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Repositorio de Trabajo Fin de Máster Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic Mª Rosario Mayoral Blasco de la Universidad de Zaragoza – Zaguan http://zaguan.unizar.es Trabajo Fin de Máster Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation Autor Mª Rosario Mayoral Blasco Director Dr. Javier Sesé Monclús Facultad de Ciencias 2014 http://zaguan.unizar.es Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic ACKOWLEDGES I wish to thanks: • Dr. Javier Sesé Monclús, my supervisor, for its untiring guidance given to me throughout the research, despite his busy schedule. • The technicians of the Nanoscience Institute of Aragón (INA), for their permanent scientific and human support At last but not least, thanks to my lovely parents, Angel and Charo, whom have always been driving force for all my achievements, and to my sisters Susana and María, my brother Javi, my brother-in-law Pablo and my aunt Chari, for their wholehearted support during the time of this research. i IDEX EXECUTIVE SUMMARY …………………………………………..................... 1 ITRODUCTIO ………………………………………………………………... 2 1.- Types of magnetic materials ……………………………………………….. 2 2.- History of diamagnetic levitation ………………………………………….. 5 PRESET MAGETIC MEASUREMET TECHIQUES …….................... 7 1.- The SQUID (Superconducting Quantum Interference Device) …………. 7 2.- The VSM (Vibrating Sample Magnetometer) ……………………………. 9 3.- MFM (Magnetic Force Microscope) ………………………………………. 10 4.- The SERF (Spin-exchange relaxation-free) magnetometer ……………... 12 5.- itrogen Vacancy (V) Magnetometry …………………………………... 14 THE TESTED PROTOTYPE ……………………………………....................... 19 1.- Basics ………..…………………………………………………………......... 19 2.- The equipment ……………………………………………………………… 20 2.1.- The diamagnetic levitation system…………………………………… 21 2.2.- Solenoid ………………………………………………………............ 23 2.3.- A magnetic Hall sensor ………………………………………………. 23 2.4.- The electronic control………………………………………………… 25 2.4.1.- The current generator ……………………………………..... 25 2.4.2.- The Hall sensor control …………………………………….. 27 2.4.3.- The microprocessor ………………………………………… 28 2.5.- The micrometric gears ……………………………………………….. 28 3.- The program …………………………………………………………........... 29 4.- The wafer (samples) …………………………………………………........... 31 MEASUREMETS ……………………………………………………………… 34 1.- Silicon wafer (100): 10 nm Fe, 10 nm Au ..................................................... 37 2.- Glass wafer: 20 nm Fe, 10 nm Au ................................................................. 39 3.- Glass wafer: 20 nm Fe, 20 nm Al .................................................................. 41 3.1.- M2: cylindrical, diameter 1.5 mm, thickness 1 mm …………………. 41 3.2.- M2: spherical, diameter 3 mm ……………………………………….. 42 3.3.- M2: cubic, side 1 mm ………………………………………………... 43 3.4.- M2: cubic, side 2.5 mm ……………………………………………… 45 3.5.- M2: cubic, side 3 mm ………………………………………………... 45 3.6.- M2: cylindrical, diameter 1 mm, thickness 1 mm …………………… 45 COCLUSIOS …………………………………………………………………. 46 REFERECES …………………………………………………………………... 48 Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 1 Mª Rosario Mayoral Blasco EXECUTIVE SUMMARY Within the field pertaining to the measurement of very small quantities of magnetic materials, there are nowadays different devices capable of accurately measuring the weak magnetic fields present in samples under study. Primarily, these devices are based on the technology of SQUID systems (superconducting quantum interference devices) which are able to measure magnetic fields up to 10 -18 Tesla (T), being the most sensitive magnetometers known till nowadays. These SQUID devices have a high precision in the measurement of magnetic fields but its use is made in very demanding technical conditions because it needs to incorporate an associated cryogenic cooling system. Other recent magnetometers, such as SERF based devices (spin-exchange relaxation free devices, based into the exchange of the spin without relaxation) allows also to measure very weak magnetic fields, without resorting to cryogenic conditions, although they can only operate at practically zero fields, being unable to measure higher-intensity fields. Furthermore, their conditions of use are technically demanding, requiring a preheating of an alkali metal vapor and a special medium used to that end associated to the magnetometer. To avoid the aforementioned inconvenients it is necessary to develop technical alternatives to get accurate measures of weak magnetic fields whose operation requirements don´t need to have technically complex processes prior to the sensing (such as obtaining cryogenic temperatures, vacuum technology or heating sensing atoms), and also involving low manufacturing costs 1 . That is the reason why this master thesis has been developed. On it, the aim is to obtain a high sensitive magnetometer, based on diamagnetic levitation principles, to measure weak magnetic samples. The device comprises a system of two permanent magnets in which one magnet is in a stable equilibrium levitating position by means of the presence of a diamagnetic element being the magnetic study specimen subjected to the action of the magnets of the device. This specimen has been designed and produced by optical lithography in form of microstructures with variable size that will allow to do systematic measurements and to analyze the answer of the sensor. Also, the prototype Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 2 Mª Rosario Mayoral Blasco has been tested with different measurement strategies and with different geometry as regards to the size of the magnet, magnet-sample distance, and so on. Finally, the measurements done with the prototype have been compared with the one obtained by the high sophisticated technique of the SQUID. ITRODUCTIO Since the first magnetic needle compass used by the Chinese to improve the accuracy of navigation, many studies have been done to achieve a better knowledge about how the magnetic field acts and to find applications to use it in the real life. Was Hans Christian Oersted, a professor at the University of Copenhagen, who discovered the relationship between electricity and magnetism in 1819. Several other experiments followed. AndréMarie Ampère, in 1820, proves that the magnetic field circulating in a closed-path was related to the current flowing through the surface enclosed by the path. In the same year Carl Friedrich Gauss, Jean-Baptiste Biot and Félix Savart, came up with the Biot–Savart law giving an equation for the magnetic field from a current-carrying wire. Later on, in 1831, Michael Faraday found that a time-varying magnetic flux through a loop of wire induced a voltage. James Clerk Maxwell synthesized and expanded these insights into Maxwell's equations, unifying electricity and magnetism into the field of electromagnetism. Electromagnetism and magnetism knowledge continues to develop, being incorporated into the more fundamental theories of gauge theory, quantum electrodynamics, electroweak theory, and finally the standard model. As result of all this, the magnetic materials are nowadays divided basically into three types, and gives place to the respective well known magnetic effects: Ferromagnetism, Paramagnetism and Diamagnetism. 