Uncovering the magnetic properties of the AgxNiy (x + y = 55) nanoalloys in the whole composition range

Uncovering the magnetic properties of the AgxNiy(x+y= 55) nanoalloys in the whole composition range R. H. Aguilera-del-Toro,1, 2 P.G Alvarado-Leyva,3and A. Vega2 1Instituto de F´ısica, Universidad Aut´onoma de San Luis Potos´ı, San Luis Potos´ı, M´exico 2Departamento de F´ısica Te´orica, At´omica y ´ Optica, Universidad de Valladolid, Spain 3Facultad de Ciencias, Universidad Aut´onoma de San Luis Potos´ı, San Luis Potos´ı, M´exico (Dated: October 4, 2018) 1 Abstract Nickel and silver are metals with interesting properties of technological relevance: nickel is a well known ferromagnet and silver has antibacterial properties. Both exist in the face centered cubic phase but are immiscible. In the context of alloys at the nanoscale, one can play with the size to fine tune a desired property, or to achieve new properties and functionalities that do not exist at the macroscopic regime. In this work, we explore how the subtle interaction between Ni and Ag triggers the chemical order, the electronic structure, and the magnetic properties of a AgNi nanoalloy of 55 atoms, a size that can accommodate core/shell configurations with sizable parts. Calculations are conducted within the density functional theory at the generalized gradient approximation for exchange and correlation. We determine, in the whole composition range, the chemical order, absolute and relative stabilities by means of binding energy, excess energy and second energy difference, as well as total and part-projected spin-polarized electronic densities of states and local charge and spin magnetic moments distribution. Ni-core/Ag-shell structures are particularly stable, but contrary to what one would expect by simply extrapolating the properties of the pure Ag and Ni clusters or of pure fcc bulks, we find unexpected behaviors along the composition range, such as quenched magnetic moments in Ni, total magnetic moments essentially contributed in some cases by Ag, or electronic charge transfer that changes its sign depending on the stoichiometry. These behaviors lead to magnetic transitions as a function of the composition, and differ, in some cases, from those of the smaller 13-atoms AgNi nanoalloys of the same symmetry with which we compare, a further demonstration of the complex nature of nanostructures. The above trends are robust against ionization and electron capture. PACS numbers: 75.75+a; 36.40Cg; 75.30.Pd; 75.50.-y Keywords: nanoalloys, nanomagnetism, density functional theory, electronic structure 2 I. INTRODUCTION One of the most interesting and long-standing research field in Materials Science is the design and characterization of alloys, and the seek of new routes to improve their properties in order to make them more efficient for specific purposes. Taking advantage of the cooperative effects of the constituent elements, one can envisage a large variety of applications depending on the composition and stoichiometry. Perhaps the most well known example is the combination of Fe and Cr to create stainless steel, whose properties can even be improved by the addition of other elements. At present, we have already collected a large amount of thermodynamic data, such as binary and ternary phase diagrams, chemical compositions and crystalline structures1and we understand the physical and chemical properties of many alloys2. In the macroscopic regime, one can play with the constituent elements, stoichiometry and growth conditions in order to create alloys with specific properties. For example, Mpourmpakis et al. studied Fe-Co in bulk regime3and they found that alloys with Co concentration of 30% were those having the highest magnetic moment. However, the physical and chemical properties of a material can be drastically modified at the nanoscale, as a consequence of quantum-confinement effects, and this is why nanoparticle research has become such a fascinating branch of Material Science. Therefore, in the context of alloys at the nanoscale, one can also play with the size as a new degree of freedom to fine tune a desired property, or to achieve new properties and functionalities that do not exist at the macroscopic regime. The often unexpected and difficult to rationalize behavior of nanoalloys poses a great challenge, but at the same time is a breeding ground for surprising discoveries and innovative technological applications4,5. An intense effort has been devoted in the