seems to be due to the metallic core of the microwire, the addition of the glass coating does not seem to contribute significantly in the fracture toughness. The glass around the fracture point breaks, not because of the stress, but because of the sound wave produced by the rupture or the metallic core [26]. 1.3.2. Effect of composition on magnetic properties The energy balance between long and short-range interactions determines the magnetic properties of a material. In the case of amorphous materials, the absence of magnetocrystalline anisotropy, gives a main role to the magnetoelastic anisotropy, Kme, given as [27,28]: 𝐾𝑚𝑒 = 3/2λ𝑆 σ (1.1) where λs is the magnetostriction coefficient, σ = σi + σapp the total stresses and σi and σapp the internal and applied stresses, respectively. Therefore, in amorphous microwires, stress and magnetization are linked and stress can either be sensed, or used as a mean to tune the magnetic properties. The λs sign and value of amorphous materials primary depends on the chemical composition. Accordingly, the easiest way to tune the λs sign and value in amorphous alloys is to modify their chemical composition [27,28]. Thus, Fe-rich compositions possess high and positive λs -values (up to λs ≈ 40 x 10-6), while for the Co-rich alloys the magnetostriction is low (up to λs ≈ -5 x 10- Introduction 7 6) [28]. Even lower λs values can be obtained by doping of Co-rich alloy with Fe or Mn: λs can take vanishing values in Co1-xFex or Co1-xMnx amorphous alloys at 0.05 ≤ x ≤ 0.1 [27,28]. Alternatively, low λs -values can be achieved in Ni1-xFex alloys, while such alloys present a low saturation magnetization, Ms, and hence are less interesting for applications [28]. Internal stresses in glass-coated microwires (of the order of 100-1000 MPa) arise from the difference in the thermal expansion coefficients of metallic nucleus and glass coating [29]. They strongly depend on the ratio between the glass coating thickness and metallic core diameter, increasing with the glass coating thickness. Such large internal stresses give rise to a drastic change of the magnetoelastic energy, Kme, even for small changes of the glass-coating thickness at fixed metallic core diameter [11]. Magnetic behaviour of each group of microwires depends on the internal stresses value and distribution. Therefore, magnetic properties of the glass–coated microwires can be tailored through the change of magnetic anisotropy by tailoring the internal stresses with adequate post-processing (furnace annealing, chemical etching, etc.) or changing the compositions of the metallic nucleus. 1.3.3. Hysteresis loops and domain structure Depending on the magnetostriction sign and value amorphous glasscoated microwries can be divided in three groups. Figure 1.2 reflects the hysteresis behaviour and domain structure of the amorphous-glass coated microwires related to each group. Co-based microwires with negative magnetostriction coefficient usually possess circular magnetic easy axis [30] and therefore are characterized by a domain structure consisting of circular domains [31]. Magnetization process in axial direction runs through reversible rotation of magnetic moments inside Fundamentals: Chapter I 8 domains. Almost linear loop with quite low hysteresis is observed for these microwires when an axial magnetic field is applied (Figure 1.2a). Nearly zero or low magnetostriction coefficients are found for Co-Febased glass-coated microwires. The domain structure of such microwires consists of axial domain structure surrounded by circular domains [26]. Hysteresis loops of such microwires present very low coercivity and high permeability (Figure 1.2b). Finally, Fe-based based glass-coated microwires with positive magnetostriction usually present rectangular hysteresis loop related to their domain structure consisting of a large axially magnetized single domain Figure 1.2. Typical hysteresis loops and domain structures of glass-coated microwires with negative (a), nearly zero (b) and positive (c) magnetostriction coefficient. Adapted from [32]. Introduction 9 surrounded by outer domains with radial magnetization orientation. In addition to small closure domains at the microwire ends in order to decrease the stray fields [32] (Figure 1.2c). Magnetic bistability presented for such microwires will be further discussed later. 1.3.4. Induced anisotropies The metastable amorphous structure of glass-coated microwires makes them quite sensitive to their environment and past history. One of the important sources of anisotropies is the stress induced during their fabrication. Anisotropy control is extremely important for specific technological applications. Annealing, at temperatures below crystallization, allows to relax the induced anisotropies as well as to create new ones. However, the rate of change of structural relaxation is a complex function depending on the annealing temperature and time. Thus in order to understand how anisotropies are affected by annealing processes, the relaxation phenomena itself has to be understood [33]. The relaxation mechanism that comprises changes in volume, diffusivity or viscosity of the metallic glass is of irreversible and monotonic character (except very close to and above glass transition temperature, Tg) [34]. On the other hand, a reversible relaxation phenomena occurs when achieving a saturated pseudo-equilibrium state after prolonged annealing. Usually, the system can move from one equilibrium state to another changing the annealing temperature [35]. Several mechanisms are proposed for induced anisotropies including: ordering of atomic pairs that results in directional ordering; easy-axis alignment; structural relaxation; shape anisotropy influence due to mechanical Fundamentals: Chapter I 10 grain alignment or structural anisotropy associated to small anisotropic structural rearrangements in short atomic range [36,37]. Annealing at modest temperatures and annealing times causes a decrease in the magnetoelastic anisotropy. Accordingly, elevated annealing temperature induces macroscopic magnetic anisotropy with the preferential axis determined by the direction of magnetization during the annealing [37]. Here, as an example the complex mechanism of induced anisotropies is described for the case of Fe-rich microwires subjected to stress-annealing (see Figure 1.3) [38-40]. In this case, stress-annealing induced anisotropy is associated to so called “back-stresses”. Annealing induces transversal anisotropy and the stress applied during the annealing induces longitudinal anisotropy, resulting in drastic decrease in the longitudinal stress component and appearance of compressive longitudinal stress. Magnetoelastic energy is minimized, with the redistribution of the internal stresses and/or local microstructure. Figure 1.3. Schematic illustration of effect of stress annealing in Fe-based glass-coated microwires (Adapted from [39]). Introduction 11 1.3.5. Nanocrystalline glass-coated microwires Nanocrystalline soft magnetic materials are two-phase materials consisting of nanocrystallites randomly distributed in a soft magnetic amorphous phase. This group of magnetic materials is considered of great interest due to their exceptional soft magnetic properties [10]. The nanocrystalline state is achieved by crystallization of conventional Fe-Si-B amorphous alloys, produced since the ‘70s [41] with small addition of Cu and Nb [42]. Fe-Si-B-Cu-Nb alloys obtained are usually known by trademark name Finemet. Ultrafine grain structure with small crystallites (around 10 nm grain size) embedded in a residual amorphous matrix is obtained after carefully annealing the amorphous precursor, at temperatures between partial and full crystallization processes in order to avoid the deterioration of soft magnetic properties. The adjustment of the chemical compositions and the annealing parameters for the devitrification process allow obtaining materials with rather different microstructures. Although, most results have been reported on ribbons and wires, recently great attention has been paid also on nanocrystalline microwires [43,44]. The origin of excellent soft magnetic properties in nanocrystalline microwires as well as the routes for their optimization will be further address in the section particularly devoted to them. 1.4. Giant magnetoimpedance (GMI) effect First discovered in the ‘30s [45], it was not until the late ‘90s [46-48], when high frequency equipment was available, that GMI research took off. The GMI effect is a skin effect where the electrical impedance of a material is linked to its magnetization, thus becoming an ideal way of probing magnetization Fundamentals: Chapter I 12 remotely [49]. Initially studied in wires, GMI has been also reported in glasscoated microwires [50], ribbons [51], micro-patterned ribbons [52] and multilayers [53]. The key advantage of magnetic sensors based on GMI is their ultra-high sensitivity (up to 10% / A/m) [5,54]. When combining the large effect of GMI, with the capability to perform remote measurements, and the relatively inexpensiveness of soft magnetic materials, with their low coercivities, the mixture produces an ideal combination to produce sensors at a low-cost and with high signal-to-noise ratio. Consequently, for the magnetic microwires studied here, the research pays attention on this effect to track magnetization, and through magnetization changes sense other magnitudes (e.g., stress). Figure 1.4 schematically shows the GMI behaviour exhibited by Fe-rich microwires with axial magnetic anisotropy and nearly zero magnetostriction Corich glass-coated microwires. GMI response of Fe-rich glass-coated microwires presents a single maximum for H = 0 (Figure 1.4a). On the other hand, doublepeak behaviour is observed for nearly zero magnetostriction samples (Figure 1.4b). The later samples are the most interesting due to the larger GMI effect Figure 1.4. Typical GMI behaviour of Fe-rich microwires (a) and nearly zero magnetostriction Co-rich microwires (b). Introduction 13 and better softness. However, Co belongs to critical raw materials; therefore, great efforts are paid to optimize the GMI response in less–expensive Fe-rich glass-coated microwires as promising solution [55]. 1.5. Magnetic bistability and Fast domain wall (DW) propagation A magnetic material is considered bi-stable when its magnetization has two preferred orientations, and the transition between these two states occurs through a single domain wall (DW) that travels the material without suffering any pinning. This is a desired behavior in certain situations, because it simplifies analyzing the behavior of the material. Such DW propagation can be driven either by a magnetic field [56] or by an electric current [50]. Roughly linear dependencies of DW velocity, v, on magnetic field, H, reported for a magnetic field driven DW dynamics are well understood in terms of the viscous DW motion [56]. DW propagation in a viscous regime with a velocity, v, can be given as [56]: 𝑣 = 𝑆(𝐻 − 𝐻0) (1.2) where S is the DW mobility, H is the axial magnetic field and H0 is the critical propagation field. Fundamentals: Chapter I 14 Figure 1.5. Typical v(H) dependence for magnetic field driven DW dynamics [57]. Non-linear v(H) dependencies can be observed either in low field or at high field regions (see Figure 1.5). After S. Parkin racetrack memory proposal in 2008 [58], using the concept of DWs to store information, DW motion control has attracted increasing attention for a vast number of promising applications (racetrack memories, magnetic sensors, magnetic tags, etc.). Such applications require fast magnetization switching and controllable DW propagation. Despite their great stability, thermal activation and pinning lead to stochastic behavior of the DW motion that needs to be addressed [59]. Amorphous glass coated microwires with positive magnetostriction constant generally exhibit spontaneous magnetic bistability originated by a single and large Barkhausen jump between two remanent states with opposite magnetization. As above described, perfectly rectangular hysteresis loops observed for these microwires are related to axial magnetization orientation within the most part of the metallic core of the microwire [60,61]. The magnetization switching (between the two remanent states) runs by fast DW propagation, starting from the closure domains at the microwire ends [62]. Thus, magnetically bistable microwires are a unique material for DW Introduction 21 [34] T. Egami, Magnetic amorphous alloys: physics and technological applications, Rep. Prog. Phys. 47 (1984) 1601-1725. [35] A. Zhukov, J. Gonzalez, J.M. Blanco, M.J. Prieto, E. Pina, M. 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Shuvaeva, A. Stepashkin, M. Zhdanova, A. Aronin, O. Aksenov, P. Arakelov, V. Zhukova, А. Zhukov, Non-contact method for stress monitoring based on stress dependence of magnetic properties of Fe-based microwires, J. Alloys Compd. 748(5) (2018) 199-205. [87] D.P. Makhnovskiy, L.V. Panina, Field dependent permittivity of composite materials containing ferromagnetic wires, J. Appl. Phys. 93 (2003) 4120–4129. Fundamentals: Chapter II 25 2. Experimental techniques This chapter is dedicated to the description of the different experimental techniques employed in this research work. A brief description of the fundamental background of each technique and the particular experimental set-up conditions used is given, from sample preparation to magnetic, microstructural and compositional characterization of the glass coated microwires produced. 