1.- Types of magnetic materials To introduce the different types of magnetism the best way is to describe how materials respond to magnetic fields, having as a basic that the origin of magnetism lies in the orbital and spin motions of electrons and how the electrons interact with one another 2 . Magnetic measurements of nanometric means of a new sensor based on diamagnetic levitation. Mª Rosario Mayoral Blasco  Ferromagnetic: In these materials the atomic moments exhibit very strong interactions which are produced by electronic exchange forces due to the relative orientation of the spins of two electron large net magnetization even in the absence of a magnetic field (H). This effect is called spontaneous magnetization and is a characteristic of these materials (figure 1a). Also, the ferromagnets c removed. This behavior is called hysteresis and gives place to the well known hysteresis loop, which shows the variation of magnetiza field as can be seen in figure 1b). a) Alignment of moments in absence of H. Figure 1: Ferromagnetic order.  Paramagnetic: Paramagnetic materials are composed of atoms or ions that have a net magnetic moment due to unpaired electrons in partially filled orbitals interact magnetically having a zero magnetization when there is no field (figure 2a). In the presence of a field there is a partial alignment of the atomic magnetic moments appearing a magnetic moment a net positive magnetization and positive susceptibility (χ). This the ratio of M to the field applied: χ = M/H. The efficiency of the field in Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 3 Mª Rosario Mayoral Blasco In these materials the atomic moments exhibit very strong interactions which are produced by electronic exchange forces due to the relative orientation of the spins of two electron s. As a result, the alignment of moments gives place to a large net magnetization even in the absence of a magnetic field (H). This effect is called spontaneous magnetization and is a characteristic of these materials Also, the ferromagnets c an retain a memory of an applied field once it is removed. This behavior is called hysteresis and gives place to the well known hysteresis loop, which shows the variation of magnetiza tion (M) with magnetic as can be seen in figure 1b). Alignment of moments in b) Hysteresis loop. Figure 1: Ferromagnetic order. Paramagnetic materials are composed of atoms or ions that have a net magnetic moment due to unpaired electrons in partially filled orbitals , but they do not interact magnetically having a zero magnetization when there is no field (figure In the presence of a field there is a partial alignment of the atomic magnetic appearing a magnetic moment in the direction of the field, resul a net positive magnetization and positive susceptibility (χ). This the ratio of M to the field applied: χ = M/H. The efficiency of the field in Mr: Remanent Magnetization Hc: Coercitivity In these materials the atomic moments exhibit very strong interactions which are produced by electronic exchange forces due to the relative orientation of the s. As a result, the alignment of moments gives place to a large net magnetization even in the absence of a magnetic field (H). This effect is called spontaneous magnetization and is a characteristic of these materials an retain a memory of an applied field once it is removed. This behavior is called hysteresis and gives place to the well known tion (M) with magnetic b) Hysteresis loop. Paramagnetic materials are composed of atoms or ions that have a net magnetic , but they do not interact magnetically having a zero magnetization when there is no field (figure In the presence of a field there is a partial alignment of the atomic magnetic in the direction of the field, resul ting in a net positive magnetization and positive susceptibility (χ). This χ is defined as the ratio of M to the field applied: χ = M/H. The efficiency of the field in Ms: Saturation magnetization Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 10 Mª Rosario Mayoral Blasco Nowadays the technique has been improved but the basic principle of operation for a vibrating sample magnetometer (a changing magnetic flux will induce a voltage in a pickup coil) remains. Also the basic measurement of the magnetic moment is accomplished by oscillating the sample near a detection (pickup) coil and synchronously detecting the coefficient of the sinusoidal voltage response from the detection coil. In the VSM systems that are being used today the loudspeaker transducer has been change by a linear motor transport (head) for vibrating the sample. Also the electronics for driving the linear motor transport and detecting the response from the pickup coils has been developed. The rest remains the same 21 . The way of working is as follows: the sample is attached to the end of a sample rod which is driven sinusoidally. The center of oscillation is positioned at the vertical center of a gradiometer pickup coil. By using an optical linear encoder signal readback from the VSM linear motor transport, the precise position and amplitude of oscillation is controlled. Then, the voltage induced in the pickup coil is amplified and lock-in detected in a VSM detection module using the position encoder signal as reference for the synchronous detection. By averaging the in-phase and quadrature-phase signals from the encoder and from the amplified voltage from the pickup coil the final value is obtained. The system is able to resolve magnetization changes of less than 10 -9 Am 2 at a data rate of 1 Hz 22 . 3.- MFM (Magnetic Force Microscope) Magnetic force microscopy imaging is a useful technique to locally study the magnetic state of nanostructures. It provides simultaneously information about the topography and the magnetization of the samples. Usually, their images complete the magnetic characterization performed by standard macroscopic methods such as SQUID or VSM. But other times, it can also be used to give a quantitative value of the magnetization 23, 24 in nanostructures by means of the quantitative MFM imaging analysis as can be seen in the next figure 25 . Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 11 Mª Rosario Mayoral Blasco Figure 7: Hysteresis loop of a ferromagnetic sample measured by SQUID magnetometry (solid line). The data points were obtained from the MFM images 23 . For mapping the magnetic forces of the sample the magnetic tip of the MFM interacts with the sample’s stray magnetic field. According to Hooke’s Law the force (F) detected depends on the spring constant (k) of the cantilever (assuming that the cantilever is oriented parallel to the sample surface) and the variation on the position in the z-axis 26 . F = - k∆z (1) Figure 8: Interaction of the magnetic tip with the sample stray magnetic field. There are two modes of the tip-sample interaction: static MFM (dc) and dynamic MFM (ac). In the static MFM mode the interaction force is measured through the detection of the cantilever deflection from the equilibrium position, while in the dynamic MFM mode is registered the force gradient, that is to say, the change in resonant properties of   S S SUBSTRATE MAGNETIC SAMPLE MFM TIP Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 12 Mª Rosario Mayoral Blasco the vibrating system cantilever-sample. The dynamic mode operation is more sensitive to the magnetic field variation than the static one 27 . Since it is based on the force or force derivatives detection, the relation with the energy of tip-sample interaction (E tip-sample ) is: F = E tip - sample (2) The E tip-sample can be expressed in terms of a convolution of the tip stray field H tip and the sample magnetization M sample , where integration is performed over the whole magnetic volume of the sample. E tip-sample ~ ∫ sample M sample H tip (3) Therefore, having measured the forces (or their derivatives) acting between a tip and a sample, it is theoretically possible to restore the magnetisation distribution M sample within an unknown sample upon some model assumptions on distribution of the stray field from MFM tip H tip and having assessed this value numerically 28 . The sensitivity of this measurement technique is found to be in the 10 -18 Am 2 range under ambient conditions 29 . But it is limited by the tip's magnetic moment and the noise level of the instrument. 4.- SERFs (Spin-exchange relaxation-free) magnetometers A spin exchange relaxation-free magnetometer is a type of magnetometer developed in the early 2000s. It measures magnetic fields by using lasers to detect the interaction between alkali metal atoms in a vapor and the magnetic field. The general idea of the method is that light that is near-resonant with an optical transition creates long-lived orientation and/or higher-order moments in the atomic ground state, which subsequently undergo Larmor spin precession in the magnetic field 30 . The modification of the optical absorptive and dispersive properties of the atoms that this precession causes is detected by measuring the light transmitted through the atomic medium. Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 13 Mª Rosario Mayoral Blasco The resonant medium is usually a vapor of alkali atoms (Rubidium (Rb), Cesium (Cs) or Potassium (K)) contained in a glass bulb. As the depolarization caused by collisions with the cell walls that enclose the atomic vapor limit the spin-relaxation time, cells filled with buffer gas are commonly used. This gas ensures that the atoms optically polarized in the central part of the cell take a long time to diffuse to the walls. The surface relaxation can also be reduced by using a coating on the cell walls that has low adsorption energy for atoms, so they spend less time bound to the surface of the cell. Among such coatings, materials with long chains of hydrocarbons as paraffin work well with alkali metals 31 . Another way to improve the magnetometer sensitivity is to increase the density of alkali-metal atoms. This has been done typically by increasing the temperature of the cell, although alternative approaches using light-induced desorption have been investigated 32 . Regarding to light sources used for atomic magnetometers, originally they were discharge lamps but today the light sources of choice are diode lasers 33 . The atomic magnetometers can be configured so that their output is directly related to the absolute magnitude of the magnetic field through fundamental physical constants. Therefore, no calibration is required. In the figure 9, a scheme of a general SERF is depicted. As can be seen, the magnetometer consists of a cell containing an alkali vapor and a buffer gas. The alkali vapor is generated by heating a droplet of potassium, rubidium or cesium inside a Tshaped glass cell. The unpaired electrons on the alkali atoms are spin-polarized by a pump laser (high power diode laser) circularly polarized, pointing the electron spins along the direction of circular polarization. A perpendicular probe laser (single frequency diode laser) detects the orientation of the electron spins as they precess in a magnetic field. This laser is detuned from the alkali resonance and as it passes through the polarized vapor, the laser polarization angle is rotated due to the circular dichroism of the vapor. The degree of rotation is proportional to the degree to which spins are pointing along the probe beam 34 . Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 14 Mª Rosario Mayoral Blasco To obtain the magnetic field this probe beam is focused onto an array of photodiodes. Figure 9: Schematic of a SERF system 34 . As explained before, the SERFs are fundamentally limited by spin-exchange relaxation. Hence, if the spin-exchange collisions happen fast enough and in a sufficiently low magnetic field the spins do not have enough time to precess and decohere between collisions. To achieve these conditions, the oven heats the droplet of alkali in the cell (acquiring the required density), and the shield of the cell from external magnetic fields reduce the precession frequency. To conclude, the potential capability in sensitivity of this magnetic magnetometer is on the order of 10 -18 T regarding to the magnetic field. 5.- itrogen Vacancy (V) Magnetometry The nitrogen-vacancy (NV) color center in diamond has recently emerged as highly versatile optical emitters that exhibit room temperature spin properties. What sets it apart from other color centers is that it is magnetic (i.e., of nonzero spin) and that the luminescence is coupled to the spin state, such that the luminescence intensity can be modulated by magnetic fields 35 . Their remarkable properties include single photon emission, a spin-triplet ground state with long spin coherence time at room temperature, and spin dependent photoluminescence. These properties enable NV centers to locally Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 15 Mª Rosario Mayoral Blasco detect and measure magnetic fields acting as highly sensitive magnetic field sensors with nanoscale spatial precision 36 . The NV center is formed by removing two adjacent carbon atoms and replacing one of them with a nitrogen atom while leaving the other site vacant. The NV center has been shown to exist in three different electronic forms, the negatively charged NV − , the neutral NV 0 and the positively charged NV + . Of them, only the NV − is magnetooptically active. The electronic