last years to investigate different kinds of nanoalloys, but the collected data is still scarce in comparison with what we have for macroscopic alloys. It is well known now that the most stable stoichiometries and chemical orders of nanoalloys do not correspond, in general, with those of their macroscopic counterparts. The relative position of the different atoms in a nanoalloy of a given composition leads to a large number of homotops that correspond to different chemical orders. Therefore, from a theoretical point of view, the determination of the lowenergy isomers is a challenging task6. In the case of magnetic nanoparticles, the low-energy spin states (spin isomers) have to be also characterized. In some cases, structure, chemical 3 order and spin configuration are competitive from the energetic point of view. Bimetallic nanoparticles, made up of atoms of two different chemical species, are the simplest kind of nanoalloys. At the macroscopic level, Ni and Ag are known to be inmiscible for all compositions1. Annealing studies of Ni/Ag films also show clustering of Ni atoms to form Ni nanoparticles embedded in a Ag matrix, a similar trend as that observed in chemically similar CoAg films7. Ni belongs to the ferromagnetic elements of the 3d series, and pure Ni nanoparticles have been extensively studied due to their magnetic properties which make them good candidates for their use in high density magnetic recording devices8,9 . The unavoidable oxidation in environmental conditions, however, reduces in general their magnetic moment due to the appearance of antiparallel magnetic couplings10–15. Ag nanoparticles have been shown to exhibit antibacterial properties16–18. The Ag-Ni system has been synthesized by several methods, such as laser-liquid-solid interaction technique19, by laser induced plasma20 and borohydride reduction method21. Synthesis methods have been also developed for tecnological applications such as sensors22, and for enhancement of photo catalytic activity23. Through Raman diffusion at low frequency, Portales et al. found core-shell structures for NiAg nanoparticles24, in which Ni atoms form the core and Ag the shell, with a weak bonding between the Ni and Ag atoms. The segregation is driven by the lower surface energy of Ag and the large size mismatch (the Ni atomic radii is 1.25˚ A, and that of Ag 1.45˚ A). This segregation was also observed by Gaudry et al. in Ni0.5Ag0.5nanoparticles25. Recent simulations26,27 further showed the tendency of NiAg nanosystems to form core-shell structures. In those studies, global optimizations with a empirical Gupta potential, were performed for NiAg clusters with 34 and 38 atoms for all possible compositions. For fixed size and variable composition, perfect core-shell structures turned out to be the most stable chemical orders, in qualitative agreement with the experimental findings. Calvo et al.28 have demonstrated through Montecarlo simulations, that the core/shell configuration is stable up to 810K. The empirical approach with the Gupta potential, relies on structural parameters, so that electronic effects that could drive the stabilization of certain structures or homotops, or that could be essential for certain properties, are not taken into account, in contrast to a DFT approach. Although systems with a large number of atoms can be investigated with low computational cost, the description of the energy landscape provided by the empirical approach is less accurate than that provided by a DFT approach, although a good sampling 4 can be achieved. The icosahedral Ag-Ni nanoalloy of 13 atoms was studied by Harb and co-workers29 using density functional theory. In a similar work, Harb et al30 studied the smaller nanoalloys AgnNipwith n+p≤6. They found that Ni atoms are brought together maximizing the number of Ni-Ni bonds, and that the Ag atoms are located around a Ni subcluster maximizing the number of Ag-Ni bonds. They found a very important contribution of the d-electrons of silver atoms located at surface in the optical response of the system. Those small 13-atoms nanoalloys, however, can not accommodate a core/shell structure with a core of more than one atom. All the above studies point to the possibility of designing magnetic NiAg nanoalloys in which the magnetic moment of Ni could be protected in environmental conditions (against oxidation for instance), or other environments like those existing in the human body. At the same time, the Ag content should provide a functionalization