2.1. Glass-coated microwires fabrication: Taylor Ulitovsky method Taylor Ulitovsky rapid solidification technique for glass-coated microwires manufacturing allows the preparation of thinnest amorphous microwires (with Figure 2.1. Glass coated microwires casting machine. Experimental techniques 26 metallic nucleus diameters ranging from 0.5-40  m). This fabrication method consists of melting a pre-prepared ingot of metallic alloy inside a glass (typically Pyrex or Duran) tube using a high frequency inductor [1,2]. Figure 2.1. shows the casting machine for the glass-coated microwires production. Few grams of the metal alloy with the suitable chemical composition are placed inside a glass tube. A high frequency inductor melts the metal forming a droplet which softens the glass tube adjacent allowing a capillary to form. Then, the capillary filled with the molten alloy is drawn and wound on a rotating bobbin. As a result, a microwire with metallic core and flexible and insulating glass coating is obtained. Table 2.1. Compositions and geometry of studied glass-coated microwires. Composition Metallic Nucleus Diameter d (μm) Total Diameter D (μm) Ratio ρ=d/D Magnetostriction Coefficient λs × 10−6 Fe77.5B15Si7.5 15.1 35.8 0.42 38 Fe75B9Si12C4 15.2 17.2 0.88 38 Fe70B15Si10C5 3 18,75 0.16 35 Fe70B15Si10C5 6 23,08 0.26 35 Fe70B15Si10C5 10.8 22.5 0.48 35 Fe70B15Si10C5 15 23,8 0.63 35 Fe71.7B13.4Si11Nb3Ni0.9 103 158 0.65 35 Fe71,8Cu1Nb3,1Si15B9.1 7.0 24.8 0.282 30 Fe71,8Cu1Nb3,1Si15B9.1 18.2 39 0.467 30 Fe70.8Cu1Nb3.1Si14.5B10.6 11.8 14.4 0.8 30 Fe70.8Cu1Nb3.1Si14.5B10.6 15.6 21.8 0.7 30 Fe70.8Cu1Nb3.1Si14.5B10.6 10.7 16.4 0.6 30 Fe62Ni15.5Si7.5B15 14.35 33.25 0.43 27 Fe47.4Ni26.6Si11B13C2 29 32.2 0.9 25 Fe49.6Ni27.9Si7.5B15 14.2 33.85 0.42 20 (Fe0.7Co0.3)83.7Si4B8P3.6Cu0.7 26.5 22.3 0.84 Fe83.7Si4B8P3.6Cu0.7 15.5 17.5 0.89 Co65.4Fe3.8Ni1B13.8Si13C1.65Mo1.35 18.8 22.2 0.85 −1 Co69.2Fe3.6Ni1B12.5Si11C1.2Mo1.5 22.8 23.2 0.98 −1 Co69.2Fe4.1B11.8Si13.8C1.1 25.6 30.2 0.85 −0.3 Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 25.6 26.6 0.96 −0.29 Co64.04Fe5.71B15.88Si10.94Cr3.4Ni0.03 95 130 0.73 Co66Cr3.5Fe3.5B16Si11 20.1 24.8 0.81 Fundamentals: Chapter II 27 Fe-, Ni-, Fe-Coand Cobased microwires with minor metalloid additions (Si, B, P, C) or non-magnetic metals have been prepared and studied. The compositions, geometry and magnetostriction coefficient, λs, of studied microwires are shown in Table 2.1. 2.2. Post-processing techniques: Annealing procedures 2.2.1. Conventional furnace annealing The most extended annealing technique is the heating of the sample at a given temperature, Tann, in air or vacuum for a given time, tann, in a conventional furnace. A single piece or a bunch of microwires can be treated at the same time. The samples were heat treated at a temperature, Tann, typically ranging from 200 °C to 500 °C in a conventional furnace, Thermolyne 62700. Typically, the crystallization of amorphous microwires was reported for Tann ≥ 490 °C. The advantage of amorphous microwires is their superior mechanical properties typically reported for amorphous materials [3]. In most cases, we fixed the annealing time, tann, of 60 min which is usually used for heat treatment of amorphous and nanocrystalline materials [4]. The samples were slow cooled to room temperature within the furnace. 2.2.2. Stress annealing In several cases, tensile stress was applied with a mechanical load attached to one microwire end during the annealing, as well as during the sample cooling in the furnace. The stress value in the metallic nucleus, σm, was evaluated considering different Young’s modulus of metal, E2, and glass, E1, as follows [5]: 𝜎𝑚=𝐾∙𝑃 𝐾∙𝑆𝑚+𝑆𝑔𝑙 ; 𝜎𝑔𝑙 =𝐾 𝐾𝑆𝑚+𝑆𝑔𝑙 (2.1) Experimental techniques 28 where K = E2 / E1, P is the applied mechanical load and Sm, and Sgl are the cross sections of the metallic nucleus and the glass coating, respectively. 2.2.3. Current annealing Also know as Joule heating, in this technique a sample is annealed by the current that passes through it causing its heating by Joule effect. It is widely used due to its simplicity and low cost, the equipment needed is similar as the one used for resistivity measurements [6]. Current annealing allows a better control of the annealing time without compromising the mechanical and chemical properties of the microwires as compared with conventional furnace annealing [7]. The current density is directly related to the sample heating [8]. The dc current value, I, needs to be set clearly below the value that can produce magnetic hardening and/or crystallization of the samples in order to avoid the deterioration of magnetic properties [9]. Structural relaxation and crystallization also depend on a great extend on the annealing time [10]. For our studies, electrical contacts were prepared by mechanically removing the insulating glass coating on the very end of microwires. Current annealing, with different durations and applying different currents was performed in air on 8 cm long samples. The insulating glass-coating of the microwires allows performing the thermal treatments in air. In order to avoid the inhomogeneities of the microwire diameter (and corresponding current density variation) and stresses related to the sample cutting, we used the same microwire for studies of the influence of annealing time, for a fixed DC current value, on magnetic properties and GMI effect. Fundamentals: Chapter II 29 2.3. Magnetic characterization techniques 2.3.1. Hysteresis in ferromagnetic materials The graphical representation of the magnetization versus the applied field for a ferromagnet in the processes of magnetization and demagnetization gives as a result a closed curve, called the hysteresis loop. Figure 2.2. Typical hysteresis loop of a ferromagnetic material. Hysteresis loops characterize the state of the sample studied. Figure 2.2 shows a typical hysteresis loop of a bulk ferromagnetic sample [11]. Initially, the material is demagnetized and the applied field is zero (M = H = 0), increasing the value of the field H the first magnetization curve Oabc is obtained. From zero to the point a the sample is magnetized by the reversible process of the domain frontiers movement. Between a and b the magnetization increases by an irreversible process of the domains frontiers movement and between b and c increases mainly by the domains magnetization rotation, being c the point of magnetization saturation, Ms. Decreasing from c the value of the field H up to zero we reach the point of remanent magnetization or Experimental techniques 30 remanence, Mr, since the magnetization of the sample is not cancelled due to the non reversibility of the domains frontiers movement, the sample magnetization does not return to the initial demagnetized state, each magnetization domain rotates back to the nearest easy direction. To cancel this magnetization it is needed to apply a field with the appropriate value and in the opposite direction, called coercive field or coercivity, Hc. Increasing the field in this direction the saturation is also reached. The saturation magnetization, Ms, is determined by the composition, internal structure and temperature of the material and the coercive field, Hc, and remanence Mr, are determined by the anisotropy of the sample. The coercivity also depends on the imperfections (internal stresses distribution or defects). The ratio between the magnetization and the applied field, given by the slope of the hysteresis curve, is called the susceptibility, 𝜒, of the material [12]: 𝜒=𝑀 𝐻 (2.2) The area enclosed by the hysteresis loop is equal to the energy dissipated by the sample in a magnetization cycle. Hard magnetic materials typically have a square shape hysteresis loop, with high coercive field, Hc, (a requirement for many applications, such as memory devices), as the material is softer the hysteresis loop tends to be more linear, the area inside the cycle is smaller and hence, the hysteresis loss is lower, a desirable characteristic of soft magnetic materials (for applications like magnetic sensors). 2.3.2. Flux-metric method for hysteresis loops measurements One of the main and first steps of the characterization of magnetic microwires is its hysteresis loop analysis, that will allow us to obtain magnetic parameters such us coercive field, Hc, anisotropy field, Hk, remanent magnetization, Mr and magnetic saturation, Ms. Hysteresis loops can be obtained by the induction fluxmetric method based on the Faraday-Lenz law, that establishes that with the magnetic flux,   Fundamentals: Chapter II 37 A specially designed microstrip sample holder (shown in Figure 2.6) placed inside a solenoid sufficiently long to provide a homogeneous field allows measuring of the magnetic field dependence of sample impedance, Z(H), using vector network analyzer (Agilent N5230A VNA) from the reflection coefficient, S11, taking into account the following expression [21]: 𝑍= 𝑍0(1+𝑆11) (1−𝑆11) (2.14) being Z 0 = 50  the characteristic impedance of the coaxial line and S11 is the reflection coefficient. Described technique allows measuring the GMI effect in an extended frequency, f, range, up to GHz frequencies. 2.3.5. Free-space electromagnetic parameters measurement system Free-space technique offers several advantages for measurement of electromagnetic parameters of composite materials. This non-contact method allows non-destructive measurements under different temperature or environmental conditions [22,23]. The experimental set-up used in this work for reflection (R) and transmission (T) coefficients measurement consists of a pair of broadband horn antennas (1-17 GHz), a Figure 2.6. Microstrip line for GMI measurements of the microwires. Experimental techniques 38 vector network analyzer (Agilent N5230A VNA) and an anechoic chamber (see Figure 2.7). The composite is placed in the middle of the anechoic chamber with the microwires orientation along the electric-field of the incident electromagnetic wave. The desired frequency range for measurement of the scattering parameters, determines the requirements to the operating frequency of the VNA, antennas and to the chamber size (distance between antennas and sample) [23]. The size of the sample needs to be larger than the wavelength of the incident electromagnetic wave in order to achieve convincing results. In fact, to further minimize the effects of the scatterings from the sample boundary, the sample size should be at least twice larger than the wavelength [24]. According to this, in our experiments, the composite was placed in 20 x 20 cm2 window to avoid the edge effects. This window limits the applicable frequency range in 4-17 GHz. Figure 2.7. Free space microwave measurement set-up for measurement of the electromagnetic parameters in composite material at the Applied Physics Dept. of UPV/EHU. Fundamentals: Chapter II 39 2.3.6. Domain Wall (DW) propagation measurements The magnetic field driven domain wall (DW) propagation has been studied using modified Sixtus-Tonks method c The main differences of used method from the classical Sixtus-Tonks [25] set-up are the following: a system of three pick-up coils is employed (see Figure 2.8) [26], instead of a nucleation coil, since small closure domains spontaneously appear at the end of the wire in order to decrease the stray field. In addition, one sample end is placed outside the magnetization coil to ensure a single DW propagation avoiding multiple DW propagation and hence overestimating the magnitude of DW velocity. Studied microwire samples (usually of about 10 cm long) were placed inside the three coaxially pick-up coils. Rather homogeneous axial magnetic field was generated by a 140 mm long solenoid (10 mm in diameter). The DW travelling along the sample induces an electromotive force (EMF) in the pick-up coils that is recorded by an oscilloscope. Then, velocity, v, of a DW travelling along the sample can be estimated as [27]: Figure 2.8. Schematic picture of the experimental set-up for DW dynamics measurements in microwires [27]. Experimental techniques 40 v = l Δt (2.15) with l the distance between pick-up coils and Δt the time interval between the EMF peaks generated when moving DW crosses the pick-up coils [26]. For evaluation of the DW injection inside the sample and nucleation field profile, we used a short magnetizing coil to apply local magnetic field [28,29]. Located next to the short pick-up coil, the short magnetizing coil allows detecting local magnetization reversal at sufficiently large distance from the ends of the wire. Then, by slowly moving the wire through the short magnetizing coil is possible to measure the length distribution of the local magnetization reversal (DW injection) fields of each sample. 