structure of the NV center involves six electrons. Three of them come from the dangling sp3 bonds of the carbon atoms surrounding the vacancy and other two from the lone pair of electrons located on the nitrogen. The sixth electron is captured from another site in the lattice often coming from other nitrogen impurities, making the overall charge state NV − . Figure 10: Scheme of a NV center. The dashed lines represent dangling bonds which all overlap in the vacancy. The carbon atoms each contribute one electron , the nitrogen atom contributes two electrons, and one more electron comes from other lattice defects to generate the negatively charged NV center 37 . A simple energy-level diagram of the NV center, is shown in Figure 11. There are various electronic levels in the NV center which includes a ground state |g> of symmetry 3 A2, an excited state |e> of symmetry 3 E, and a metastable singlet state |s> that involves two levels with symmetries 1 A1 and 1 E. As two out of six electrons are unpaired, the spin states of ground and first excited states are both triplet states (S=1) and are further split into three spin sublevels. Because the NV center is not spherically symmetric, the two m S = ±1 states are degenerate, and the m S =0 state is energetically lower. The ground state zero-field splitting (ZFS) energy is given by D=2.87 GHz whereas the energy difference between N VC C C Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 16 Mª Rosario Mayoral Blasco spin sublevels is D=1.42 GHz for the excited state. Thus, a transition from ms = 0 to ms= ±1 can be achieved by absorption of microwaves at around 2.87GHz.The spinlattice relaxation time, T1, gives the transition rate between m S =0 and m S = ±1 sublevels and is of a few milliseconds at room temperature. Finally, by applying magnetic fields the m S =±1 levels shifts in opposite directions (Figure 11, inset). Figure 11: Energy-level diagram of the NV − . |g>, |e>, and |s> denotes the electronic ground state, the electronic excited state, and the metastable singlet state respectively. Wiggly arrows indicate the radiative transition, whereas the black arrows indicate strong and weak nonradiative decay via the singlet state. The inset depict the three spin sublevels with m S = 0 and m S = ±1 at zero and nonzero magnetic field B. D is the zero-field splitting and 2γ B is the Zeeman splitting, where γ is the electron gyromagnetic ratio. By convention, the lower energy transition is associated with ms = −1 35 . The metastable singlet state |s> is mainly populated from |e, m S = ±1> owing to differing crossover rates (Figure 11), what implies a pivotal role in the magneto-optic behavior of the NV center. An electron in the |e, m S = ±1> state decay via the long-lived singlet state, whereas an electron in |e, m S =0> mostly decays via the fast radiative transition leading to an optical contrast between the m S =0 and m S = ±1 states of approximately 30%. Then, the optical emission is seen as fluorescence from the NV center, and a change in fluorescence gives information about the spin state. The promotion to either the ms = +1 or ms = -1 states can be detected by a decrease in fluorescence 38 . To obtain the magnetic field is used the EPR (electron paramagnetic resonance) by D= 2.87 GHz Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 17 Mª Rosario Mayoral Blasco slowly sweeping an auxiliary microwave field. As the microwave frequency is resonant with the EPR transition the fluorescence intensity is reduced due to the excitation from m S =0 to m S = ±1. This effect, called optically detected magnetic resonance (ODMR), provides a means to modulate the fluorescence intensity dependent on the magnetic interactions of the single electron spin. There are different mechanism by which the ODMR lines in the NV center can be split: the strain, the Zeeman-effect and the hyperfine coupling. Of them, the Zeeman-effect is used here by coupling a static B-field (nominally aligned along the NV axis) to the NV-dipole moment. As the NV dipole is magnetic it wants to align itself to the applied magnetic field. The three spin states, m S =+1, 0, -1 correspond to the dipole being oriented directly along, perpendicular to, and directly against, the NV axis. Consequently, the energy of the +1 spin state would increase and that of the -1 state would decrease in energy, while the zero state remains unchanged. This leads to a reduction in the frequency for the m S =0  -1 transition and in an increase in the frequency for the m S =0  +1 transition 37 . Thus, two resonances appear in the ODMR spectrum as a magnetic field is applied. The absorption at this two resonant microwave frequencies yields information about the degree of Zeeman splitting and hence magnetic field. The separation between this two resonance frequencies is given by 2γ Bz, where γ =2π ×2.8 GHz/T is the electron gyromagnetic ratio and Bz is the magnetic field parallel to the NV axis. As a result, measurements of the ODMR frequency immediately yield the absolute value of the magnetic field 35 . One aspect of diamond impurities is that they are highly stable, even if the host crystal is only a few nanometers in size. This small size provides numerous opportunities to employ them as local probes to monitor external perturbations, such as magnetic fields, with high sensitivity and spatial resolution. Then, the basic idea is to embed an NV center at the apex of a very sharp tip (<10-nm tip radius) into a scanning device and to scan this tip over the structure of interest. By mapping the position-dependent Zeeman shift of a single defect center, the magnetic field of a magnetic nanostructure is obtained. This Zeeman shift is typically measured by selectively exciting the transition |0 〉  |-1 〉 of the triplet spin ground state with a microwave pulse and reading out population of the | 0〉 spin state optically 39 . Thus, an optical image of the magnetic field of a magnetic nanostructure is obtained by measuring the NV center fluorescence while scanning the tip over the surface. This technique has shown excellent sensitivity to nanotesla changes in magnetic field as well as nanometer spatial resolution in ambient Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 18 Mª Rosario Mayoral Blasco conditions and is theoretically expected 38 that with a further develop it should achieved a field resolution of 10 -18 T. Figure 12: Basic principle of scanning magnetometry. A sharp tip with a NV center at the apex is used to map out the three-dimensional magnetic field vector above a magnetic nanostructure, such as an isolated electronic spin 40 . To sum up this section, the table 1 shows a comparative of the minimum detectable magnetic moment of the MPMS (SQUID system), the VSM and the MFM. As the SERFs and NV magnetometry are recent techniques to measure the magnetic properties, the studies developed till today have been based into the measurement of the magnetic field. This is the reason why their sensitivities are compared here regarding to the magnetic field sensitivity of the MPMS instead of the magnetic moment. Table 1: Comparative sensitivities between the different magnetic measurement techniques. MPMS 1E-10 1E-18 VSM 1E -9 ----------- MFM 1E-18 ----------- SERF ---------------- 1E-18 NV magnetometry ----------------- 1E -9 Magnetic moment sensitivity (Am2) Magnetic field sensitivity (T) Magnetic measurement technique Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 19 Mª Rosario Mayoral Blasco THE TESTED PROTOTYPE 1.