Ab initio study of FeRh multilayers supported on MgO(0 0 1)

Journal of Magnetism and Magnetic Materials 502 (2020) 166488

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Research articles

Ab initio study of FeRh multilayers supported on MgO(0 0 1) a

b

M. Julia Jiménez , Alejandro Butera , Gabriela F. Cabeza

a,⁎

T

a Grupo de Materiales y Sistemas Catalíticos, Instituto de Física del Sur (IFISUR), Departamento de Física, Universidad Nacional del Sur (UNS), CONICET, Av. Alem 1253, Bahía Blanca B8000CPB, Argentina b Centro Atómico Bariloche and Instituto Balseiro, Comisión Nacional de Energía Atómica (CNEA), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Universidad Nacional de Cuyo (UNCUYO), Av. Bustillo 9500, 8400 Bariloche, Río Negro, Argentina

A R T I C LE I N FO

A B S T R A C T

Keywords: FeRh film MgO(0 0 1) Magnetism DFT

Low dimensional films are materials of interest for the changes of the structural, electronic and magnetic properties they undergo, especially when they form interfaces with a substrate. The iron-rhodium (FeRh) alloy is an excellent example. Experimentally, FeRh films are deposited on single crystal substrates like MgO, sapphire or silicon. Particularly, MgO (0 0 1) is an excellent support for FeRh because it is possible to deposit high quality epitaxial films on it. MgO is also highly stable at high temperatures and tensile in-plane strain favors the FM over the AFM state. In order to improve the knowledge of the supported bimetallic systems properties, theoretical calculations using density functional theory (DFT) have been carried out. The different thicknesses considered for the multilayers are 0.6 nm, 0.9 nm and 1.2 nm for both, terminated in Fe or Rh. To complete the study, we present the results obtained on the influence of the termination of the surfaces, the number of alloy layers, the different magnetic configurations (FM – AFM), the charge transfer and the adhesion of the films to the MgO substrate. The analysis of the results shows that as the thickness of the film grows, the adhesion energy tends to an average value of the order of 1.5 J/m2; on the other hand, the AFM coupling facilitates the takeoff compared to the FM coupling. Moreover, comparing the difference between FM and AFM results for different thicknesses, the percentages are slightly lower for. –Rh terminated films. Regarding the out-of-plane relaxation percentages, they depend on the thickness of the film and the magnetic coupling. For the AFM coupling of films -Rh terminated, lower values are observed compared to those obtained for the FM coupling and this behavior is maintained for all three thicknesses studied. However, for the -Fe terminated films as the film grows the relaxations are practically twice those corresponding to the cases of films terminated in Rh tending to tetragonal structures. With respect to magnetic properties, in the three presented systems for -Rh terminated multilayers, the tendency of magnetic moments values for the FM coupling is maintained in around 3.2 μB/at for the case of Fe and 1.0 μB/at for the case of Rh. For AFM the most noticeable difference is the cancellation of the magnetic moments of Rh. However, the situation is different for the Fe atoms in the -Fe terminated multilayers. For 0.9 nm the Fe atoms in contact with the substrate undergo the least relaxation and their magnetic moments are parallel and equal to −1 μB/at. The Fe atoms of the other layers recovered their values of ± 3 μB/at. But when the film grows the Rh atoms acquire a small magnetization in increasing order as it approaches to the free surface. The presence of residual ferromagnetism in the interfaces of the FeRh films deposited on MgO (0 0 1) has also been observed experimentally by other groups. In summary, we can conclude that the obtained results are mostly influenced by the surface termination. (-Rh or -Fe).

1. Introduction The well-known equiatomic FeRh alloy with crystal structure B2 CsCl-type presents interesting magnetic properties due to its first-order ⁎

phase transition [1] from an antiferromagnetic (AFM) at low temperatures to a ferromagnetic (FM) phase as the temperature is increased to around 350 K [2–5]. This transition is accompanied by an isotropic increase in volume around 1–2%, a reduction in resistivity [6] and a

Corresponding author. E-mail address: [email protected] (G.F. Cabeza).

https://doi.org/10.1016/j.jmmm.2020.166488 Received 22 August 2019; Received in revised form 23 November 2019; Accepted 20 January 2020 Available online 23 January 2020 0304-8853/ © 2020 Elsevier B.V. All rights reserved.

Journal of Magnetism and Magnetic Materials 502 (2020) 166488

M.J. Jiménez, et al.