2.3.7. Small angle magnetization rotation (SAMR) technique for magnetostriction measurements Magnetic properties of amorphous alloys strongly depend on the magnitude of the magnetostriction, which causes the change in the dimensions of a magnetic material during the magnetization. Direct magnetoelastic effect has small influence (of the order of ≈ 10-5-10-7) but the inverse effect, i.e., the change in the magnetization of a ferromagnetic material due to the applied mechanical stress is significant. Therefore, for the optimization of the magnetic properties of magnetic microwires it is relevant to quantify the value of the magnetostriction. There are several indirect methods for the determination of the saturation magnetostriction constant, 𝜆𝑆. In the present work, Small Angle Magnetization Rotation (SAMR) technique, introduced in 1980s [26,28], is employed. Figure 2.9. Schematic picture of the set-up for magnetostriction measurements in microwires. Fundamentals: Chapter II 41 As can be seen from Figure 2.9, during the measurements the initial tensile stress, σ0, is created by a weight, P, attached to the microwire end. In this method the sample (of about 10 cm long) is saturated by an axial DC magnetic field, Hz, created along the microwire z -axis using a solenoid, while applying simultaneously a small ac transverse field, Hy, created by an AC electric current flowing along the sample. The combination of these fields leads to a reversible rotation of the magnetization within a small angle,  , out of the axial direction. The induction voltage, V(2  ), due to the magnetization rotation, is detected by a pick-up coil wounded around the microwire. This signal is amplified for its detection in the measuring block. The AC current value, flowing through the wire is selected to avoid possible Joule heating of the sample: the current amplitude does not exceed 10-30 mA. The magnetostriction coefficient,  s, is determined from the measurement of the dependence on axial magnetic field, Hz, versus applied stress  for different mechanical loads, at fixed value of induction voltage V(2  ), according to the expression [30,31]: 𝜆𝑆= −𝜇0𝑀𝑆 3 (𝑑𝐻 𝑑𝜎) (2.16) where  oMs is the saturation magnetization of the sample obtained from magnetization curves measured at high applied field and room temperature. Experimental techniques 42 Additional details on SAMR method and set-up features designed for evaluation of magnetostriction coefficient,  s, can be found in refs. [30,31]. The SAMR method is successfully employed for the evaluation of Co-rich glasscoated microwires with negative magnetostriction coefficient as it was originally developed for magnetic materials in which magnetization rotation governs the magnetization process. Recently, it has also been extended for evaluation of microwires with positive magnetostriction coefficient [32,33]. Indeed, in Co-rich microwires circular magnetization orientation was experimentally observed by various experimental techniques (Figure 2.10a), while Fe-rich microwires present radial magnetization orientation (Figure 2.10b) [34]. Accordingly, magnetization rotation in the outer domain shell can be observed in both kinds of microwires [32,33]. Figure 2.10. Schematic picture illustrating domain structure of Co-rich (a) and Fe-rich (b) microwires. Fundamentals: Chapter II 43 2.4. Microstructural characterization techniques 2.4.1. Powder X-ray diffraction (XRD) X-ray diffraction allows the structural characterization of amorphous and crystalline materials. Electromagnetic waves, in this case X-rays, are diffracted when they encounter an obstacle, and this effect is increased when the size of the obstacle is comparable to the wavelength incident on the material. Then, it is possible to explore the structure of solids by studying the diffraction patterns of an incident wave with wavelength comparable to the distance between atoms. When an X-ray beam strikes a solid material, part of this beam is scattered in all directions by the electrons associated with the atoms of the material or ions that encounters along the way, but the rest of the beam can give rise to the X-ray diffraction phenomenon, which takes place if there is an ordered arrangement of atoms (long range) and are fulfilled the conditions given by Bragg's Law [35] (Figure 2.11) that relate the wavelength,  of the X-rays and the interatomic distance, dhkl, between the family of planes (hkl), with the angle of incidence of the diffracted beam,  (Bragg angle). This law is described by the following equation [35]: 𝑛𝜆=2𝑑ℎ𝑘𝑙𝑠𝑖𝑛𝜃 (2.17) where n is an integer that represents the order of reflection. This equation allows us to obtain the angular position of the diffraction peaks of the crystalline solid that is analyzed. Experimental techniques 44 The structure of the samples in the present work has been analyzed using Bruker (D8 Advance) X-ray diffractometer (Figure 2.12) with CuKα (λ = 1.54 Å) radiation, operated at applied voltage of 40 KV and filament current of 30 mA. The sample is attached to the diffractometer sample holder and each scan is made over the two theta angular range of 30 to 90 degrees, step size of 0.05°and a step time of 30 second for each step. The diffraction peaks are indexed using JCPDS (Joint Committee on Powder Diffraction Standards) database. Figure 2.12. Bruker (D8 Advance) X-ray diffractometer picture [36]. Figure 2.11. Schematic picture illustrating Bragg's Law of diffraction. Fundamentals: Chapter II 45 A wide halo characteristic of completely amorphous materials was observed in the case of amorphous (as-prepared or annealed) glass-coated microwires. 2.4.2. Optical Microscopy (OM) The diameters of the metallic nucleus and glass coating of the different microwires employed in this work and the homogeneity along their length was checked by means of an optical microscopy, in our case Microscope Axio Scope A1 (as shown in Figure 2.13), that uses visible light and a system of lenses to magnify images. This microscopy allows to obtain a two-dimensional image of the microwires. The microwire is placed in the microscope stage on a slide (a thin flat piece of glass) to check its geometry. Figure 2.13. Microscope Axio Scope A1. Source Carl Zeiss Microscopy GmbH and own elaboration (Adapted from Microscope Axio Scope A1 user manual). Experimental techniques 46 The system contents various lenses, which are placed in the microscope column below the emission chamber and situated one above the other. The condenser lens allows to obtain a parallel and thin beam of light form the illuminator to proper illuminate and focus the light on the sample. The objective lens collects the light diffracted from the sample and forms the first image of the object and the intermediate lens or group of lenses (called the eyepiece) amplify this image that finally is projected by the projection lens. The quality of the image depends on the contrast, resolution and the focal depth of the microscope. Illumination sources and objectives can be manipulated to adjust the image. 2.4.3. Scanning Electron Microscopy (SEM) Chemical composition, microstructure and external morphology of the microwires once they are obtained and after the thermal treatments, were characterized by Scanning Electron Microscopy, (SEM). The equipment employed at the UPV/EHU was a MEB JEOL JSM-7000F (Figure 2.14) with energy-dispersive X-ray spectroscopy (EDX) option with an Inca Energy 350 spectrometer. The microscope has a field emission source (Schottky type). In this technique, a thin beam of high-energy accelerated electrons is concentrated by electromagnetic lenses and focuses on the surface of a thick an opaque sample. The beam scans the surface of the sample in a raster scan pattern, with a velocity synchronized with the position in a computer screen to create the image. As a result of the interaction, different types of radiation are produced. The emitted electrons and those that bounce off the surface (Auger electrons, secondary and backscattered electrons) are collected by a sensor. Secondary electrons emitted by the nearest to the surface atoms of the sample allow to obtain the images of the surface. Their intensity depends on the incident angle and thus, on the topography of the surface, and it is proportional to the correspondent spot on the image of the sample at the screen. To facilitate the emission of the electrons the sample is coated with a conductive metal, usually Au. Fundamentals: Chapter II 53 [34] Y. Kabanov, A. Zhukov, V. Zhukova, J. Gonzalez, Magnetic domain structure of wires studied by using the magneto-optical indicator film method, Appl. Phys. Lett. 87 (2005) 142507, doi:10.1063/1.2077854. [35] D.B. Cullity, Elements of x-ray diffraction, 2-Edition: Addison-Wiley Publishing Company Reading (1978). [36] Bruker Corporation, https://www.bruker.com/en/products-and-solutions/diffractometers and-scattering-systems/x-ray-diffractometers/d8-advance-family/d8-advance.html. Results and discussion: Chapter III 54 Part II: Results and discussion 3. Engineering of magnetic properties of Co-rich microwires As mentioned before, non-existence of magnetocrystalline anisotropy in amorphous materials makes the magnetoelastic anisotropy the main source of magnetic anisotropy [1]. Magnetoelastic anisotropy depends on the magnetostriction coefficient, λs, and the applied and internal stresses (eq. (1.1)). The λs sign and value of amorphous materials is mainly given by the chemical composition. Therefore, chemical composition modification allows to adjust λs sign and value [1,2]. Co-based alloys posses low magnetostriction values (up to λs ≈ -5 x 106) and early zero magnetostriction values can be obtained doping Co-based alloys with Fe or Mn [1,2]. The other important parameter is the internal stresses, σi, value. Once the composition is chosen, the magnetic properties can be optimized by modifying the internal stresses with the selection of the sample geometry, described by the  -ratio between the metallic nucleus diameter, d, and the total microwire diameter, D, and the appropriate post-processing. In this chapter, Co-based microwires of different characteristics, i.e., compositions and diameters, and hence different magnetostriction coefficients,  s, will be presented with the description and discussion of the postprocessing selected for them with the aim to optimize its magnetic softness and improve the Giant Magnetoimpedance (GMI) effect and domain wall dynamics. The magnetic softness is intrinsically related to the GMI effect originated by the dependence of the skin depth, δ, of a magnetic conductor on applied magnetic field, H, as previously defined by eq. (2.8) [1]. For characterization of the GMI effect it will be used the GMI ratio,  Z/Z, as defined in eq. (2.9) [1]. The GMI ratio optimization is linked to improvement of magnetic softness. Engineering of magnetic properties of Co-rich microwires 55 The influence of each controllable parameter in all the post-processing types selected has been studied, in order to get a complete overview of the adjusting parameters for the optimization of the magnetic properties. Table 3.1 summarizes the main characteristics of the Co-rich microwires studied. Table 3.1. Compositions, geometry and magnetostriction coefficients of studied Co-rich glasscoated microwires. Sample Nº Composition d (μm) D (μm)  = d/D λs x 10-6 1 Co69.2Fe3.6Ni1B12.5Si11Mo1.5C1.2 22.8 23.2 0.98 -1 2 Co69.2Fe4.1B11.8Si13.8C1.1 25.6 30.2 0.85 -0,3 3 Co65.4Fe3.8Ni1B13.8Si13Mo1.35C1.65 18.8 22.2 0.85 -1 4 Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 25.6 26.6 0.96 -0.29 5 Co64.04Fe5.71B15.88Si10.94Cr3.4Ni0.03 95 130 0.73 6 Co66Cr3.5Fe3.5B16Si11 20.1 24.8 0.81 3.1. As-prepared Co-rich microwires Figure 3.1a-d shows the hysteresis loops of 4 of the Co-rich microwires selected. The microwire samples have negative magnetrostriction coefficient and in asprepared state exhibit quite soft magnetic properties, reflected in a typical linear and inclined hysteresis loop with low coercivity [1], below Hc ≈ 10 A/m. Results and discussion: Chapter III 56 X-ray diffraction (XRD) patterns of studied microwires present a wide halo, in as-prepared and annealed state, characteristic of completely amorphous materials [3], as can be seen in Figure 3.2 for sample 3. -600 -300 0 300 600 -1 0 1 Co69.2Fe3.6Ni1B12.5Si11Mo1.5C1.2 M/M0 H (A/m) (a) Sample 1 -1000 -500 0 500 1000 -1 0 1 H (A/m) M/M0 Sample 2 Co69.2Fe4.2B11.8Si13.8C1.1 (b) -1000 -500 0 500 1000 -1 0 1 Co65.4Fe3.8Ni1B13.8Si13Mo1.35C1.65 M/M0 H(A/m) Hk (c) Sample 3 -200 -100 0 100 200 -1 0 1 Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 M/M0 H (A/m) Sample 4 (d) -75 0 75 -1 0 1 Figure 3.1. Hysteresis loops of as-prepared Co69.2Fe3.6Ni1B12.5Si11Mo1.5C1.2 (a), Co69.2Fe4.1B11.8Si13.8C1.1 (b), Co65.4Fe3.8Ni1B13.8Si13Mo1.35C1.65 (c) and Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 (d) microwires. Engineering of magnetic properties of Co-rich microwires 57 From the studied microwires, in Figure 3.3a are presented the samples with similar composition for comparison of the evolution of the hysteresis loop with the  −ratio increase. In Figure 3.3b can be seen the decrease of the anisotropy field, Hk, as the  −ratio increases. 40 60 80 100 0 500 1000 1500 2000 Sample 3 I (arb. unit.) 2 (deg.) Figure 3.2. XRD diffraction pattern of as-prepared Co65.4 Fe3.8Ni1B13.8Si13Mo1.35C1.65 microwire. -900 -600 -300 0 300 600 900 -1 0 1  = 0,98 Sample 1  = 0,85 Sample 3  = 0,96 Sample 4 M/M0 H (A/m) (a) 0,80 0,85 0,90 0,95 1,00 200 300 400 500 600 Hk (A/m)  (b) Figure 3.3. Hysteresis loops of as-prepared Co-rich microwires of similar composition studied (a) and Hk (  ) dependence of microwires samples 1, 3 and 4 (b). Results and discussion: Chapter III 58 3.2. Post-processing effect on magnetic properties, GMI effect and DW dynamics for Co-rich microwires 3.2.1. Conventional furnace annealing in Co-rich microwires After annealing at sufficiently high temperature, similarly to reported results for Co-rich microwires with vanishing λs [4], the hysteresis loop shape turns into rectangular. Co69.2Fe3.6Ni1B12.5Si11Mo1.5C1.2 microwires (sample 1) annealed at 250 °C and 350 °C during 60 min present considerable magnetic hardening, perfectly rectangular hysteresis loops with almost the same coercivity, Hc ≈ 90 A/m, can be seen in Figure 3.4, for the different annealing temperatures, and an increase in the remanent magnetization, Mr, is observed. The influence of the annealing temperature on GMI ratio presented in Figure 3.4 was studied at a frequency of 200 MHz, given that Co-rich microwires present maximum GMI ratio values at a frequency, f, ranging from 100 to 200 MHz [5]. -600 -300 0 300 600 -1 0 1Sample 1 M/M0 H (A/m) As-prepared 250 ºC 350 ºC Figure 3.4. Hysteresis loop of Co69.2Fe3.6Ni1B12.5Si11Mo1.5C1.2 microwire as-prepared and annealed at different temperatures during 60 min. Engineering of magnetic properties of Co-rich microwires 59 Similar tendency was observed in several Co-rich microwires with vanishing magnetostriction coefficient [1,4]. Consequently, observed tendency in hardening of Co-rich microwires and transformation of inclined hysteresis loops into rectangular is of general character. ΔZ/Z(H) dependences observed in Figure 3.5 show a decrease after annealing at 200 °C, however, annealing at higher temperatures, Tann of 250 °C and 300 °C, give as a result an increase in the maximum GMI ratio, ΔZ/Zmax. Hmax, the field of maximum ΔZ/Z(H), becomes lower with increasing the annealing time, changing ΔZ/Z(H) dependence shape, from the double-peak dependence shown in as-prepared and annealed at 200 °C samples to a shape of decay with the magnetic field increase presented for the samples annealed at higher annealing temperature, Tann. ΔZ/Z(H) dependence shape, can be explained in terms of the magnetic anisotropy distribution of the microwire metallic nucleus and the skin penetration depth,  , and its dependence on the frequency given by eq. (2.8) [1,6]. According to eq. (2.8),  as a function of the ratio between RDC, the DCresistance of the wire, and RAC, the real component of the impedance, RDC/RAC, can be expressed as [7]: -15 -10 -5 0 5 10 15 0 100 200 Sample 1 Z/Z (%) H (kA/m) As-prepared 200 ºC 250 ºC 350 ºC Figure 3.5. ΔZ/Z(H) dependences measured at 200 MHz for Co69.2Fe3.6Ni1B12.5Si11Mo1.5C1.2 microwire as-prepared and annealed at different temperatures during 60 min. Results and discussion: Chapter III 60 𝛿 = 𝑟[1−(1−𝑅𝐷𝐶/𝑅𝐴𝐶)1/2] (3.1) where r is the wire radius. The inner axially microwire radius, Rc, is related to the remanent magnetization and therefore, can be estimated from the reduced remanence, Mr/Ms, using the relation [1,3]: 𝑅𝐶= 𝑟(𝑀𝑟/𝑀𝑆)1/2 (3.2) One of the important parameters for GMI effect characterization is the maximum GMI ratio, ΔZ/Zmax, determined from the ΔZ/Z(H) dependencies [1,3]. ΔZ/Zmax evolution upon annealing, as it is reflected in Figure 3.6, for annealing temperatures of 250 °C and 300 °C gives higher ΔZ/Zmax values for the whole frequency range studied. It is important to note, that for Co-rich microwires with magnetic bistability induced by annealing it was previously reported a decrease in the GMI ratio [4]. The magnetic hardening observed in Figure 3.4 can be explained by the change of the magnetostriction coefficient from negative to positive associated to the internal stresses relaxation or to the domain structure modification consisting of the onset and growth of the inner axially magnetized single domain at the expense of the outer domain shell with transverse magnetic anisotropy [1,4,5]. Obviously, conventional furnace annealing cannot be considered as appropriate processing for magnetic softness improvement of Co-rich microwires. Engineering of magnetic properties of Co-rich microwires 61 Accordingly, additional efforts have been paid to improve magnetic softness of Co-rich microwires. 