- Basics The main macroscopic behavior of diamagnetic materials is that they are repelled by magnetic fields. This property has been used in this master thesis to obtain a stable and free diamagnetic levitation system, in order to measure ferromagnetic thin films and to characterize its sensibility to nanometric ferromagnetic structures. To levitate diamagnetic materials the first step is to set up a geometry that can support the object against gravity and at the same time ensure the stability. To achieve it there are two basic approaches: passive or active. The term active is used for systems using a feedback control loop, in opposition to systems levitating passively which do not require any control and do not need any energy. In this project, passive levitation has been chosen due to the simplicity of these systems. Within the passive levitation there are three basic configurations allowing stable free levitation of permanent magnets 41 as is shown in figure 13. Figure 13: Basic configurations used to achieve passive levitation of a permanent magnet M2 42 . Looking to the levitation configuration on the left of the figure 13, to stabilize the equilibrium state of the small magnet M2 a diamagnetic material has been placed closely below it. This exercises an upward force of repulsion upon M2 which increases if M2 comes closer to the diamagnetic material. Maintaining M1 and the diamagnetic body without changes on their position, any slighting lowering of M2 from the equilibrium state results in an increase in the repulsion exercised by the diamagnetic body and a decrease of the attraction force between the two magnets M1 and M2. The Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 26 Mª Rosario Mayoral Blasco To achieve the desired current a third voltage VO, supplied by a microprocessor, is also involved on the system. Figure 19: Shematic of the current generator. Then, to get the variable current the first step is to fix the voltage VM to a value of 1.25V (Volts) by means of the stable reference REF03 and a potentiometer. The second step has been to construct the circuit in such a way that the voltage VP be equal to the difference between the reference voltage 2.5 V given by the REF03 and the voltage VO deal by the microprocessor multiplied by the gain of the instrumentation amplifier. This gain can be calculated by the next formula 45 : Gain = 100 KΩ (8) RG therefore, choosing RG equal to 100 KΩ the gain is 1 and the value of VP follows the equation: VP = Gain (2.5 V – VO) = (2.5 V – VO) (9) As the variable voltage VO is given by the microprocessor, the current (i) flowing in the coil is related to the different elements of the circuit by the next equations: Assuming VO= 0 V: VM = 1.25 V (fixed) VP= (2.5 V – VO) = (2.5 V – 0 V) = 2.5 V VO VM VP 11.18 Magnetic measurements of nanometric means of a new sensor based on diamagnetic levitation. Mª Rosario Mayoral Blasco By consequence, the maximum i = 2.5 V – 11.18 Ω where the resistor of 11.18 Now, a ssuming VO= 2.5 V VM = 1.25 V (fixed) VP= (2.5 V – VO) = (2.5 V Thus, the maximum current able to flow i = 0 V – 1.25 V 11.18 Ω Thereby , by the different values of VO inside t microprocessor a variable current generating the different fields needed. 2.4.2.- The H all sensor control The Hall sensor ( explained in the section 2.3 exposed the ma gnet 1, the magnet 2, the pyroly transforms these measurements correspondent to the different positions of the second levitated magnet respect to its equilibrium. Basically, when there is the maximum of field it gives the maximum voltage whereas at the minimum field is on the contrary. Figure 20: Schematic of the Hall sensor control. Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 27 Mª Rosario Mayoral Blasco maximum current that flows in the coil is defined by 1.25 V = 111 mA (positive current) 11.18 Ω Ω is one chosen as shunt. ssuming VO= 2.5 V : (2.5 V – 2.5 V) = 0 V maximum current able to flow in the coil is: 1.25 V = - 111 mA (negative current) 11.18 Ω , by the different values of VO inside t he range (2.5 V, - 2.5 V) give current in the range (-111 mA, 111mA) will flow in fields needed. all sensor control explained in the section 2.3 ) detects the variations in field at which are gnet 1, the magnet 2, the pyroly tic graphite and the magnetic sample these measurements into a voltage (the H all voltage VH) different positions of the second levitated magnet respect to its equilibrium. Basically, when there is the maximum of field it gives the maximum voltage whereas at the minimum field is on the contrary. Schematic of the Hall sensor control. defined by : (10) (11) 2.5 V) give n by the will flow in the coil the variations in field at which are tic graphite and the magnetic sample . It all voltage VH) that is different positions of the second levitated magnet respect to its equilibrium. Basically, when there is the maximum of field it gives the maximum Magnetic measurements of nanometric means of a new sensor based on diamagnetic levitation. Mª Rosario Mayoral Blasco As can be seen in the figure proportional voltage that is inside the range of voltages that the microprocessor can register. Then, the microprocessor analyze the Y axis that will be shown on the screen of program chosen as interface a zero value at the minimum and the maximum voltage at the maximum the middle point is achieved dividing these two values between two. magnetic propert ies of the sample sensor. 2.4.3.- The microprocessor It is well known that the microprocessor is the chip that controls all the traffic of whatever electronic application Figure 21: The microprocessor. 2.5.- The micrometric gears Two micrometric gears have been used the M1-pyrolytic graphitethe wafer. Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 28 Mª Rosario Mayoral Blasco figure 20, the Hall sensor control adapts these variations proportional voltage that is inside the range of voltages that the microprocessor can register. Then, the microprocessor analyze them and gives the correspondent value to that will be shown on the screen of a computer by means of the M interface . As the operation of the system has been chosen a zero value at the minimum and the maximum voltage at the maximum the middle point is achieved dividing these two values between two. This will help ies of the sample by looking at the variation measurements of the The microprocessor the microprocessor is the chip that controls all the traffic of electronic application , being the nucleus of every complex circuit. It has been used here to give the variable VO needed to obtain the desirable c flowing through the coil. Furthermore reads also the voltages VM, VP and VH making the correspondent logic operations so as to obtain the values of the current flowing in the coil in order to show them into the X axis of t he screen of the M program. The micrometric gears have been used . One of them, to change the distance between M2; the other, to control the distance among these variations to a proportional voltage that is inside the range of voltages that the microprocessor can correspondent value to a computer by means of the M atlab the system has been chosen as to have a zero value at the minimum and the maximum voltage at the maximum the middle This will help to estimate the by looking at the variation measurements of the the microprocessor is the chip that controls all the traffic of circuit. give the variable obtain the desirable c urrent flowing through the coil. Furthermore , it reads also the voltages VM, VP and VH making the correspondent logic operations values of the current the coil in order to show them he screen of the M atlab to change the distance between the distance among magnet 2 and Magnetic measurements of nanometric means of a new sensor based on diamagnetic levitation. Mª Rosario Mayoral Blasco In the f irst case the aim is to achieve second, to do possible that the magnetic fields of the sample and the levitating magnet can interact between themselves. 3.-The program The program used as interface to analyze Figure 22: Matlab program. Values to choose. As shows in the figure 22 through the coil by writing it in the value box corresponding to (<10 mA), being 10 milliamp ( gives the rate in seconds (s Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 29 Mª Rosario Mayoral Blasco irst case the aim is to achieve the best stable diamagnetic levitation. In the second, to do possible that the magnetic fields of the sample and the levitating magnet can interact between themselves. used as interface to analyze the measurements is Matlab. Matlab program. Values to choose. 22 it is possible to choose the range of current that will flow through the coil by writing it in the value box corresponding to Max. Current, Imax milliamp ( mA) the maximum in absolute value. The in seconds (s ) at which the current changes between the maximum and the best stable diamagnetic levitation. In the second, to do possible that the magnetic fields of the sample and the levitating magnet it is possible to choose the range of current that will flow Max. Current, Imax The Period, T (s) at which the current changes between the maximum and Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 30 Mª Rosario Mayoral Blasco minimum value during the process and the Sampling,  are the number of points (N) displayed into the screen in each complete cycle. The boxes Current, I (mA), Hall Voltage, Vh (V) and Elapsed Time, t (s) shows respectively during the measurement the values of the current flowing by the coil, the Hall voltage correspondent to these current and the time elapsed from the beginning of the measure. In the figure 23 is displayed the graph that appears on the screen after the realization of a measurement. On it, the Y axis exhibits the value of the Hall voltage (in Volts) and the X axis the value of the current (in milliamp) flowing in the coil. The system has been connected so that the current at which the levitated magnet falls onto the sample is higher than the current at which the magnet returns to its equilibrium position. Figure 23: The Matlab program screen shows the fall of the magnet onto the wafer and its recover to equilibrium position. As the force necessary to recover the equilibrium position of the magnet is higher than the one needed to make it to fall, the current value correspondent to the return to equilibrium position has been chosen to get the final measure. This last is achieved by making the difference between the measure obtained having only the wafer and the one with the sample in order to avoid the magnetic contribution of the substrate. Magnet falls onto the wafer Magnet returns to levitated equilibrium position M2 wafer M2 wafer M2 wafer Magnetic measurements of nanometric means of a new sensor based on diamagnetic levitation. Mª Rosario Mayoral Blasco 4.-The wafer (samples) Finally, to un derstand the results obtain used to do th e measurements. In the figure 24 is depicted a picture sample. Figure 24: Mask used for the deposition of the magnetic nanometric structures. of 100 mm. As can be seen it comprise different widths. Their values as follows: 1.- Ten squares of 100 µm x 100 µm. 2.- From left to right, squares of side: 50 µm, 100 µm, 15 0 3.- Ten squares of 500 µm x 500 µm. 4.- Five squares of 200 µm x 200 µm. Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 31 Mª Rosario Mayoral Blasco (samples) derstand the results obtain ed, is impor tant to know how are the s e measurements. is depicted a picture of the lithography mask used to fabricate the deposition of the magnetic nanometric structures. The circle has a diameter As can be seen it comprise s a variation of shapes (square and lines) which have values regarding to width and length in micrometers ( of 100 µm x 100 µm. squares of side: 0 µm, 200 µm, 400 µm, 600 µm, 800 µm and of 500 µm x 500 µm. of 200 µm x 200 µm. tant to know how are the s tructure lithography mask used to fabricate the wafer The circle has a diameter of shapes (square and lines) which have also in micrometers ( µm) goes 1000 µm. Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 32 Mª Rosario Mayoral Blasco 5.- A line of 400 µm width x 42000 µm length. 6.- Ten lines of 10000 µm length and a width varying from left to right between 10 µm to 100 µm with an increase of 10 µm each one. 7.- Twenty lines of 10000 µm length and a width varying from left to right between 10 µm to 100 µm with an increase of 10 µm every two. That is to say, they are equal in width every two. 8.