of such nanoparticles with antibacterial properties, which would broaden their range of applications. The aim of the present work is to characterize, in the framework of the density functional theory, the chemical order, electronic structure, and related properties like structural parameters, thermodynamical stability, relative stoichiometric stability and magnetism, of AgxNiy icosahedral nanoalloys of 55 atoms, in which core/shell structures with sizable Ni subclusters can be achieved along the composition range. Pure Ag55 and Ni55, that are the limits of compositions, have been shown to stabilize in the icosahedral ground state31–33, contrary to what happens in the smaller nanoalloy of 13 atoms for which Pereiro and co-workers found the icosahedron as the global minimum energy34, whereas Fern´andez et al, found a BBP-like structure35.The size of this 55-atoms nanoalloy is, on the other hand, closer to what can be experimentally attained. For simplicity, we assume the Mackay icosahedral structure along the full composition range. Although icosahedral structures are more plausible in the 55-atoms nanoalloy than in the 13-atoms one, we note that due to the large Ag and Ni size mismatch and resulting stress, poli-icosahedral structures, irregular or antimackay icosahedral structures could appear at intermediate sizes instead of Mackay ones. These facts have been already shown for NiAg nanoalloys, mostly for larger ones where quiral shells can be also formed26,36–38. We have considered all possible homotops, as well as the different spin isomers, so that metastable chemical orders and spin excitations are also characterized. We complement our investigation with the study of the effects of an electron deficit or excess, 5 which is important upon ionization or electron capture. The paper is organized as follows. In Sec. II, we describe the theoretical and computational approach. In section III are discussed the stability, chemical order, structural parameters and electronic structure; section IV is devoted to the magnetic properties. The conclusions are summarized in the last section. II. THEORETICAL APPROACH AND COMPUTATIONAL DETAILS We performed fully self-consistent DFT calculations using the SIESTA code39, an efficient DFT implementation that solves the spin-polarized Kohn-Sham equations within the pseudopotential approach to treat the core interactions, and employs numerical pseudoatomic orbitals in the basis set. For the exchange and correlation potential we used the PerdewBurke-Ernzerhof form of the generalized gradient approximation (GGA).40 We employed norm-conserving scalar relativistic pseudopotentials41 in their fully nonlocal form42, generated from the atomic valence configuration 3d84s2for Ni (with core radii 2.00, 2.44 and 2.50 a.u. for s,pand dorbitals, respectively), and 4d105s1for Ag (with core radii 2.17, 2.82 and 2.40 a.u. for s,pand dorbitals, respectively) Non-linear partial core corrections43, which are known to be important for transition metal pseudopotentials, are included at the core radius of 0.7 ˚ A. Valence states were described using double-ζbasis sets for Ni and Ag, with maximum cutoff radii of 4.931 ˚ A (2p) and 7.998 ˚ A (3d, 4s), respectively. A 4ppolarization orbital was also considered for Ni, with cutoff radius 7.998 ˚ A6.599 ˚ Afor nickel an silver respectively. The energy cutoff used to define the real-space grid for numerical calculations involving the electron density was 250 Ry. The Fermi distribution function that enters in the calculation of the density matrix was smoothed with an electronic temperature of 15 meV. We used an energy criterium of 10−4eV for converging the electronic density. In the calculations, the individual clusters were placed in a cubic supercell of 20×20×20 ˚ A3, a size large enough to neglect the interaction between the cluster and its replicas in neighboring cells. It was considered only the Γ point (k= 0) when integrating over the Brillouin zone, as usual for finite systems. The equilibrium geometries resulted from an unconstrained conjugate-gradient structural relaxation using the DFT forces. Icosahedral structures are considered. We relaxed each homotop and spin state until interatomic forces were smaller than 0.001 eV/˚ A. In all cases, 6 different spin isomers were checked in order to ensure the correct ground state. The strategy for sampling the chemical orders was as follows. First of all, we took advantage of the symmetries to define those inequivalent positions