3.2.2. Stress-annealing in Co-rich microwires A systematic study of the influence of applied tensile stress during the annealing for different applied stresses, temperatures and annealing times was carried out for Co69.2Fe3.6Ni1B12.5Si11Mo1.5C1.2 microwire, corresponding to labeled sample 1 and Co69.2Fe4.1B11.8Si13.8C1.1, sample 2. The tensile stress within the metallic nucleus, applied to the sample hanging a mechanical load to one end of the microwire during the sample heating and slow cooling within the furnace, has been evaluated following the equation previously described (eq.(2.1)): 𝜎𝑚=𝐾 ∙𝑃 𝐾 ∙ 𝑆𝑚+𝑆𝑔𝑙 (3.3) being K = E2/E1, the ratio of the Young’s moduli at room temperature of the metallic alloy, E1, and the glass, E2. P is the mechanical load applied and Sm and Sgl are the cross 200 400 600 800 1000 0 50 100 150 200 Z/Zmax (%) f (MHz) As-prepared 200 ºC 250 ºC 350 ºC Sample 1 Figure 3.6. Maximum GMI ratio dependences on frequency for Co69.2Fe3.6Ni1B12.5Si11Mo1.5C1.2 microwire as-prepared and annealed at different temperatures for Tann = 60 min. Results and discussion: Chapter III 62 sections of the metallic nucleus and glass coating, respectively. The applied stress within the metallic nucleus ranges from 0 to 472 MPa. Similarly to the case shown in Figure 3.4, magnetic hardening is achieved upon conventional annealing [8]. The linear hysteresis loop of as prepared sample turns into rectangular (Figure 3.7a) for the sample annealed without applied stress, with an increase in the coercivity, from H ≈ 5 A/m up to Hc ≈ 93 A/m. Stress-annealing allows to manipulate the hysteresis loop character and the magnetic softness: at intermediate Tann and σm with the application of stress during the annealing, the coercivity experiments a noticeable decrease and the remanent magnetization increases. Figure 3.7b shows the influence of the temperature in the stress-annealing treatment, coercivity decreases with the temperature increase. This tendency changes with the increase of Tann and σm, at Tann = 300 oC, Hc continues to decrease, while Mr/M0 begins to decrease with increasing σ (see Figure 3.8a). Stress-annealed at Tann = 300 oC samples present rectangular hysteresis loops shape with rather low Hc (Figure 3.8a). -200 -100 0 100 200 -1,0 -0,5 0,0 0,5 1,0 Sample 1 M/M0 H (A/m) As-prepared 0 MPa 118 MPa 354 MPa 472 MPa Tann= 350 ºC tann = 60 min (a) -200 -100 0 100 200 -1,0 -0,5 0,0 0,5 1,0 M/M0 H (A/m) Asprepared Tann=200 oC Tann=300 oC Tann=350 oC Tann=375 oC (b)  = 354 MPa tann = 60 min Sample 1 Figure 3.7. Hysteresis loop of as-prepared and stress annealed with different applied stresses at 350 °C (a), as-prepared and stress annealed with 354 MPa at different temperatures (b) Co69.2Fe3.6Ni1B12.5Si11Mo1.5C1.2 microwires. Engineering of magnetic properties of Co-rich microwires 69 Therefore, the DW propagation was measured for the samples presenting induced magnetic bistability. Obtained v(H) dependencies are presented in Figure 3.14, where it can be appreciated the influence of annealing temperature. High DW velocity is observed for the microwires annealed at 325 oC (see Figure 3.14) with a non-monotonic dependence of the DW velocity on the annealing temperature. The latter can be associated to the annealing influence on the sign and value of the magnetostriction coefficient, λs, [12]. As a rule, an increase of λs upon annealing is found for Co-based microwires [13]. Consequently, the annealing influence on the magnetoleastic anisotropy, i.e, stresses relaxation and magnetostriction coefficient modification, is reflected on the evolution of the DW dynamics and as well as in the GMI effect previously analyzed. Stress annealing was presented as a useful tool for the improvement of the GMI effect. The stress-induced anisotropy is expected to affect both GMI ratio and DW dynamics. At selected stress-annealing conditions, where the hysteresis loops shape remains rectangular, it can be assumed that the samples can present single domain wall propagation related to a single Barkhausen jump. 020 40 60 0 1000 2000 3000  = 354 MPa Tann = 200ºC Tann = 300ºC Tann = 325ºC Tann = 350ºC v (m/s) H (A/m) (a) tann = 60 min 030 60 90 120 0 1000 2000 3000 tann = 60 min Tann = 350ºC  = 0 MPa  = 118 MPa  = 236 MPa  = 354 MPa v (m/s) H (A/m) (b) Figure 3.15. v(H) dependences measured for Co69.2Fe4.1B11.8Si13.8C1.1 microwires stress-annealed with 354 MPa at different Tann (a) and for the sample annealed at Tann = 350 oC with different applied stresses during the annealing. Results and discussion: Chapter III 70 Figure 3.15a presents the influence of the annealing temperature for a fixed value of the applied stress during the annealing. It can be observed upon increase of the annealing temperature a gradual increase of the mobility, S, (slope of the curve) and the DW velocity. In the same way, in Figure 3.15b there is reflected an increase of S -values upon  rising for a fixed Tann. Figure 3.16 shows the influence of the tensile stress applied during the annealing at Tann = 300 oC for tann = 60 min. All the samples present single DW propagation with almost perfectly linear v(H) dependencies (described by eq. (1.2)) and quite high DW velocities. Fe3.6Co69.2Ni1B12.5Si11Mo1.5C1.2 microwires annealed without stress present the highest DW velocity of about 3 km/s (Figure 3.16). However, the field range of single DW propagation is rather short (between 83 and 93 A/m). Extended field range is observed for stress-annealed Fe3.6Co69.2Ni1B12.5Si11Mo1.5C1.2 microwires. DW velocity and S -values are affected by  values, similarly to the case of Tann = 350 oC (Figure 3.15b). There is a gradual increase of the mobility upon increase of the stress applied during the annealing. The observed shift of the linear v(H) dependences of stressannealed microwires with induced magnetic bistability to low field region (Figure 3.15b and Figure 3.16) is explained by the lower coercivity values of stress-annealed samples (see Figure 3.8). 020 40 60 80 100 0 1000 2000 3000 tann = 60 min Tann = 300ºC  = 0 MPa  = 118 MPa  = 236 MPa  = 354 MPa v (m/s) H (A/m) Figure 3.16. v(H) dependencies for Fe3.6Co69.2Ni1B12.5Si11Mo1.5C1.2 microwires annealed at Tann = 300 oC for tann =60 min without stress (σm = 0 MPa) and under different stresses. Engineering of magnetic properties of Co-rich microwires 71 3.2.4. Joule heating in Co-rich microwires Throughout this section the influence of Joule heating on the magnetic properties of Co-based microwires and its comparison with conventional furnace annealing is systematically investigated. Accordingly, the experimental results of Co69.2Fe4.1B11.8Si13.8C1.1 and Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 microwires, samples 2 and 4, respectively, are presented. The microwires were subjected to a series of current annealing treatments in which different currents were applied during different time. Direct current (DC) values for the heat treatments were selected clearly below the values that could produce hardening and/or crystallization of the samples, as described in annealing procedures section [14]. Current densities of 58.3 and 77.7 A/mm2 were selected for time ranging from 3 to 20 minutes for both samples. Accordingly, Co69.2Fe4.1B11.8Si13.8C1.1 microwire (sample 1), with d = 22.8 μm, was subjected to currents of 24 and 32 mA. Hysteresis loops of current annealed samples are presented in Figure 3.17. Joule heated at I = 24 mA samples, Figure 3.17a, present similar character as hysteresis loops of as-prepared microwire, with low coercivity values. A slight decrease in the magnetic anisotropy field can be observed (Figure 3.17c). Current annealed samples at I= 32 mA (Figure 3.17b), show similar behaviour, linear hysteresis loop with a decrease in Hk, that becomes more remarkable for tann = 10 min (Figure 3.17c). Although Joule heating at j ≈ 80 A/mm2 causes a sample heating up to approximately 200 oC [12], as compared with conventional furnace annealing of studied microwire at 200 oC presented in Figure 3.17b, Joule heated samples present lower Hc. Results and discussion: Chapter III 72 Magnetic hardening observed for Co-rich microwires after conventional furnace annealing is avoided with current annealing, as is also observed in amorphous ribbons [14]. ΔZ/Z(H) dependence of Joule heated sample with j = 24 mA during 3 min, presented in Figure 3.18a for f = 150 MHz, shows a remarkable improvement of ΔZ/Zmax from ΔZ/Zmax ≈ 100% to ΔZ/Zmax ≈ 300 %, as compared to as-prepared sample. Double-peak shape of ΔZ/Z(H) dependencies, similar to as-prepared sample, is observed for all Joule heated samples at all frequencies measured (see Figure 3.18b and Figure 3.18c, where results for Joule heating for tann = 3 min are shown). -200 0 200 -1 0 1 As-prepared 3 min 24 mA 10 min 24 mA M/M0 H (A/m) (a) Sample 2 -200 0 200 -1 0 1 M/M0 H (A/m) As-prepared 3 min 32 mA 10 min 32 mA 20 min 32 mA Tann=200 0C (b) Sample 2 0 5 10 15 20 180 200 220 240 260 Hk (A/m) t (min) 24 mA 32 mA (c) Sample 2 Figure 3.17. Hysteresis loops of sample 1 as-prepared and Joule heated at 24 mA (a), Joule heated at 32 mA and annealed at 200 oC for 60 min (b) and Hk (tann) dependence evaluated from hysteresis loops of current annealed samples (c). Engineering of magnetic properties of Co-rich microwires 73 The double-peak ΔZ/Z(H) dependence observed is associated to circumferential magnetic anisotropy and the maximum field, Hm, to magnetic anisotropy field [15]. Joule heated samples present lower Hm values than those of as-prepared sample (Figure 3.18a), that correlate with lower Hk values for Joule heated sample than for asprepared, obtained from bulk hysteresis loops measured of both samples (see Figure 3.17a,b). Maximum GMI ratio, ΔZ/Zmax, dependence on frequency presented in Figure 3.19a shows a GMI ratio improvement, with ΔZ/Zmax close to 300% for all current annealed samples in an extended frequency range. It is important to note, that the optimum frequency, at which maximum on ΔZ/Zmax(f) dependence is observed is -15 -10 -5 0 5 10 15 0 100 200 300 Z/Z (%) H (kA/m) As-prepared 24 mA 3 min (a) Sample 2 -5 0 5 0 50 100 150 200 250 300 Sample 2 10 MHz 100 MHz 150 MHz 200 MHz 500 MHz Z/Z (%) H (kA/m) 24 mA 3 min (b) -10 -5 0 5 10 0 100 200 300 Sample 2 10 MHz 100 MHz 150 MHz 200 MHz 500 MHz Z/Z (%) H (kA/m) 32 mA 3 min (c) Figure 3.18. Co69.2Fe4.1B11.8Si13.8C1.1 microwire ΔZ/Z(H) dependencies measured in as-prepared and Joule heated (24 mA, 3 min) samples measured at 150MHz (a), ΔZ/Z(H) dependencies measured at different frequencies for Joule heated 3 min at 24 mA (b) and at 32 mA (c), respectively. Results and discussion: Chapter III 74 shifted to higher frequencies of about 150-200 MHz as compared to as prepared sample, in which such maximum takes place at a frequency of about 100 MHz (Figure 3.19a). Comparison of ΔZ/Zmax (f) dependencies of as-prepared, stress-annealed and Joule heated samples presented in Figure 3.19b reflects the beneficial influence of Joule heating, Joule heated sample presents the highest ΔZ/Zmax -value up to f = 400 MHz. Influence of Joule heating on the hysteresis loops and GMi effect for Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 microwire, sample 4, is studied below. The hysteresis loops of the samples current annealed are presented in Figure 3.20, coercive field, Hc, and effective anisotropy field, Hk, evaluated from the knee area just before the approach of magnetization saturation, Ms, were obtained from the hysteresis loops and compiled in Table 3.2. 