- Ten lines of 10000 µm length and a width varying from left to right between 100 µm to 1000 µm with an increase of 100 µm each one. To achieve the above structures, it has been necessary to use a process of optical lithography known as lift-off because of the nanometric thickness of the samples. The way to obtain them is shown in the next figure. Figure 25: Lift-off process with positive photoresist. In this lift-off process the first step has been to spin coat the positive photoresist (PR) onto a 4-inch wafer substrate. Next, this PR has been irradiated by U.V. rays through a mask (1) changing the structure of the PR: the bonds between molecules are broken 2) DEVELOP 4) ACETONE IMMERSION FINAL RESULT 1)IRRADIATION POSITIVE PHOTORESIST SUBSTRATE 3) GROW OF THE SAMPLE SAMPLE MASK U.V. RAYS SAMPLES SUBSTRATE Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 33 Mª Rosario Mayoral Blasco when exposed, whereas the rest maintained polymerized. By wet chemical develop (2) only the PR in exposed areas is dissolved 46 , creating the pattern of the geometry wanted. Then, the ferromagnetic material used for the measurements has been grown onto this pattern (3) by means of an e-beam evaporator. Finally, by immersion of the wafer into acetone (4) the parts with positive PR have been eliminated giving place to the structure of the ferromagnetic nanometric samples desired. As is well known, the resist used for lift-off processes is usually negative in order to achieve the best profile of the pattern. In the case of the structures that have been produced here, as they have a micrometric size and very small thickness, it is possible to use a positive resist without problem. To get the results of this master project three different 4-inch wafers have been processed. One of them with a substrate of double side polished silicon (100) and the other two with a substrate of glass. Regarding to the thickness of the nanometric structures, onto the silicon wafer it has been deposited 10 nm (nanometer) of iron (Fe) covered by 10 nm of gold (Au), whereas the two glass wafers have been structured with 20 nm of Fe being covered one of them with 10 nm of Au and the other by 20 nm of Al. This last change of Al instead of Au so as the increase of 10 nm in the quantity of the covering material deposited has been done because of problems of oxidation observed on the first glass wafer. With regard to the measurements made in this master thesis, by the presence of the magnetic field of the sample in the vecinity of the levitated magnet its position is altered. This convey a correspondent variation on the magnetic field measured by the equipment that gives the possibility to quantify the magnetic properties of the sample by means of a correct calibration of the device. To conclude, the sensing principle comprises the use of a magnetic material (sample) situated next to the levitated magnet in such a way that the magnetic fields of the sample and the levitated magnet could interact between them. Then, by the comparison between the position of this magnet in absence of sample and in the presence of it, is possible to derivate the magnetic moment of the sample by means of a correct calibration. Magnetic measurements of nanometric means of a new sensor based on diamagnetic levitation. Mª Rosario Mayoral Blasco MEASUREMETS To position the samples under the made : four of them for the different square samples and the last samples. This is necessary because the structures are difficult to see by eye. In all of them, it has been drawn line of 400 µm width x 42000 µm length and the horizontal line correspondent to the position of the squares of 500 µm of side. The next figures show the process to example, in the case of the 500  The first step is to c template for the 500 µm side squares Figure 26: Template for the 500 µm side squares just to show the center point which has been used to calculate the distance to the location of the 500 side squares. Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 34 Mª Rosario Mayoral Blasco the samples under the levitated magnet, five different templates : four of them for the different square samples and the last one This is necessary because the structures are difficult to see by eye. has been drawn the vertical line correspondent to the 400 µm width x 42000 µm length and the horizontal line correspondent to the position of the squares of 500 µm of side. the process to position the sample in the correct location. example, in the case of the 500 µm side squares: step is to c hoose the appropriate template. In this example, the template for the 500 µm side squares . Template for the 500 µm side squares with location lines. The horizontal line in the middle is which has been used to calculate the distance to the location of the 500 templates have been one for the line This is necessary because the structures are difficult to see by eye. the vertical line correspondent to the location of the 400 µm width x 42000 µm length and the horizontal line correspondent to the the sample in the correct location. For In this example, the The horizontal line in the middle is which has been used to calculate the distance to the location of the 500 µm Magnetic measurements of nanometric means of a new sensor based on diamagnetic levitation. Mª Rosario Mayoral Blasco  The second step is to vertical line of of correspondent to the position of the squares of 500 µm of side Figure 27: Position of the wafer  Finally, the sample lines drawn on th e basic template used to locate Figure 28: Centering of the template with the wafer regarding to the position of the magnet M2. Vertical location of 400 µm width x 42000 µm length line L400 Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 35 Mª Rosario Mayoral Blasco step is to place the wafer in the accurate position by means of the 400 µm width x 42000 µm length and the horizontal line correspondent to the position of the squares of 500 µm of side . on the template. the sample is positioned under the magnet by means of the centering e basic template used to locate the magnet M2. Centering of the template with the wafer regarding to the position of the magnet M2. Vertical location of the ten 500 µm side squares Horizontal location of 500 µm side squares 108 97654321 in the accurate position by means of the 400 µm width x 42000 µm length and the horizontal line under the magnet by means of the centering Centering of the template with the wafer regarding to the position of the magnet M2. Vertical location of the ten 500 side squares Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 42 Mª Rosario Mayoral Blasco The measurements have been made doing two complete cycles to see the reproducibility. As can be seen, the low side squares have a big deviation in the data what means that the system is not able to measure them correctly. Also the behavior at high sides deviated from the one expected (see figure 36). This shows that from a determined side value of the squares the magnetic moment detected is saturated, giving an upper limit of the size structures capable to be measured depending on the magnet employed. Figure 36: Expected behavior of the squares regarding its side. Therefore, the measure of the 400 µm can be considered as the lower limit capable to be measured, giving a value of 3.46 x 10 -9 Am 2 for the magnetic moment. 