of the Ni and Ag atoms for each composition; this reduces the number of homotops to calculate. Then, by selecting pertinent minimal sets of homotops, we determined general trends that allowed us to exclude certain kind of chemical orders and several of their corresponding homotops. In particular, we determined the preference of Ni atoms to occupy central sites, as well as to form Ni subclusters within the system. As a first step, we calculated the AgNi nanoalloy of 13 atoms with icosahedral structure for two purposes. One was to benchmark our theoretical approach against previous results for the same system in the Ag rich phase by Harb and co-workers29 using the Gaussian code with GGA-PB86 and LANL2DZ relativistic effective core potential. In the supplementary information (SI) we provide several low-energy homotops. The second purpose of this calculation was to have a reference to compare with the 13-atoms core of the larger 55-atoms nanoalloy with compositions up to 13 Ni atoms, in order to assess the role played by the interaction with the remaining 42 Ag atoms at the shell. This will be discussed in the following sections. Our ground states (see the SI) are the same as theirs, except for Ag10Ni3, for which our predicted ground state corresponds to their first isomer (nearly degenerated with the ground state). We complete the study of the AgNi nanoalloy of 13 atoms to cover all the composition range, not reported so far. For selected compositions or homotops for which we found different states very close in energy, or untypical magnetic arrangements, additional calculations were performed using the VASP code44,45 with the same GGA functional as that employed in SIESTA. VASP solves the Khon-Sham equations using a plane-waves basis set instead of numerical pseudoatomic orbitals, and the core interactions are treated be means of the projector-augmented wave (PAW) approach instead of pseudopotentials. This approach is consistent with the exact all-electron potential and provides a more accurate description of the core interactions. However, VASP is more demanding than SIESTA from the computational point of view. In all cases tested, VASP and SIESTA yielded similar results. A comparison of the magnetic moment obtained from both approaches in three of those selected compositions of the 13-atoms nanoalloy can be found in the SI. The local electronic charge and magnetic moments distribution within the nanoalloys were determined from the Mulliken population (see the SI), although in those same cases where additional 7 VASP calculations were conducted, we performed this analysis using Bader’s method46,47 which divides the nanoalloy into atomic volumes by locating the zero-flux surfaces of the electron density field. III. CHEMICAL ORDER, STABILITY AND ELECTRONIC PROPERTIES The ground state configurations of AgxNiy(x+y= 55) nanoalloys are shown in Fig.1. In the SI, the reader can find several low-energy homotops for each composition, corresponding to metastable chemical orders. Regarding the inter-atomic distances of the nanoalloys, we find that Ni-Ni bonds are shorter than Ag-Ni bonds, and these are shorter than Ag-Ag ones. The average inter-atomic distances remain almost constant as a function of stoichiometry (2.75 ˚ A for Ag-Ag, 2.65 ˚ A for Ag-Ni, and 2.46 ˚ A for Ni-Ni). An electron excess or deficit does not modify the chemical order, since the corresponding ground state homotops are the same as in the neutral nanoalloy. The chemical order pattern is clear. Ni atoms tend to occupy the internal positions, building up a Ni subcluster. This is consistent the lower atomic volume and the larger cohesive energy of Ni as compared to Ag. The lower average interatomic distances in Ni55 than in Ag55 creates a size mismatch when the nanoalloy is formed, causing a steric effect that tends to favor segregation of the bigger atomic species (Ag) to the surface positions. The larger cohesive energy of Ni as compared to Ag favor segregation of Ni to the interior positions so that a larger number of the more cohesive Ni-Ni bonds can be generated. Therefore, segregation always occurs, and a core/shell structure tends to be formed, in agreement with the experimental findings24,25 and calculations of smaller AgNi nanoalloys26,27,29,30 and larger ones36–38.When the number of Ni atoms is lower than 14, all them occupy the most internal positions. Ag42Ni13 is a perfect core/shell cluster, and the next Ni atom in Ag41Ni14 starts occupying the outer shell of