0200 400 600 800 1000 0 100 200 300 Sample 2 As-prepared 24mA 3 min 5 min 10 min 32 mA 3 min 5 min 10 min 20 min Z/Zmax (%) f (MHz) (a) 0200 400 600 800 1000 0 100 200 300 Sample 2 As-prepared 24 mA 10min 200 oC 354 MPa 375 oC 354 MPa Z/Zmax (%) f (MHz) (b) Figure 3.19. Co69.2Fe4.1B11.8Si13.8C1.1 microwire ΔZ/Zmax (f) dependences observed in as-prepared and Joule heated at different annealing conditions samples (a) and ΔZ/Zmax (f) dependencies of as-prepared, stress-annealed (Tann = 200 and 375 oC, with 354 MPa, for 60 min) and Joule annealed (24 mA, 10 min) samples (b). Engineering of magnetic properties of Co-rich microwires 75 Current annealed Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 glass coated microwires present extremely soft magnetic properties. The samples current annealed at 30 mA for 3 min and 5 min present the lowest coercivities of about 2 A/m and Hk ≈ 32 A/m, as can be seen from Hk evolution with Joule heating time, in Figure 3.18d. Increasing the annealing time a slight increase in the coercivity and the anisotropy field is observed. The character of the hysteresis loop remains the same for longer current annealed time [16]. Similar behaviour is observed for the sample current annealed at 40 mA. -50 0 50 -1,0 -0,5 0,0 0,5 1,0 Sample 4 -100 -50 0 50 100 -1,0 -0,5 0,0 0,5 1,0 M/MS H (A/m) 10min 30mA 20min 30mA M/Ms H (A/m) As-prepared 3min 30mA 5min 30mA 10min 30mA (a) -50 0 50 -1,0 -0,5 0,0 0,5 1,0 Sample 4 (b) M/Ms H (A/m) As-prepared 3min 40mA 5min 40mA 10min 40mA -50 0 50 -1,0 -0,5 0,0 0,5 1,0 Sample 4 (c) M/Ms H (A/m) As-prepared 5 min 30 mA 5 min 40 mA 010 20 0 20 40 60 80 Hk (A/m) tann (min) (d) Figure 3.20. Hysteresis loops of Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 microwires Joule heated at 30 mA for 3, 5, 10 and 20 min (inset) (a), Joule heated at 40 mA for 3, 5 and 10 min (b) and comparison between the hysteresis loops of the sample Joule heated at 30 mA and 40 mA for 5 min (c) and Hk dependence on Joule annealing time for I = 30 mA (d). Results and discussion: Chapter III 76 Table 3.2. Magnetic properties of studied Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 microwires subjected to different post-processing. Post-processing type I applied (mA) Duration (min) Hc (A/m) Hk (A/m) As-prepared 7 65 Joule heated 30 3 2 32 5 2 32 10 6 75 20 6 75 40 3 5 50 5 5 55 10 4 63 Annealed (Tann = 300 °C) 60 6 21 The results obtained for Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 microwire annealed in conventional furnace, at 300 °C during 60 min (Figure 3.21a) and its comparison with Joule heated sample with 30 mA during 40 min (Figure 3.21b) show that in contrast to Joule heated sample, conventional annealing leads to a drastic magnetic hardening of the sample [17]. -50 0 50 -1,0 -0,5 0,0 0,5 1,0 Sample 4 As-prepared Annealed M/M0 H (A/m) (a) (300 ºC 60 min) -50 0 50 -1,0 -0,5 0,0 0,5 1,0 Sample 4 M/M0 H(A/m) Joule heated (30 mA 40 min) Annealed (300 ºC 60 min) (b) Figure 3.21. Hysteresis loops of Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 microwire as-prepared and annealed at 300°C 60 min (a) and annealed at the same conditions and current annealed with 30 mA for 40 min (b). Engineering of magnetic properties of Co-rich microwires 77 ΔZ/Z(H) representation of as-prepared and current-annealed Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 microwires gives as a result a double-peak dependence (Figure 3.22) typically reported for Co-rich microwires with low negative magnetostriction coefficient and weak circumferential magnetic anisotropy [15,18]. Even in as-prepared state, Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 microwire presents high ΔZ/Z(H) values with a maximum GMI ratio, ΔZ/Zmax, of about 550% at a frequency of 300 MHz (Figure 3.22 and Figure 3.23). An increase in the GMI ratio is observed after Joule-heating at the selected conditions. Highest GMI ratio enhancement is attained for short current-heating times as can be appreciated in Figure 3.22, for samples annealed at 30 and 40 mA during 3 min and 5 min, related to the magnetic softening observed in the hysteresis loops of current annealed microwires at these conditions. The highest ΔZ/Zmax value of about -3 0 3 0 100 200 300 400 500 600 -3 0 3 0 100 200 300 400 500 600 700 -3 0 3 0 100 200 300 400 500 600 -3 0 3 0 100 200 300 400 500 600 700 (c) (a) (d) (b) Z/Z(%) 100MHz 200MHz 300MHz 1.00GHz Z/Z(%) H(kA/m) 100MHz 200MHz 300MHz 1.00GHz Sample 4 Sample 4 Sample 4 Sample 4 Z/Z(%) H(kA/m) 100MHz 200MHz 300MHz 1.00GHz H(kA/m) Z/Z(%) H(kA/m) 100MHz 200MHz 300MHz 1.00GHz Figure 3.22. ΔZ/Z(H) dependences for Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 microwire as-prepared (a) current annealed at 40 mA for 3 min (b), 5 min (c) and 10 min (d) measured at different frequencies. Results and discussion: Chapter III 78 650% is obtained for sample current-annealed at 40mA during 5 minutes. An increase in the annealing time correlates with a decrease in ΔZ/Zmax (Figure 3.22d). A noticeable improvement of the GMI ratio is obtained for the whole MHz frequency range. The optimum frequency moves from 300 MHz for as-prepared sample to 200 MHz for current-annealed ones. 0200 400 600 800 1000 300 400 500 600 Sample 4 Z/Zmax (%) f (MHz) As-prepared 30mA 3min 30mA 5min 40mA 5min Figure 3.23. Maximum GMI ratio dependences on frequency for Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 microwire as-prepared and current annealed at different conditions. In the current annealing process, the sample, besides the heating, is affected by the circumferential magnetic field associated to the current flowing through it. The circumferential magnetic field, Hcirc, produced from the current passing through the microwire (Oersted’s law) can be estimated in the metallic nucleus as following [3]: 𝐻𝑐𝑖𝑟𝑐 = 𝐼/2𝜋𝑟 (3.4) with I the current value and r the radial distance. Hcirc values change to zero to its maximum value at the surface of the microwire, which is the one involved in the GMI effect. Obtained values for the studied microwire for the applied currents are Hcirc ≈ 0.375 kA/m and 0.5 kA/m for I = 30 mA Engineering of magnetic properties of Co-rich microwires 85 Fe3.6Co69.2Ni1B12.5Si11Mo1.5C1.2 microwire stress-annealed for σ ≥ 470 MPa changes form axial to transverse) [8,9]. Furthermore, the difference in the hysteresis loops of both stress-annealed samples can be also related to the difference in chemical compositions and thus different λs –values. As previously shown, the stress-annealing induced magnetic anisotropy of microwires depends on the annealing conditions, Tann, tann and σ [10]. Consequently, stress-annealing of Ferich microwires under temperature gradient was satisfactorily employed for obtaining controllable spatial distribution of the magnetic anisotropy [10]. The same concept is used for studied Co-rich microwires. In fact, as can be seen in Figure 3.29 and Figure 3.30, there is a gradual modification of the hysteresis loop (measured by the short pick-up coil along the samples length) of both samples stressannealed at variable Tann. As has been evaluated from the hysteresis loops (shown in Figure 3.29 and Figure 3.30), both samples present variation of the magnetic properties along the wires length that correlate with Tann gradient during the stress-annealing. Accordingly, -200 -100 0 100 200 -1 0 1 -200 -100 0 100 200 -1 0 1 -200 -100 0 100 200 -1 0 1 -200 -100 0 100 200 -1 0 1 -200 -100 0 100 200 -1 0 1 -200 -100 0 100 200 -1 0 1 M/M0 (a) 0 mm 80 mm (b) (c) 90 mm 110 mm (d) (e) 150 mm H(A/m) 200 mm (f) Figure 3.30. Hysteresis loops of sample 6 stress-annealed (σ = 400 MPa) at variable Tann. Tann evaluated from Figure 3.23b are: 25 oC (a); 160 oC (b); 251 oC (c); 290 oC (d); 295 oC (e) and 300 oC (f), respectively. Results and discussion: Chapter III 86 Figure 3.31a and Figure 3.31b show the evolution of the hysteresis loops in terms of remanent magnetization, Mr/M0, and magnetic anisotropy field, Hk, variation along the microwire length, L, for sample 5. Likewise, Figure 3.32 shows the evolution of the hystereis loops of sample 6 subjected to stress-annealing in Tann gradient, reflected in Mr/M0, and coercivity, Hc, variation along the microwire length. The evolution upon stress-annealing under Tann gradient presents features similar to those reported for stress-annealing induced anisotropy in Co-based microwires [29]. Both samples present an increase in Mr/M0 followed by a decrease with Tann increasing. 050 100 150 200 0,0 0,3 0,6 -1000 -500 0 500 1000 -1 0 1 M/M0 H (A/m) 137 mm -1000 -500 0 500 1000 -1 0 1 M/M0 H (A/m) 95 mm -1000 -500 0 500 1000 -1 0 1 M/M0 H (A/m) 215 mm -1000 -500 0 500 1000 -1 0 1 M/M0 H (A/m) 0 mm Mr/Mo L (mm) Microwire (a) 050 100 150 0 300 600 900 -1000 -500 0 500 1000 -1 0 1 M/M0 H (A/m) 0 mm 95 mm 107 mm 127 mm 137 mm 215 mm Hk (A/m) L (mm) (b) Figure 3.31.Variation of Mr/M0 (a) and Hk (b) along the sample length in the sample 5 annealed at variable Tann. The lines are just guides for the eyes. Engineering of magnetic properties of Co-rich microwires 87 The hysteresis loops modification is explained by the microwires domain structure, which is affected by the λs value and sign, the internal stresses distribution and the shape magnetic anisotropy. As a consequence, axial magnetization alignment is promoted by the exchange energy contribution, especially relevant for thin and long enough magnetic microwires, with high shape anisotropy [30,31]. The internal stresses origin in glass-coated microwires is explained taking into account that in addition to quenching internal stresses, σiq, arising from the rapid melt quenching itself, there are two more internal stresses contributions: the difference in thermal expansion coefficients of the metallic alloy and the glass coating, σit, and the drawing stresses, σid, [32,33]. Different theoretical approaches and indirect experimental results (e.g., effect of glass-coating etching, influence of applied stresses) manifest that the σit contribution arising from the difference in thermal expansion coefficients of metal and glass is the most relevant [15,31]. Correspondingly, σit ≫ σiq and σit ≫ σid. The value of internal stresses is affected by the microwire geometry: glasscoating thickness, metallic nucleus diameter, d, and total microwire diameter, D. In the most simplified approximation σit has been expressed as [34]: 𝜎𝜙= 𝜎𝑟= 𝑃 = 𝜀𝐸𝑘Δ (𝑘 3+1)Δ+4 3 ; 𝜎𝑧= 𝑃(𝑘 +1)Δ+ 2 (𝑘Δ+1) (3.7) where σ  , σr and σz are circular, radial and axial stresses, Δ = (1−𝜌2)/𝜌2 , 𝑘 = 𝐸𝑔/𝐸𝑚, 𝐸𝑚, 𝐸𝑔Young modulus of metallic nucleus and glass, respectively, 𝜀 = (𝛼𝑚−𝛼𝑔)(𝑇𝑚−𝑇𝑟𝑜𝑜𝑚) αm αg are thermal expansion coefficients of metallic nucleus and glass, respectively, and Tm, Troom are melting and room temperatures. Therefore, the hysteresis loops variation, seen in Figure 3.31 and Figure 3.32, is the result of the balance between the shape magnetic anisotropy, the magnetoelastic anisotropy and the stress-annealing induced anisotropy. Results and discussion: Chapter III 88 According to the core-shell domain structure model the modification in Mr/Mo along the microwire can be associated with the change in the inner axially magnetized core radius, Rc, related with Mr/Mo, by eq. (3.2). Consequently, the spatial distribution of the hysteresis loops, must be consequence of the gradual modification of the domain structure along the microwires stress-annealed under a temperature gradient. 0100 200 0,5 1,0 0100 200 5 10 15 -100 -50 0 50 100 -1 0 1 M/M0 H (A/m) 110 mm -100 -50 0 50 100 -1 0 1 M/M0 H (A/m) 200 mm -100 -50 0 50 100 -1 0 1 M/M0 H (A/m) 0 mm Mr/M0 (a) (b) Hc (A/m) L (mm) Microwire Figure 3.32. Variation of Mr/M0 (a) and Hc (b) along the sample length for the sample 6 annealed at variable Tann. The lines are just guides for the eyes. Engineering of magnetic properties of Co-rich microwires 89 3.3. Concluding remarks Amorphous Co-rich microwires can present excellent magnetic softness and giant magnetoimpedance (GMI) effect. High GMI effect, obtained even in as-prepared Co-rich microwires, can be further improved by appropriate heat treatment (including conventional annealing, stress-annealing and Joule heating). It is worth mentioning the considerable improvement of ΔZ/Zmax values up to 650%, obtained for Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 microwire after appropriate current annealing conditions. Such microwires current annealed at optimal conditions, additionally present enhanced magnetic softness. Conventionally furnace annealed and stress-annealed, under appropriately selected conditions, Co-based microwires can present rectangular hysteresis loops and therefore single and fast domain wall propagation. However, generally Co-based stress-annealed microwires present high magnetoimpedance ratio. 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Engineering of magnetic properties of microwires with positive magnetostriction coefficient (Fe-, Fe-Niand Fe-Co-rich) This chapter summarizes the results obtained by selecting different chemical compositions and post-processing steps with the aim to optimize the magnetic properties for different Fe-rich compositions and geometric characteristics of amorphous glass coated microwires as presented in the table below (Table 4.1). The microwires selected pretend to give a complete overview of the behaviour of Fe-rich microwires from the metallic alloy groups CoxFe1-x and NixFe1-x, for 0 ≤ x ≤ 1, and Finemet-type FeCuNbSiB microwires. Table 4.1. Compositions, geometry and magnetostriction coefficients of studied Fe-rich glass-coated microwires. Composition d (μm) D (μm)  = d/D λs x 10-6 Fe77.5B15Si7.5 15.1 35.8 0.42 38 Fe70B15Si10C5 3 18,75 0.16 35 Fe70B15Si10C5 6 23,08 0.26 35 Fe70B15Si10C5 10.8 22.5 0.48 35 Fe70B15Si10C5 15 23,8 0.63 35 Fe75B9Si12C4 15.2 17.2 0.88 38 Fe71.7B13.4Si11Nb3Ni0.9 103 158 0.65 35 Fe47.4Ni26.6Si11B13C2 29 32.2 0.9 25 Fe49.6Ni27.9Si7.5B15 14.2 33.85 0.42 20 Fe62Ni15.5Si7.5B15 14.35 33.25 0.43 27 Fe70.8Cu1Nb3.1Si14.5B10.6 11.8 14.4 0.8 30 Fe70.8Cu1Nb3.1Si14.5B10.6 15.6 21.8 0.7 30 Fe70.8Cu1Nb3.1Si14.5B10.6 10.7 16.4 0.6 30 Fe71.8Cu1Nb3.1Si15B9.1 7.0 24.8 0.282 30 Fe71.8Cu1Nb3.1Si15B9.1 18.2 39 0.467 30 (Fe0.7Co0.3)83.7Si4B8P3.6Cu0.7 26.5 22.3 0.84 Fe83.7Si4B8P3.6Cu0.7 15.5 17.5 0.89 Fe38.5Co38.5B18Mo4Cu1 10 16.6 0,6 Engineering of magnetic properties of microwires with positive magnetostriction coefficient (Fe-, Fe-Niand Fe-Co-rich) 94 4.1. As-prepared Fe-rich microwires 4.1.1. FeBSiC microwires As-prepared Fe75B9Si12C4 amorphous glass coated microwire with metallic nucleus diameter d = 15.2 μm and total diameter D = 17.2 μm, and with magnetostriction coefficient, λs, positive value of about 35 x 10-6, presents a rectangular hysteresis loop (Figure 4.1) with Hc ≈ 48 A/m. Amorphous state of the as-prepared microwire was confirmed by XRD pattern (Figure 4.2a) and DSC curve of as-prepared Fe75B9Si12C4 microwire (Figure 4.2b) shows a crystallization temperature, Tcr1, of about 522 °C, and the estimation of the Curie temperature is about Tc = 413 °C. Therefore, the annealing temperatures, Tann, for this sample, in order to prevent crystallization, should be maintained below these temperatures. -100 0 100 -1 0 1 M/M0 H (A/m) Hs Hc Figure 4.1. Hysteresis loop of as-prepared Fe75B9Si12C4 amorphous glass-coated microwire. 