3.2M2: spherical, diameter 3 mm The magnet used here has been a spherical one with a diameter of 3 mm. Due to its spherical shape, it has an effect of rotation when it is over the sample. This rotation affects to the sensor Hall detection doing impossible to obtain any useful data, as can be seen in the next figures that show the behavior under the effect of the substrate without a sample and with the sample of the maximum area (1000x1000 µm 2 ). 0 10 20 30 40 50 60 70 80 90 0,E+00 2,E+02 4,E+02 6,E+02 8,E+02 1,E+03 Current (a.u.) Side of the squares (micrometers) Expected behavior of the squares regarding its side Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 43 Mª Rosario Mayoral Blasco Figure 36: Measurement of the substrate without sample and the spherical magnet of 3 mm diameter. Figure 37: Measurement of the square of 1000 µm side with the spherical magnet of 3 mm diameter. 3.3M2: cubic, side 1 mm It has been observed that this magnet rotates during its levitation state doing that sometimes it falls onto the wafer in a non-parallel side position over the square samples. 3,04 3,06 3,08 3,1 3,12 3,14 3,16 3,18 -50 -40 -30 -20 -10 0 10 20 30 40 50 Positioning by the Hall voltage V H (V) Current (mA) Measurement of the substrate without sample Spherical M2 magnet : 3 mm diameter Wafer glass: 20 nm Fe, 20 nm Al 3,04 3,06 3,08 3,1 3,12 3,14 3,16 3,18 -50 -40 -30 -20 -10 0 10 20 30 40 50 Position giving by the Hall voltage V H (V) Current (mA) Measurement of the square of 1000 µm side Spherical M2 magnet : 3 mm diameter Wafer glass: 20 nm Fe, 20 nm Al Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 44 Mª Rosario Mayoral Blasco As a consequence, it can´t interact with all square surface of the bigger samples. However, this is not a problem for the small ones. Then, to analyze the data in the figure 38 it is necessary to have in mind the position of the magnet over the wafer. On this sense, the square of 1000 µm side has a large error because the magnet recovers its original levitated position the first cycle (where the magnet falls in a non-parallel position) and don´t do the second cycle (the magnet stay over the sample in the correct position). Regarding to the squares of 800, 600 and 400 µm the magnet is over the sample in a perfect parallel location. The samples of 200, 150, 100 and 50 µm are enough small to avoid this problem. On behalf of the results achieved, the graphic shows that this magnet is able to detect the square of 200 µm side, whereas the negative data of the 50 µm square side is due to the noise of the system. With all this it is possible to conclude that the lower limit is given by the square of 200 µm side, obtaining a value of the magnetic moment by means of the calibration constant of 8 x 10 -10 Am 2 . Figure 38: Current versus side of squares with the cubic magnet of 1 mm side. -5 5 15 25 35 45 55 65 0,0E+00 2,0E+02 4,0E+02 6,0E+02 8,0E+02 1,0E+03 1,2E+03 Current (mA) Side of the squares (micrometers) Current versus side of the squares Cubic M2 magnet : 1mm side Wafer glass: 20 nm Fe, 20 nm Al Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 45 Mª Rosario Mayoral Blasco 3.4M2: cubic, side 2.5 mm This magnet exhibits a behavior regarding to the data obtained similar to the spherical magnet. Furthermore, it has the rotation effect explained in the section 3.3. The next graphic depict this. Figure 39: Behavior of the cubic magnet of side 2,5 mm. 3.5M2: cubic, side 3 mm As this magnet shows the same characteristics as the one explained before a new magnet has been probed. 3.6M2: cylindrical, diameter 1 mm, thickness 1 mm This cylindrical magnet has no problems with the rotation because the axis of rotation is an axis of symmetry of the magnet. Therefore, it has been chosen to compare with the previous results. However, it has been not possible to achieve a position on which the hysteresis loop used to obtain the current at which the system recovers the magnet is null for the non-sample state as displays the figure 40. 3,08 3,09 3,1 3,11 3,12 3,13 3,14 3,15 3,16 3,17 3,18 3,19 -50 -40 -30 -20 -10 0 10 20 30 40 50 Positioning giving by the Hall voltage V H (V) Current (mA) Measurement of the samples Cubic M2 magnet : 2,5 mm side Wafer glass: 20 nm Fe, 20 nm Al Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 46 Mª Rosario Mayoral Blasco Figure 40: Hysteresis loop of the non-sample state measure by the cylindrical magnet of 1mm diameter, 1mm thickness. COCLUSIOS A new magnetic sensor based on a levitated magnet has been successfully tested. It has been proved to be useful in the characterization of magnetic thin film structures with nanometric thickness. The measurements done with the cylindrical magnet of 1.5 mm diameter and 1 mm thickness exhibit a good behavior respect to the linearity of the samples as well as a doubling on the values due to the double deposition regarding to the thickness of material. Respect to the best magnet to be used, is clear that the cubic of 1 mm side gives the best resolution even when its rotation in the levitated state that does it sometimes to fall over the sample in a tilted position makes it unable to be used correctly with samples bigger than 400 µm side. On behalf of magnets of bigger size, they produce unexpected behavior on the Hall sensor because of its rotation over the sample (as the spherical 3 mm diameter one) or by its rotation in the levitated state (the cubic 2.5 and 3 mm sides ones). 2,535 2,54 2,545 2,55 2,555 2,56 2,565 2,57 2,575 2,58 2,585 2,59 0 0,5 1 1,5 2 2,5 3 3,5 4 Position giving by the Hall voltage V H (V) Current (mA) Measurement of the substrate without sample Magnet recover its levitated position fisrt cycle Magnet falls onto the wafer Magnet recover its levitated position second cycle Cylindrical M2 magnet : 1 mm diameter, 1 mm thickness Wafer glass: 20 nm Fe, 20 nm Al Magnetic measurements of nanometric thin films by means of a new sensor based on diamagnetic levitation. 47 Mª Rosario Mayoral Blasco Regarding to this, cylindrical magnets don´t have the effect of perturbation due to the rotation in the levitated state nor the effect of the tilt over the sample. But the relationship between their diameter and thickness need to be controlled in order to achieve a non-hysteresis loop when measuring the non-sample position. There is also, depending of the size and shape of the magnet used, a moment when a saturation step is reach. This shows an upper limit to have in mind for the structure and quantity of ferromagnetic material of the samples to be measured. About the prototype itself, it suffers from a problem due to the positioning of the samples under the magnet which now is a manually and delicate operation. It is important to say that smaller the magnet is, bigger the necessity is of an accurate positioning due to the smaller surface covered by it. Then, this is a big handicap to solve to achieve a system easy to be use. Finally, it has been prove in this master project that the lower limit of detection achieved by the system is of 8 x 10 -10 Am 2 at room temperature. 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