the 55-atoms icosahedral structure in positions as close as possible to the already formed Ni13 core. The chemical order pattern is, thus, the one that maximizes the number of Ni-Ni bonds with a Ni subcluster surrounded by Ag atoms. The robustness of this chemical order pattern is demonstrated by the fact that for all 55-atoms nanoalloys with less that 14 Ni atoms, except Ag52Ni3and Ag48Ni7, their 13-atoms core has the same chemical order (corresponds to the same homotop) as the ground state of the 13 atoms nanoalloy of the corresponding stoichiometry. This also points to the fact that the outer 42 Ag atoms may provide protection to the core. We will 8 come to this point later. Another result showing the robustness of the described chemical order pattern is that the Ag12Ni43 homotop with the 12 Ag atom at the 12 vertices of the shell results 1.8 eV less stable than the putative ground state (both fully relaxed). The high cohesive energy of Ni favors the Ni-Ni bonds, as discussed above. On the other hand, this result could be seen, in some sense, as a manifestation of the tendency to off-center cores as increasing the core size37 We calculated the second energy difference (∆2E) to determine the relative stabilities of the different stoichiometries with respect to their neighboring ones. This magnitude is defined as follows: ∆2E(x, y)0/±=E(x+ 1, y −1)0/±+E(x−1, y + 1)0/±−2×E(x, y)0/± In order to compare the nanoalloy with an ideal mixture of the pure clusters, we evaluated the excess energy (Eexc)48 Eexc(x, y) = E(x, y)−xE(Agx+y) x+y−yE(Nix+y) x+y where E(Agx+y) and E(Nix+y) are the energies of the pure clusters in their ground states. A negative excess energy indicates that formation of the corresponding nanoalloy is energetically favorable as compared to an ideal mixture. The ideal mixture would follow a simple Vegard law, according to which the total energy of the nanoalloys follows a linear behavior connecting the energies of the pure clusters. Fig.2 collects the data of ∆2Eand Eexc for the different stoichiometries. The excess energy (Fig.2 upper panel) shows that, although all the nanoalloys are stable, according to their binding energy (given in the SI), only the formation of few of them, corresponding to certain stoichiometries with less than 14 Ni atoms, is favourable with respect to an ideal mixing of Ag55 and Ni55, reflecting the strong tendency to segregation, instead of to maximize the number of Ni-Ag bonds. In all those stoichiometries, the Ni subcluster is completely covered by Ag. Eexc exhibits marked minima for Ag54Ni, Ag48Ni7, Ag42Ni13, Ag26Ni29, Ag23Ni32. The first one, Ag54Ni, corresponds to the smallest perfect core/shell configuration with the Ni atom in the center of the 55-atoms icosahedron. 9 FIG. 1: (Color online) Ground state geometries of [AgxNiy] clusters with x+y= 55. The numbers below the structures are the binding energy per atom (in eV) and the total spin magnetic moment (in µB), respectively. 16 Ag54Ni Ag52Ni3 Ag50Ni5 Ag48Ni7 Ag46Ni9 Ag44Ni11 Ag42Ni13 Ag40Ni15 Ag38Ni17 Ag36Ni19 Ag34Ni21 Ag32Ni23 Ag30Ni25 Ag28Ni27 Ag26Ni29 Ag24Ni31 Ag22Ni33 Ag20Ni35 Ag18Ni37 Ag16Ni39 Ag14Ni41 Ag12Ni43 Ag10Ni45 Ag8Ni47 Ag6Ni49 Ag4Ni51 Ag3Ni53 Ni55 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 Excess energy (eV) Ag55 Ag53Ni2 Ag51Ni4 Ag49Ni6 Ag47Ni8 Ag45Ni10 Ag43Ni12 Ag41Ni14 Ag39Ni16 Ag37Ni18 Ag35Ni20 Ag33Ni22 Ag31Ni24 Ag29Ni26 Ag27Ni28 Ag25Ni30 Ag23Ni32 Ag21Ni34 Ag19Ni36 Ag17Ni38 Ag15Ni40 Ag13Ni42 Ag11Ni44 Ag9Ni46 Ag7Ni48 Ag5Ni50 Ag3Ni52 AgNi54 -0.2 0.0 0.2 0.4 0.6 2nd difference (eV) AgxNiy AgxNiy + AgxNiy - Ag48Ni7 Ag42Ni13 Ag26Ni29 Ag23Ni32 Ag54Ni FIG. 2: (Color online) Excess energy (upper panel) and second energy difference (lower panel) of [AgxNiy] clusters with x+y= 55. The local minima of excess energy are highlighted. 17 Ag55 Ag53Ni2 Ag51Ni4 Ag49Ni6 Ag47Ni8 Ag45Ni10 Ag43Ni12 Ag41Ni14 Ag39Ni16 Ag37Ni18 Ag35Ni20 Ag33Ni22 Ag31Ni24 Ag29Ni26 Ag27Ni28 Ag25Ni30 Ag23Ni32 Ag21Ni34 Ag19Ni36 Ag17Ni38 Ag15Ni40 Ag13Ni42 Ag11Ni44 Ag9Ni46 Ag7Ni48 Ag5Ni50 Ag3Ni52 AgNi54 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 Magnetic Moments (µΒ) AgxNiy AgxNiy + AgxNiy - FIG. 3: (Color online) Total spin magnetic moment of the [(AgxNiy)0/±] clusters with x+y= 55 as a function of the composition. 18 FIG. 4: (Color online) Local electronic charge transfer and magnetic moment of Ag54Ni cluster. For charge transfer, numbers in black (red) indicate gain (loss) of charge; for the magnetic moment, numbers in black (red) indicate spin up (down). Contributions of the inner 13 atoms and the outer 42 are separated for the sake of clarity. 