40 60 80 100 0 1000 2000 3000 4000 5000 I (arb. unit.) 2 (deg.) (a) 200 300 400 500 0 1 2Tcr1 = 522 oC DSC signal (mW/mg) T (oC) Tc = 413 oC (b) Figure 4.2. XRD diffraction pattern (a) and DSC curve (b) of as-prepared Fe75B9Si12C4 microwire. Results and discussion: Chapter IV 101 4.6c, in sample annealed at 550 °C during 3 h, it can be seen that first crystallization peaks, related to the precipitation of fine Fe3B crystals, begin to appear in the XRD pattern. The overlap between the broad halo and the sharp peaks can be understood as the coexistence of both phases, amorphous and crystalline (consisting of α-Fe, Fe3B). By means of a Scanning Electron Microscope (MEB JEOL JSM-7000F), the chemical composition and microstructure of the microwire in as-prepared and annealed state was characterized (Figure 4.7). The images were obtained working at 5 kV and I ≈ 0.1 nA. For the compositional analysis, we employed the energy-dispersive X-ray spectroscopy (EDX) mode, with an Inca Energy 350 spectrometer, adjusting the measurement conditions at 20 kV and I ≈ 1 nA. SEM analysis of as-prepared and annealed samples, presented in Figure 4.7, correlates with the XRD patterns. SEM image of the metallic nucleus of asprepared sample (Figure 4.7a) is typical for amorphous samples. In Figure 4.7b, of SEM picture of annealed microwire at 550 °C during 3 h, crystallites of about 25 nm size can be appreciated. Nanocrystalline structure can be explained due to the particular composition of the microwires under study, given that the Nb impedes hinders the crystallites upon annealing [9]. Figure 4.7. SEM images of the metallic nucleus of Fe71.7B13.4Si11Nb3Ni0.9 microwires as-prepared (a) and annealed at 550 °C for tann = 3 h (b). Engineering of magnetic properties of microwires with positive magnetostriction coefficient (Fe-, Fe-Niand Fe-Co-rich) 102 As prepared hysteresis loop of Fe71.7B13.4Si11Nb3Ni0.9 microwire (Figure 4.8) is characterized by its rectangular shape with low coercivity, Hc ≈ 25 A/m, correspondingly with the amorphous structure. 4.2. Post-processing effect on magnetic properties and GMI effect for Fe-rich microwires 4.2.1. Effect of annealing on magnetic properties and GMI effect in nanocrystalline and devitrified microwires The devitrification of amorphous nucleus reached by post annealing process is a useful tool allowing considerable modification of the magnetic properties and even magnetic softening in some Fe-rich microwires [9,18,19]. In the case of FeSiBNbCu (so-called Finemet) alloys low magnetostriction values and better magnetic softness can be achieved by the devitrification of amorphous precursor [9,18-20]. The magnetic softening of the devitrified Finemet alloys is commonly explained considering the vanishing magnetocrystalline anisotropy, as well as the vanishing λs –value of the material, consisting of nano-sized grains with an average size on the order of 10 -200 -100 0 100 200 -1 0 1 M/M0 H (A/m) As-prepared Figure 4.8. Hysteresis loop of as-prepared Fe71.7B13.4Si11Nb3Ni0.9 microwire. Results and discussion: Chapter IV 103 nm, embedded in an amorphous matrix obtained by nanocrystallization of the amorphous precursors [9,17,18]. The average magnetostriction coefficient takes nearly zero values [9,17,18], due to the control of the crystalline volume fraction: the existence of two phases (amorphous and crystalline) provides a good balance of a negative magnetostriction of α-Fe-Si nanocrystallites of about (𝜆𝑠 𝐹𝑒𝑆𝑖 ≈ -6 x 10-6) and a positive one for the amorphous matrix of about (𝜆𝑠 𝑎𝑚 ≈ 20 x 10-6) resulting finally in vanishing net magnetostriction values [9]: 𝜆𝑠 𝑒𝑓𝑓 ≈ 𝑉𝑐𝑟 𝜆𝑠 𝐹𝑒𝑆𝑖 + (1 − 𝑉𝑐𝑟) 𝜆𝑠 𝑎𝑚 (4.1) where λseff is the saturation magnetostriction coefficient, and Vcr is the crystalline volume fraction. -100 -50 0 50 100 H (A/m) M/Mo As-prepared Hc= 44.5 A/m (a) 1 0 -1 1 0 -1 0 -1 Hc = 15.9 A/m Hc = 34.9 A/m Hc = 32.5 A/m 1 0 400 oC -1 1 0 -1 500 oC 550 oC 0100 200 300 400 500 600 0 20 40 60 4000 8000 12000 16000 Hc (A/m)  = 0.6  = 0.7  = 0.8 (b) Tann (oC) Figure 4.9. Hysteresis loops of as-prepared and annealed Fe70.8Cu1Nb3.1Si14.5B10.6 microwire samples at Tann between 400-600 °C (a) and Hc (Tann) dependence of Fe70.8Cu1Nb3.1Si14.5B10.6 microwires for different ρ-ratios (b). Engineering of magnetic properties of microwires with positive magnetostriction coefficient (Fe-, Fe-Niand Fe-Co-rich) 104 This nanocrystallization of FeSiBNbCu alloys is usually observed after annealing in the range of 500-600 oC for 1 h (i.e., at temperatures between the first and second crystallization stages). One of the examples of the evolution of the hysteresis loops of Finemet-type microwires upon nanocrystallization is shown in Figure 4.9. As can be observed from Figure 4.9, in the case of the Fe70.8Cu1Nb3.1Si14.5B10.6 microwire, annealing at Tann up to 550 oC allows considerable decrease of coercivity. For these annealing conditions the character of hysteresis loops does not change: all the hysteresis loops present rectangular shape. In some cases rectangular hysteresis loops are reported not only upon devitrification of Finemet-type, but even after second crystallization process when values up to 2400 A/m are observed [17-19]. One of the examples is shown in Figure 4.10, where hysteresis loop of Fe71.8Cu1Nb3.1Si15B9.1 microwire (  = 0.282) annealed at Tann = 700 oC is shown. However, Fe71.8Cu1Nb3.1Si15B9.1 microwire (  = 0.467) present rather different step-wise hysteresis loops (see Figure 4.10) that can be attributed to partially crystalline (bi-phase) structure. Such partially crystalline magnetic microwires, with step-wise hysteresis loops related to magnetic interaction between crystals or mixed amorphous- -8000 -4000 0 4000 8000 -1 0 1 M/M0 H (A/m)  = 0,282  = 0,467 Figure 4.10. Hysteresis loops of Fe71,8Cu1Nb3,1Si15B9,1 microwires with different  -ratios annealed at 700 oC. Results and discussion: Chapter IV 105 crystalline structure, can be interesting for applications in electronic surveillance systems [17-20]. The microwires obtained by devitrification exhibit higher saturation magnetization and at certain annealing conditions can present better magnetic softness and GMI response than as-prepared Fe-rich microwires and therefore they are useful for GMI sensors and metacomposites applications [9,20,21]. In fact, microwires with nanocrystalline structure can be obtained even directly in as-prepared state without annealing [9,20,21]. The advantage of such microwires is that they can present better mechanical properties [9,20,21]. It is worth mentioning, that the use of specially designed compositions allows further increase of saturation magnetization, μoMs, and also obtain extremely magnetically soft nanocrystalline materials [21]. In the case of microwires, the use of a similar chemical composition allows preparation of nanocrystalline microwires with improved DW mobility without any post -10 -5 0 5 10 -1 0 1 -1,0 -0,5 0,0 0,5 1,0 -1 0 1 (Fe0,7Co0,3)83,7Si4B8P3,6Cu0,7 mw Fe83,7Si4B8P3,6Cu0,7 mw 0Ms(T) H(kA/m) (Fe0,7Co0,3)83,7Si4B8P3,6Cu0,7 microwire Fe83,7Si4B8P3,6Cu0,7 microwire 0Ms(T) H (kA/m) Figure 4.11. Hysteresis loops of (Fe0.7Co0.3)83.7Si4B8P3.6Cu0.7 Fe83.7Si4B8P3.6Cu0.7 microwires as-prepared. Engineering of magnetic properties of microwires with positive magnetostriction coefficient (Fe-, Fe-Niand Fe-Co-rich) 106 processing [21]. The partially crystalline (Fe0.7Co0.3)83.7Si4B8P3.6Cu0.7 microwire presents elevated values of Hc (about 480 A/m) and rather high saturation magnetization of about 1.6 T (see Figure 4.11). Such elevated Hc -values are quite similar to that exhibited by other partially nanocrystalline microwires, i.e., Hitperm-like Fe38.5Co38.5B18Mo4Cu1 microwires with similar average grain size (about 38 nm and 23-33 nm for (Fe0.7Co0.3)83.7Si4B8P3.6Cu0.7 and Hitperm-like microwires, respectively) [21]. Accordingly, even partially crystalline or nanocrystalline microwires can present perfectly rectangular hysteresis loops. For (Fe0.7Co0.3)83.7Si4B8P3.6Cu0.7 microwire elevated μoMs -values allowed to obtain extremely fast domain wall velocity even in as-prepared state [21]. As-prepared Finemet-like and Hitperm-like glass-coated microwires also present perfectly rectangular hysteresis loops, as presented in Figure 4.12. Fe38.5Co38.5B18Mo4Cu1 microwire present nanocrystalline structure in asprepared state [22]. Higher Hc -values of Fe38.5Co38.5B18Mo4Cu1 and (Fe0.7Co0.3)83.7Si4B8P3.6Cu0.7 microwires have been attributed to elevated magnetostriction coefficient of these microwires as-compared to Finemet-type microwires. -200 -100 0 100 200 -1 0 1 M/M0 H(A/m) (a) -600 -300 0 300 600 -1 0 1 H (A/m) M/M0 (b) Figure 4.12. Hysteresis loops of Fe70.8Cu1Nb3.1Si14.5B10.6 (ρ = 0.38) (a) and Fe38.5Co38.5B18Mo4Cu1 (ρ = 0.6) (b) as-prepared microwires. Results and discussion: Chapter IV 107 For nanocrystalline materials, consisting of nano-sized grains distributed randomly in an amorphous matrix, magnetic softening and considerable GMI enhancement correlates with the devitrification process [9,17-22]. Figure 4.13a shows the XRD diffraction patterns Fe70.8Cu1Nb3.1Si14.5B10.6 amorphous glass-coated microwire with metallic nucleus and total diameters: d= 11.2 μm and D= 14.4 μm, respectively, annealed at different temperatures. The sample in as-prepared state and annealed at temperatures below Tann ≤ 450 °C, maintains amorphous structure. After annealing at temperatures between 500-600 oC the beginning of crystallization can be appreciated, with the crystalline peak between 42-45° correspondent with α-Fe (Si) phase. Various characteristics of the crystalline phase of the material can be determined by the shape of the crystalline peak, in particular, the full width at 30 40 50 60 70 80 90 500 1000 1500 I (arb. unit.) 2 (deg) Tann= 400 0C Tann= 550 0C Tann= 650 0C (a) 0 10 20 30 40 50 0200 400 6000 50 100 150 200 Dg (nm) Tann (ºC) Dg (b) Hc (A/m) Hc -10 0 10 0 20 40 60 80 100 Z/Z (%) H (kA/m) As-prepared Tann= 550 ºC (c) f = 200 MHz Figure 4.13. XRD diffraction patterns of annealed Fe70.8Cu1Nb3.1Si14.5B10.6 microwires (a), Dg (Tann) and Hc (Tann) dependencies (b) and GMI ratio dependencies (f = 200 MHz) of as-prepared and annealed at 550 °C (c) Fe70.8Cu1Nb3.1Si14.5B10.6 microwires. Engineering of magnetic properties of microwires with positive magnetostriction coefficient (Fe-, Fe-Niand Fe-Co-rich) 108 the half maximum. By means of Debye Scherrer equation can be estimated the crystal main grain size Dg [23,24]: 𝐷𝑔= 𝑘𝜆/𝜖cos2𝜃 (4.2) being k a dimensionless shape factor with value close to unity,  de wavelength, ϵ the full width at the half maximum of the crystalline peak and 2  the angular position of the crystalline peak (Bragg angle). Estimation of the average grain sizes of the nanocrystals embedded in the residual amorphous matrix (see Figure 4.13b) is below 20 nm. Magnetic softening, reflected in the Hc decrease, together with the precipitation of small α-Fe (Si) grains (Figure 4.13b), correlate with the GMI ratio improvement observed in Figure 4.13c upon annealing and the consequent devitrification of the amorphous precursor. Annealing at appropriate conditions that ensure the devitrification of Finemet-type amorphous microwires can be considered as an effective postprocessing route for the optimization of the magnetic softness and GMI effect for this group of Fe-rich microwires, but deterioration and poor mechanical properties continue to be the main disadvantage in this type of microwires [25]. Therefore, we paid special attention to search of post-processing of microwires that allows maintaining amorphous structure. 4.2.2. Tuning of magnetic properties of amorphous microwires by furnace annealing Below are presented some examples of the influence of conventional furnace annealing, focusing in the hysteresis loops of Fe-rich microwires of different compositions and on the domain wall dynamics and GMI effect and the combination of both magnetic properties in the same microwire. Results and discussion: Chapter IV 109 4.2.2.1. Effect of furnace annealing on magnetic properties of FeBSiC microwires Hysteresis loops character is not affected by the heat treatment, maintaining rectangular shape, as can be seen in Figure 4.14a and Figure 4.15a for Fe75B9Si12C4 microwires, only a slight decrease in Hc (tann) dependence is observed (Figure 4.14b). After conventional annealing at different temperatures (ranging from Tann = 250 °C to Tann = 375 °C), Fe75B9Si12C4 microwire hysteresis loops remain rectangular shaped (Figure 4.14a), as typically observed for microwires with positive  s [2-4,11,12], with a slight Hc decrease. The magnetic bistability origin is related to peculiar remagnetization process consisting of fast magnetization switching through a single DW propagation. DW propagation has been observed for this microwire in asprepared and annealed states. In Figure 4.15b a noticeable increase in the DW velocity and mobility can be appreciated after the annealing. The DW dynamics exhibits an almost perfectly linear behavior for the v(H) dependence for this sample as-prepared and annealed. -100 -50 0 50 100 -1 0 1 400 ºC 3 min 400 ºC 180 min M/M0 H (A/m) As-prepared (a) 050 100 150 80 85 90 Hc (A/m) tann (min) (b) Figure 4.14. Hysteresis loops of as-prepared and annealed at Tann = 400 °C for different tann Fe75B9Si12C4 amorphous microwires (a) and Hc (tann) dependence (b). Engineering of magnetic properties of microwires with positive magnetostriction coefficient (Fe-, Fe-Niand Fe-Co-rich) 110 Such linear v(H) dependence below the Walker breakdown field, HW, is attributed to a viscous DW propagation regime described in terms of DW mobility, S, (eq. (1.2)) [11,12]. It can be seen (Figure 4.15b) the influence of Tann on v a S values consists in increase in v and S values increasing Tann up to 375 °C. Similar DW velocity increase with the annealing temperature increase was recently reported elsewhere [11,12,26-28]. To study the Influence of annealing time, we select a temperature, Tann = 325 °C, and vary the annealing time, tann, as previously studied [2-4]. The results are presented below in Figure 4.16. Similar improvement as observed with increasing the annealing temperature is observed, for longer tann v and S values are higher. -200 -100 0 100 200 -1 0 1 M/M0 As-prepared 250 ºC 300 ºC 325 ºC 375 ºC (a) H (A/m) 20 40 60 80 200 400 600 800 1000 1200 As-prepared 250 oC 300 oC 325 oC 375 oC v m/s H (A/m) (b) Figure 4.15. Hysteresis loops (a) and v(H) dependence (b) of Fe75B9Si12C4 microwires as prepared and annealed during 60 min for different annealing temperatures. Results and discussion: Chapter IV 117 4.2.3. Stress-annealing in FeBSiC microwires 4.2.3.1. Tuning of domain wall dynamics by stress-annealing For amorphous glass coated microwires, the change in the magnetoelastic anisotropy (given by eq. (1.1)) by the stress relaxation induced by the annealing, being this the main source of magnetic anisotropy in absence of magnetocrystalline anisotropy, can explain the increase in the domain wall velocity and mobility. Then, stress-annealing was performed in this Fe75B9Si12C4 microwire. In Figure 4.24 it can be appreciated the disappearance of the rectangular shape of the hysteresis loop of as-prepared sample, that maintains up to 30 min of annealing time, with a more remarkable magnetic softening achieved increasing the annealing time, tann. It must be take into account that the difference in the thermal expansion coefficients between the metallic nucleus and the glass coating is the responsible to induce most part of the internal stresses [3-5]. -15 -10 -5 0 5 10 15 0 20 40 Z/Z (%) H (kA/m) As-prepared Tann= 410 ºC tann=16 min tann=128 min tann=256 min Figure 4.23. GMI ratio measured in as-prepared (a) and annealed at 410 °C for 16 (b), 128 (c) and 256 (d) minutes Fe47.4Ni26.6Si11B13C2 microwires measured at 600 MHz. Engineering of magnetic properties of microwires with positive magnetostriction coefficient (Fe-, Fe-Niand Fe-Co-rich) 118 v(H) dependence of stress-annealed samples (Figure 4.25a) reflects a drastic increase in the DW velocity and mobility increasing with the increase in the annealing time. -400 0 400 -1 0 1 M/M0 H (A/m) As-prepared 15min 30min 45min 60min Figure 4.24. Hysteresis loops of Fe75B9Si12C4 microwires as-prepared and stress-annealed with  = 190 MPa at Tann = 325 °C for different tann. 20 30 40 50 60 70 200 400 600 800 1000 1200 1400 As-prepared 15 min 30 min v (m/s) H (A/m) (a) 030 60 20 40 S (m2/As) tann (min) Annealed Stress-annealed (b) Figure 4.25. v(H) dependence of as-prepared and stress-annealed Fe75B9Si12C4 microwires with  = 190 MPa at Tann = 325 °C for different tann (a) and S(tann) for Fe75B9Si12C4 microwires annealed at Tann= 325 °C (b). Results and discussion: Chapter IV 119 Comparison of S (tann) values evaluated for conventional annealed and stress-annealed microwires is plotted in Figure 4.25b. S ≈ 7 m2/A∙s for asprepared sample substantially increases after annealing at 325 °C achieving S ≈ 10 m2/A∙s, while after stress-annealing a more remarkable increase, up to S ≈ 40 m2/A∙s, is obtained. This remarkable increase must be associated with transverse magnetic anisotropy induced by the stress annealing and reflected in the coercivity and remanent magnetization decrease (Figure 4.24). Stress-induced anisotropy can be tuned not only by modifying the annealing time but also changing the annealing temperature, Tann, and the stress applied during the annealing, whose influence is studied in Figure 4.27. Stress-annealing at high enough Tann and  transforms the rectangular hysteresis loop into almost linear. Considering that the magnetic domain structure of magnetic wires is assumed to be consisting of outer domain shell with transverse magnetization orientation and inner axially magnetized core [28,37], the domain structure modification can be evaluated from the squareness ratio, Mr/Ms, as described by eq. (3.1). -400 0 400 -1 0 1 Stress-annealed (  = 190 MPa) Stress-annealed (  = 760 MPa) M/M0 H (A/m) As-prepared Annealed (a) -400 0 400 -1 0 1 M/M0 H (A/m) As-prepared Stress annealed (  = 380 MPa) 300 oC 350 oC (b) Figure 4.26. Hysteresis loops of Fe75B9Si12C4 microwires as-prepared, annealed and stress-annealed at Tann= 300 °C for tann = 60 min (a) and stress-annealed (  = 380 MPa, tann = 30 min) at different temperatures (b). Engineering of magnetic properties of microwires with positive magnetostriction coefficient (Fe-, Fe-Niand Fe-Co-rich) 120 In this way from Mr/Ms-values obtained from hysteresis loops presented in Figure 4.27 we evaluated the dependence of the radius of inner axially magnetized core, Rc, on annealing conditions. As can be appreciated from Figure 4.27, Rc -values progressively decrease with increasing of σappl, Tann and tann values. At fixed annealing temperature the radius of inner axially magnetized core, Rc, is lower at higher applied stress (Figure 4.27b,c). From aforementioned analysis, we can deduce that the stress-annealing allows the increase of the volume of outer domain shell with transverse magnetization orientation increase in expense of decreasing of the radius of inner axially magnetized core. 0200 400 2 4 6 8 Rc (m) Tann (oC) (a) 0300 600 2 4 6 8 Rc (m)  appl (MPa) (b) 010 20 30 200 400 600 800 Rc (m) tann (min)  = 190 MPa  = 380 MPa Tann= 325 oC (c) Figure 4.27. Effect of annealing temperature (a), stress applied during annealing at Tann = 300 °C (b) and annealing time (c) on Rc-values of studied microwire. Results and discussion: Chapter IV 121 Consequently, beneficial effect of transverse magnetic anisotropy on DW velocity (see Figure 4.25) must be attributed to the increase of the volume of outer domain shell with transverse magnetic anisotropy. One of the obstacles limiting applications of fast DW propagation observed in microand nano-wires is that the travelling DW is essentially not abrupt [38-40]. However, the characteristic width δ of a head-to-head DW is closely related to the magnetoelastic anisotropy [39]. Thus, the reduced headto-head domain wall width δ/d (d is the metallic nucleus diameter) is determined by the value of the anisotropy constant K: for K = 104 erg/cm3, δ/d ≈ 13.5 and for K = 103 erg/cm3, δ/d = 40–50 [39]. For these estimations, it was assumed that the whole volume of the metallic nucleus diameter presents axial magnetization. In the present case, we are able to tune the volume of the inner axially magnetized core by annealing time and stress applied during the annealing (see Figure 4.27). Therefore, we may expect the modification of DW characteristic width δ upon stress annealing. The characteristic DW width can be evaluated from the EMF signals generated by a head-to-head DW moving through the microwire [39]. The EMF,  , generated within the turn of the pick-up coil by a change in the magnetic flux can be expressed as [39]: 𝜀(𝑡)=Δϕ Δ𝑡 (4.4) where ϕ = BS is the magnetic flux, S is the area of the surface, B = M + H is the magnetic induction, and M is the magnetization. Thus, the features (the amplitude and width) of the EMF peaks must be determined by 𝜕𝑀 𝜕𝑡. As can be appreciated from Figure 4.28, a decreasing of the EMF signal width from the pick-up coil can be appreciated after stress-annealing. The EMF signals,  , have been compared for as-prepared and stress-annealed for Engineering of magnetic properties of microwires with positive magnetostriction coefficient (Fe-, Fe-Niand Fe-Co-rich) 122 different tann samples (Figure 4.28a), as well as for as-prepared and those annealed under stress and without stress (Figure 4.28b). Such changes are evidenced by the evaluation of the half-width, W, of the EMF signal with annealing time provided in Figure 4.28c. As can be appreciated, a decrease of half-width of the EMF signal after stress-annealing is evidenced. 0,02504 0,02506 0,000 0,005 0,010  (V) t (ms) As-prepared 15 min 30 min (a) 0,02502 0,02504 0,02506 0,000 0,005 0,010  (V) t (ms) As-prepared 0 MPa 190 MPa (b) 020 40 60 0,012 0,014 0,016 0,018 0,020 W (ms) t (min) 0 MPa 190 MPa (c) Figure 4.28. EMF peaks induced by the magnetization change in pick-up coils measured for Fe75B9Si12C4 microwires as-prepared and stress-annealed (  = 190 MPa) for different tann (a), as-prepared and annealed at Tann = 325 °C for 30 min without stress and under stress (b) and dependence of the half-width of the EMF peaks with the annealing time (c). Results and discussion: Chapter IV 123 As discussed above, such decreasing of the half-width (full width at half maximum), W, must be associated either to the decreasing of the characteristic DW width or to the DW velocity increasing. The reason for such modifications can be stress-annealing induced transverse magnetic anisotropy as well as reduction of the volume of the inner axially magnetized core after stressannealing. Indeed as mentioned above, the δ –values are determined by the magnetoelastic anisotropy and by the diameter of the axially magnetized core. In order to separate these two factors we must analyze in more detail the EMF generated within the pick-up coil. Previously, the EMF, ε, generated within the pick-up coil turn when DW width, δ, is comparable with the distance to the coil turn, z, was analyzed [39]. The expression obtained in this case is [39]: 𝜀(𝑡)=−𝑄𝑣𝑅2√𝜋 2∫𝑑𝑧1〈𝜕𝛼𝑧 𝜕𝑧1 (𝑧1−𝑣𝑡)〉 ((𝑧−𝑧1)2+𝑅2)3/2 (4.5) where R is the radius of the coil turn, v = – dz/dt is the domain wall velocity, 1 zz    is the average linear density of the DW magnetic charge over the wire cross section and Q the magnetic charge. The eq. (4.5) is rather complex. In the simplified case, when the characteristic domain wall width, δ, is small compared with the distance z from the coil turn to the DW position, the eq. (4.5) can be simplified as [39]: 𝜀(𝑡)=−√𝜋 2𝑄𝑣𝑅2 (𝑧+𝑅2)3/2 (4.6) We can compare the EMF signals for as-prepared and stress-annealed samples if we consider the same coil parameters. In this case the only difference in EMF values must be associated to the different DW velocity, v, values and difference in remanent magnetization of as-prepared and stressannealed samples. The latter contributes through the magnetic charge, Q, given by [39]: Engineering of magnetic properties of microwires with positive magnetostriction coefficient (Fe-, Fe-Niand Fe-Co-rich) 124 𝑄=2𝑀𝑟𝑆 (4.7) where S is the sample cross section and Mr – remanent magnetization. This is attributed to the fact that only the remagnetization reversal of the inner axially magnetized core contributes to the EMF signal. These considerations allow us to evaluate if the difference in half-width of the EMF signal of as-prepared and stressannealed (Tann = 325 oC, σappl = 190 MPa, tann = 30 min) microwires is attributed only to different DW velocities or if DW shape change after stress annealing also takes place. Obtained velocities ratio taken from Figure 4.25a for H = 25 A/m for stress annealed and asprepared samples (vsa and vap, respectively) gives vsa/vap ≈ 1.25. However, considering the difference in the remanent magnetization (evaluated from Figure 4.24), the ratio Qsa vsa/ Qap vap ≈ 0.98 (where Qsa and Qap are values for stress-annealed and as-prepared samples). While the W –values ratio, i.e., Wsa/Wap (where Wap and Wsa are the half-width of the EMF peaks for asprepared and stress-annealed samples) is about 0.83. Consequently, we can assume the characteristic DW width reduction in stress-annealed microwires. 4.2.3.2. Effect of stress-annealing on GMI effect of Fe-rich microwires Similarly to Co-rich microwires, we used stress-annealing in order to improve the GMI effect. As shown above, stress-annealing allows to induce transverse magnetic anisotropy in Fe-rich microwires. A remarkable GMI ratio improvement is observed upon stress-annealing of Fe-rich microwires (see Figure 4.29). As-compared to as-prepared microwire, stress-annealing (Tann = 350 °C, tann = 60 min and σm = 190 MPa) allows an order of magnitude improvement of maximum GMI ratio,  Z/Zmax, (see Figure 4.29a and Figure 4.29b). The other relevant feature is that stress-annealed Results and discussion: Chapter IV 125 microwires present unusual  Z/Z(H) dependencies (see Figure 4.29b): low frequency  Z/Z(H) dependencies (10-50 MHz) are similar to that of as-prepared microwire, i.e., single peak dependence with a decay from H = 0. However, rising the frequency an additional maximum on  Z/Z(H) dependencies appears (Figure 4.29b). Therefore, at intermediate frequency range (100-300 MHz)  Z/Z(H) dependencies present irregular shape that recently has been interpreted as the superposition of the double-peak  Z/Z(H) dependence typical for transverse magnetic anisotropy and single-peak reported for axial magnetic anisotropy [4]. At elevated frequencies  Z/Z(H) dependencies present  Z/Z(H) dependence typical for the wires with transverse magnetic anisotropy (see Figure 4.29c). -10 0 10 0 10 20 30 Z/Z (%) H (kA/m) 50 MHz 100 MHz 400 MHz 800 MHz (a) -10 0 10 0 30 60 90 120 Z/Z (%) H (kA/m) 10 MHz 50 MHz 100 MHz 150 MHz 300 MHz (b) -10 0 10 0 50 100 Z/Z (%) H (kA/m) 100 MHz 200 MHz 500 MHz 800 MHz (c) Figure 4.29.  