19 Ag12Ni Ag11Ni2 Ag10Ni3 Ag9Ni4 Ag8Ni5 Ag7Ni6 Ag6Ni7 Ag5Ni8 Ag4Ni9 Ag3Ni10 Ag2Ni11 AgNi12 Ni13 0 1 2 3 4 5 6 7 8 Magnetic Moment (µΒ) ICO13 ICO55 CORE ICO55 SHELL ICO55 FIG. 5: (Color online) Total magnetic moment of the 55-atoms AgNi nanoalloys for compositions of Ni content up to Ag42Ni13 (black circles). Total magnetic moment of the 13-atoms AgNi nanoalloys in the whole composition range (open circles). Contribution of the 42 outer atoms (up green triangles) and of the 13 inner ones (down blue triangles) of the 55-atoms AgNi nanoalloys to their total moment. 20 FIG. 6: (Color online) Local electronic charge transfer and magnetic moment of Ag50Ni5cluster. For charge transfer, numbers in black (red) indicate gain (loss) of charge; for the magnetic moment, numbers in black (red) indicate spin up (down). Contributions of the inner 13 atoms and the outer 42 are separated for the sake of clarity. 21 FIG. 7: (Color online) Local electronic charge transfer and magnetic moment of Ag42Ni13 cluster. For charge transfer, numbers in black (red) indicate gain (loss) of charge; for the magnetic moment, numbers in black (red) indicate spin up (down). Contributions of the inner 13 atoms and the outer 42 are separated for the sake of clarity. 22 Acknowledgments This work was supported by the Spanish Ministry of Economy and Competitiveness (Project FIS2014-59279-P) in conjunction with the European Regional Development Fund (FEDER). P.G.A.L acknowledges to CONACyT for financial support through ”Proyecto Apoyado por el Fondo Sectorial de Investigacion para la Educaci´on” with reference number 237882. R.H.A-T acknowledges the fellowships from CONACyT (Mexico, scholarship 415121) and UVa (Universidad de Valladolid). V. CONCLUSIONS We investigated, using the density functional theory within the GGA approximation of Perdew-Burke-Ernzerhof, the energetic stability, chemical order, electronic structure, and magnetic properties, of AgxNiynanoalloys of 55 atoms with icosahedral shape. We also studied the effects of an electron deficit or excess. Ni atoms tend to occupy the internal positions, building up a Ni subcluster, and developing segregated atomic configurations among which core/shell structures are particularly stable, in qualitative agreement with the experimental findings and calculations of smaller AgNi nanoalloys. Although binding energies demonstrate that these nanoalloys are thermodynamically stable independently of the composition, the excess energy indicates that only the formation of Ag54Ni, Ag48Ni7and Ag42Ni13 is favourable with respect to an ideal mixing of Ag55 and Ni55. Among those, Ag54Ni and Ag42Ni13 are perfect core/shell configurations. Ag26Ni29 and Ag23Ni32 also exhibit marked minima of the excess energy. Those five stoichiometries also correspond to maxima of the second energy difference, so that they can be considered as magic compositions of the nanoalloy. The magnetic phase diagram of these nanoalloys is complex. Contrary to what one would expect, the total moment of the nanoalloy in the high Ag concentration limit tends to decrease as increasing Ni concentration up to Ag50Ni5, due to the quenching of the Ni moment associated to the charge transfer from the outer 42 Ag atoms to the inner 13 ones. Beyond this Ni concentration, the total moment linearly increases as increasing Ni content up to Ag18Ni37, where a sudden drop of 9µBtakes place, to continue the linear increase with the same slope till the pure Ni limit. This linear increase is associated to the formation of a 23 sizable Ni subcluster with non quenched spin polarization and parallel magnetic couplings, being the contribution of the outer Ag atoms to the total moment of the nanoalloy negligible now. Therefore, the formation of a sizable Ni subcluster allows it to preserve its magnetic identity to a large extent when covered or interfaced by Ag, providing the nanoparticle with a magnetic moment localized in the core. The projected densities of states show that the HOMO rapidly acquires Ni character as increasing the Ni content. The clear Ni character of the HOMO for most stoichiometries indicates that, although the Ag-Ni interaction is weak and Ag provides a physical protection to the Ni core, Ni states should play an important role in the reactivity of these nanoalloys, as they indeed do in processes like ionization. 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