Z/Z(H) dependencies observed in as-prepared (a) and stress-annealed at Tann =350 °C (for 60 min and σm = 190 MPa) Fe75B9Si12C4 microwires. Engineering of magnetic properties of microwires with positive magnetostriction coefficient (Fe-, Fe-Niand Fe-Co-rich) 126 Such frequency influence on  Z/Z(H) dependencies can be interpreted considering existence of inner axially magnetized domain inside the stressannealed microwires and frequency dependence of the skin penetration depth, δ, as described in [4]. It is worth mentioning, that such irregularity can be observed in  Z/Z(H) dependencies for stress-annealed microwires at different annealing conditions. Thus, similar irregular dependencies have been observed for microwires annealed at 250 °C (Figure 4.30a) and 300 °C (Figure 4.30b) for 60 min and 900 MPa. However, the frequency range at which such unusual  Z/Z(H) dependencies are observed depend on stressannealing conditions: for lower annealing temperature the frequency range (70-200 MHz) is shifted to lower frequencies. From above presented results it is clear that the frequency is one of the important parameters allowing GMI ratio optimization. One of the parameters that can be used as a reference is the maximum GMI ratio,  Z/Zmax. For asprepared samples  Z/Zmax corresponds to Hm = 0, however, for the stressannealed sample  Z/Zmax is observed at some field, Hm ≠ 0. Frequency -10 0 10 0 50 100 Z/Z (%) H (kA/m) 70 MHz 80 MHz 100 MHz 150 MHz 200 MHz (a) -10 0 10 0 50 100 Z/Z (%) H (kA/m) 100 MHz 150 MHz 200 MHz (b) Figure 4.30.  Z/Z(H) dependencies observed in stress-annealed at Tann = 250 °C for 60 min and σm = 900 MPa (a) and Tann = 300 °C for 60 min and σm = 900 MPa (b) Fe75B9Si12C4 microwires. Results and discussion: Chapter IV 133 of change of coercivity, ΔHc, for as-prepared Fe75B9Si12C4 sample is 160 A/m and for stress-annealed Fe75B9Si12C4 sample ΔHc = 191 A/m. This difference is most remarkable for the range of low  –values, making stress-annealing suitable for detection of low applied stresses. Similarly, squareness ratio, Mr/Ms, of stressannealed Fe75B9Si12C4 sample presents more significant changes at low  region. Observed stress dependencies of the squareness ratio must be associated with changes of domain structure. Indeed, it is commonly accepted that the domain structure of Fe-rich microwires consists of inner axially magnetized core and outer shell with transverse magnetization easy direction [38,47]. As can be observed from Figure 4.36b, Mr/Ms ratio of stress-annealed Fe75B9Si12C4 sample rapidly increases upon applied stress. Considering eq. (3.2) we obtained Rc modification under applied stress influence from 6 up to almost 7.5 μm as depicted in Figure 4.36b. Consequently, we must assume change of domain structure in stress-annealed Fe75B9Si12C4 sample under influence of applied stresses in stress-annealed Fe75B9Si12C4 sample consisting of rising of the inner axially magnetized core radius from 6 up to almost 7.5 μm. 4.2.4. Reversibility of the stress-annealing anisotropy As shown above, stress annealing of as-prepared Fe75B9Si12C4 microwires, allows the induction of transverse magnetic anisotropy that depends on the stress-annealing conditions. Figure 4.37 compares the rectangular hysteresis loop of as prepared Fe75B9Si12C4 microwires with the hysteresis loops of the microwires annealed at a fixed Tann = 350 oC and time tann = 60 min, under different applied stresses,  showing the gradual transformation of the hysteresis loop into linear and the increase in Hk (Figure Engineering of magnetic properties of microwires with positive magnetostriction coefficient (Fe-, Fe-Niand Fe-Co-rich) 134 4.37) with increasing the stress-applied during the annealing, that correlates with the decrease of the squareness ratio, Mr/Ms. Hc decreases at low applied stresses of 190 MPa and 380 MPa (inset of Figure 4.38) however for the higher stress applied Hc values are practically the same of as-prepared sample. The radius of the inner axially magnetized core, Rc (as defined in eq. (3.2)), evaluated from Mr/Ms, shows a decrease with the increase in the applied stress during the stress-annealing Figure 4.37) that can be interpreted as the inner axially magnetized core reduction as the volume of microwire with transverse magnetic anisotropy grows. To study the reversibility of the stress annealing anisotropy of a sample stress-annealed at a fixed  , we performed a subsequent annealing without stress of the stress-annealed sample (SA) at the same temperature (Tann = 350 oC) and for tann = 60 min, (SA + A), and a longer subsequent annealing, (SA + 2A), at the same temperature for tann = 150 min. -500 0 500 -1 0 1 As-prepared 190 MPa 380 MPa 760 MPa M/M0 H (A/m) Figure 4.37. Hysteresis loops of Fe75B9Si12C4 microwires as-prepared, stressannealed at Tann = 350 oC, tann = 60 min, under different applied stresses. Results and discussion: Chapter IV 135 For the case of the microwire subjected to stress-annealing with σ = 190 MPa (hysteresis loops presented in Figure 4.37 and Figure 4.39a) a partially recover of the stress-annealing anisotropy can be reached after the subsequent annealing. However, the hysteresis loop of microwire subjected to stressannealing with σ = 76 MPa is less affected by subsequent annealing: it remains almost unchanged after subsequent annealing (see Figure 4.39b). As can be interpreted from Mr/Ms and Rc (tann) dependencies obtained from the hysteresis loops and represented in Figure 4.40, Mr/Ms and Rc values obtained after annealing (tann = 150 min) of stressannealed with σ = 190 MPa sample reach values similar of those of as-prepared microwire. We can conclude that the subsequent annealing allows increasing the volume of the inner axially magnetized core. Lower coercivity values of the sample subjected to longer subsequent annealing (tann = 150 min), as compared to as prepared sample, can be associated to the stress relaxation. 0300 600 0 600 1200 0300 600 2 4 6 8 Hk 0300 600 30 60 90 Hc(A/m) (MPa) Hc Hk (A/m) Rc Rc (m)  (MPa) Figure 4.38. Hk and Rc dependencies and Hc (on the inset) dependences on stress applied during the annealing. The lines in the figure are just guides for eyes. Engineering of magnetic properties of microwires with positive magnetostriction coefficient (Fe-, Fe-Niand Fe-Co-rich) 136 As observed from Figure 4.39b, hysteresis loops of the microwire stressannealed with σ = 760 MPa followed by the subsequent annealing steps reflect much stronger induction of transverse magnetic anisotropy. The hysteresis loops of the microwire once subjected to stress-annealing do not change under subsequent annealing for tann = 60 min nor for longer tann = 150 min. In Rc (tann) representation of Figure 4.40, comparing with sample stressannealed with σ = 190 MPa, only a slight increase can be appreciated after the annealing procedures of the SA sample with σ = 760 MPa, for which the Rc (tann) dependence shows that after the stress annealing at those  values most part of the microwire metallic nucleus possesses transverse magnetic anisotropy. The comparison between Figure 4.37a and Figure 4.37b and Rc (tann) dependence for both samples (Figure 4.40), lead us to conclude that the increase in the applied stress during the stress annealing treatment implies a growth in the irreversible part of the stress-annealed induced magnetic anisotropy. -500 0 500 -1 0 1 M/M0 H (A/m) As-prepared SA SA+A SA+2A  = 190 MPa (a) -400 -200 0 200 400 -1 0 1 As-prepared SA SA+A SA+2A M/M0 H (A/m)  = 760MPa (b) Figure 4.39. Hysteresis loops of Fe75B9Si12C4 microwires as-prepared and stress annealed with σ = 190 MPa (a) and σ = 760 MPa (b) with subsequent annealing during 60 min and 150 min. Results and discussion: Chapter IV 137 One more advantage of Fe-rich microwire subjected to combined annealing (stress-annealing + subsequent annealing) is better GMI effect of such microwires. In spite of rectangular character of hysteresis loops of Fe75B9Si12C4 microwires stress annealed (SA) with σ = 190 MPa and then annealed at 350 oC for 150 min, such microwire present better GMI response as-compared to as060 120 0 3 6 Rc (m) 0 60 120 0 1 2 R c (  m) t ann (min) Rc (  = 190 MPa) tann (min) Rc (  = 760 MPa) Figure 4.40. Comparison of Rc (tann) dependence between samples stress-annealed upon σ = 190 and 760 MPa with subsequent annealing. The lines in the figure are just guides for eyes. -10 -5 0 5 10 0 50 100 Z/Z (%) H (kA/m) 10 MHz 50 MHz 100 MHz (a) -10 -5 0 5 10 0 50 100 150 Z/Z (%) H (kA/m) 200 MHz 500 MHz 1 GHz (b) Figure 4.41. ΔZ/Z(H) dependences of SA (σ = 190 MPa) and then annealed Fe75B9Si12C4 microwires measured at f ≤ 100 MHz (a) and at f ≥ 100 MHz (b). Engineering of magnetic properties of microwires with positive magnetostriction coefficient (Fe-, Fe-Niand Fe-Co-rich) 138 prepared and even stress-annealed Fe75B9Si12C4 microwire: ΔZ/Zmax –values up to 150 % are recorded at 500 MHz (see Figure 4.41). As shown in Figure 4.41a for f ≤ 80 MHz the single peak ΔZ/Z(H) dependence is observed, while f ≥ 80 MHz ΔZ/Z(H) dependence change from single-peak to double-peak type (see Figure 4.41b). The proposed postprocessing consisting of stress-annealing followed by annealing allows suppressing the irregular ΔZ/Z(H) dependence observed in stress-annealed Fe-rich microwires (see Figure 4.29) by the subsequent annealing. One more example is provided in Figure 4.42 and Figure 4.43 for stress-annealing performed at σ = 760 MPa. The stress-annealed (at σ = 760 MPa) Fe75B9Si12C4 microwire presents considerable GMI effect (see Figure 4.42a and Figure 4.42b) in spite of high transverse magnetic anisotropy that can be deduced from the hysteresis loops shown in Figure 4.39. As can be observed from Figure 4.42a, double-peak ΔZ/Z(H) dependencies are observed even for low frequencies (10-50 MHz). Rising the frequency, i.e., for intermediate frequencies (100 ≤ f ≤ 200 MHz) ΔZ/Z(H) dependencies present irregular shape (Figure 4.42b). Finally, for high frequencies (f ≥ 300 MHz) again double peak ΔZ/Z(H) dependencies are observed (Figure 4.42c). Generally, observed ΔZ/Zmax –values are below 80%. Higher ΔZ/Zmax –values (up to 120%) and double-peak ΔZ/Z(H) dependencies in a whole frequency range are observed for the Fe75B9Si12C4 microwire after SA (σ = 760 MPa) and then subsequently annealed (for 150 min) (see Figure 4.43a and Figure 4.43b). From above presented experimental results we can deduce that annealing after stress annealing allows: Results and discussion: Chapter IV 139 i) A remarkable GMI effect improvement as compared to as-prepared and even to stress-annealed Fe-rich microwires and ii) Suppression of irregularities in ΔZ/Z(H) dependencies observed in all stress-annealed samples at intermediate frequencies (see Figures 4.29, 4.41, 4.42 and 4.43). A beneficial influence of appropriate annealing after stress-annealing is evidenced from a comparison of the ΔZ/Zmax (f) dependencies presented in Figure 4.44. It is clearly seen that GMI effect improvement is observed in the whole frequency range. The highest ΔZ/Zmax ratio of about 160% is observed at 300 MHz (for the Fe75B9Si12C4 microwire SA at 190 MPa and then annealed) [48]. -10 -5 0 5 10 0 40 80 Z/Z (%) H (kA/m) 10 MHz 50 MHz 100 MHz (a) -10 -5 0 5 10 0 30 60 Z/Z (%) H (kA/m) 80 MHz 150 MHz 200 MHz (b) -10 -5 0 5 10 0 40 80 Z/Z (%) H (kA/m) 300 MHz 500 MHz 1 GHz (c) Figure 4.42.  Z/Z(H) dependences of SA (σ = 760 MPa) Fe75B9Si12C4 microwire measured at f ≤ 100 MHz (a), 80 ≤ f ≤ 200 MHz (b) and at f ≥ 300 MHz (c). Engineering of magnetic properties of microwires with positive magnetostriction coefficient (Fe-, Fe-Niand Fe-Co-rich) 140 In all the cases subsequent annealing allows ΔZ/Zmax –values improvement by up to 50%. The observed beneficial effect of annealing on the GMI effect can be explained considering that annealing promotes the enhancement of circumferential anisotropy and, hence, suppresses the irregularities in the ΔZ/Z(H) dependencies. -10 0 10 0 50 100 Z/Z (%) H (kA/m) 10 MHz 50 MHz 100 MHz (a) -10 0 10 0 50 100 Z/Z (%) H (kA/m) 200 MHz 500 MHz 1 GHz (b) Figure 4.43. ΔZ/Z(H) dependences of SA (σ = 760 MPa) + annealed Fe75B9Si12C4 microwire measured at f ≤ 100 MHz (a) and at f ≥ 200 MHz (b). 0300 600 900 30 60 90 120 150 Z/Zmax (%) f (MHz) SA (  =190MPa) SA (  =190MPa) + annealed (150min) SA (  =760MPa) SA (  =760MPa) + annealed (150min) Figure 4.44. ΔZ/Zmax(f) dependencies of SA and SA + annealed Fe75B9Si12C4 microwire for σ = 190 MPa and 760 MPa. The lines are just guides for eyes. Results and discussion: Chapter IV 141 4.2.5. GMI effect and DW propagation in “thick” glass-coated Fe-rich microwires After annealing, at 550 °C the character of the hysteresis loop of Fe71.7B13.4Si11Nb3Ni0.9 microwire does not change, as can be seen in Figure 4.45, although Hc experiments a slight increase, this magnetic hardening can be understood as the beginning of crystallization (as confirmed by the XRD pattern in Figure 4.4c). Then, we assumed that at lower annealing temperatures the microwire structure remains amorphous. Annealing at 300 °C causes a coercivity decrease, the magnetic softening in this case can be explained due to the internal stresses relaxation. The bistable behaviour of the microwire as-prepared and annealed for short annealing time observed in Figure 4.45, suggests the possibility to observe single domain wall, DW, propagation, since it is observed for other Ferich microwires [35,36]. By means of the modified Sixtus-Tonks method (described in detail in Chapter 2) the velocity dependence on magnetic field H, v(H), was evaluated and it is presented in Figure 4.45. As-prepared microwire presents practically linear v(H) dependence and relatively high v values, up to -200 -100 0 100 200 -1 0 1 M/M0 H (A/m) As-prepared 300oC 1h 300oC 4h 550oC 1h 550oC 3h Figure 4.45. Hysteresis loop of as-prepared Fe71.7B13.4Si11Nb3Ni0.9 microwire and annealed at 550 °C and 300 °C for different tann. Engineering of magnetic properties of microwires with positive magnetostriction coefficient (Fe-, Fe-Niand Fe-Co-rich) 142 700 m/s, as compared to the reported for Fe-rich microwires of similar diameter obtained by in-rotating water quenching technique [49]. 30 40 50 60 70 80 200 400 600 800 1000 S = 15,5 m2/A.s S = 11,9 m2/A.s As prepared 550 oC 1 h v (m/s) H (A/m) Figure 4.46. DW velocity dependence on magnetic field, v(H), of as-prepared Fe71.7B13.4Si11Nb3Ni0.9 microwires and annealed at 550 °C for tann = 1 h. The linear dependence of the DW velocity, v(H), along the microwire [36-38,50], as a function of the magnetic field, in a viscous regime is described by eq. (1.2). -6 -4 -2 0 2 4 6 30 40 50 Z/Z (%) H (kA/m) 100MHz 500MHz 1 GHz Figure 4.47. GMI ratio dependence of as-prepared Fe71.7B13.4Si11Nb3Ni0.9 microwire at different frequencies.