on BaTiO3(0 0 1) decrease the AFM-FM transition temperature of FeRh down to 270 K due to the compressive lattice strain. Pressaco et al. [26] modeled the FeRh(1 0 0) surface using DFT-LDA to obtain a microscopic description of the structure experimentally studied by the group. The results obtained for films with AFM configurations reveal that the magnetic moments of the Rh atoms always tend to zero independently of the initial values imposed. This is explained by the magnetic frustration induced by hybridization with Fe atoms that have opposite magnetic moments at equidistant positions. Similar conclusions have also been reported by Sandratskii [10] and by Kudrnovsky [27] in bulk by calculations of first principles. However, in the models of slabs with mixed magnetic configurations, the Rh atoms of the surface layers still preserve a finite magnetic moment with values of 1 μB and 0.6 μB. The presence of residual ferromagnetism in the interfaces of the FeRh films deposited on MgO(0 0 1) has also been observed by Fan et al. [28] in experimental tests at 80 K; this metastable phenomenon is observed in AFM thin films with thickness < 10 nm in the stressed regions of the film due to the substrate. The metal/oxide interface plays a key role in the durability of thin films deposited on substrates. Is of primary importance in many technologically applications because the yield and reliability of microelectronic devices containing multi-layer thin film structures are strongly influenced by the adhesion since it directly depends on interatomic and intermolecular forces. One of the main factors that controls film durability is the adhesion between the substrate and its surface coating [29]. Adhesion is generally a fundamental requirement of most deposited film–substrate systems and often depends on how the system is to be used. For best adhesion, the film material should chemically bond to the substrate surface [30]. For the FeRh epitaxially grown onto MgO, various authors, such as Barton et al. [17] and Ceballos [19] show that the strain affects the nucleation of the first order meta-magnetic phase transition but they don't study adhesion properties. This point is of great interest to the manufacturers because the films grow on a substrate and it could be easily separated if the adhesion is not important. In order to improve the knowledge of the bimetallic systems, theoretical calculations have been carried out. Among the main objectives proposed in this work we can mention the study of the adhesion of the films to the substrate. Another point of interest is to study how the tensions of the films affect their magnetic properties. To complete the study, we will present the results obtained on the influence of the termination of the surfaces (terminated in Fe or Rh), the number of alloy layers (5, 7 or 9 ML) and the different magnetic configurations in the properties of ultra-thin FeRh films deposited on MgO.

large change in entropy [4]. With respect to the AFM structure, several authors [3,7–10] consider that the most stable is Type II-G with spins ordered according to planes (1 1 1), with local values of magnetic moments of approximately ± 3 μB for Fe atoms (3 μB for the FM phase) and 0 μB for Rh atoms (1 μB for the FM phase) [11].The possibility of controlling the phase transition opens a way for the development of functional devices with technological applications such as heat-assisted magnetic recording (HAMR) [12], magnetic refrigeration [13], magnetic storage devices or resistive memories [14,15]. In recent years, the development of the spintronic of antiferromagnetic materials is presented as an emerging field with the purpose of replacing the active ferromagnetic components of the devices in spintronics by antiferromagnets [16]. Martí et al. [14] demonstrated that the reading and writing process in an antiferromagnetic state for FeRh is possible, expanding the availability of materials for storage devices with properties different from the known ferromagnets. However, later studies reported that during the phase transition there is a distortion of the cubic to tetragonal [5,15], orthorhombic network [7] or monoclinic [8], giving rise to a relative stability of different magnetic configurations with c/a values ranging from 1 (cubic) to 1.27. On the other hand, the high cost of rhodium, make it technologically unviable in bulk form and traditional scaling arguments imply that very thin layers will need to be employed [17], so in recent years their properties have been studied in the form of thin films deposited on different substrates such as MgO, sapphire, W, Si [2,17,18], KTaO3(KTO), SrTiO3 (STO) [19], PMN-PT [20] or heterostructures onto glass substrates [21]. In the literature there are different studies of FeRh films onto different substrates. Among these substrates MgO(0 0 1) is an excellent support for the growth of high-quality epitaxial FeRh thin films and it is also highly stable at high temperatures [6]. This is interesting because for technological applications it is important to control their properties to thicknesses below 10 nm [17], where the interfaces participate actively. Barton et al [17] showed that the magnetic properties of ultra-thin FeRh films grown on MgO(0 0 1) are highly dependent on the thickness of the film (the transition temperature increases when the thickness of the film decreases); on the termination of the surfaces, especially in thin films of the order of 5–8 monolayers, and the stress suffered due to the film-substrate lattice mismatch. Nevertheless, Han et al. [22] demonstrated that as the thickness of the sample decreases, so does the transition temperature. Other experimental studies [23] demonstrated that stressed thin films undergo a reorientation of the spins in the metamagnetic AFM-FM phase transition which has been confirmed by their own theoretical results. This transition is accompanied by a tetragonal distortion of the lattice due to the substrate (increase of the c/a ratio), leading to different magnetocrystalline anisotropies (MCA), with energy differences between states with magnetization directions out of plane and in plane [18]. It is worth mentioning that differences in the results obtained for the MCA are for films grown on substrates obtained by different techniques. Similar results were reported by Ceballos et al. [19] who studied the effects of the stress and the thickness of the films supported on different substrates on the AFM-FM transition temperature. They reported that in the FM state, when the films are stressed, the spin configurations are in plane, while when the surfaces are compressed, they are out of plane. A contrary effect is observed in the AFM films in accordance to the results reported by Bordel [23]. Contrarily, Zheng et al. [24] using DFT calculations investigated the effect of the stresses due to epitaxial growth of the ultrathin heterostructure FeRhAFM/MgO, reporting that under compression, the system presents large magneto crystalline anisotropy and that the easy axis of magnetization is in plane. When the film is stressed, an easy axis of magnetization is induced from the in plane to the out of the plane direction. Suzuki et al. [25] demonstrated that Ga-substituted FeRh thin films

2. Computational details and systems modeling Spin polarized total energy calculations were performed using Density Functional Theory (DFT) within the Generalized Gradient Approximation for the exchange and correlation energy due to PBE [31] as implemented in VASP (Viena Ab-Initio Simulation Package) [32–34]. This functional has been shown to provide a reasonable description of the structural properties [24]. The plane wave basis was generated considering 8 valence electrons for Fe (3d74s1), 9 valence electrons for Rh (4d85s1), 2 valence electrons for Mg (3 s2) and 6 valence electrons for O (2s22p4). In the standard mode, VASP performs a fully relativistic calculation for the core-electrons and treats valence electrons in a scalar relativistic approximation. The kinetic energy cut-off for the plane wave expansion of the electronic wave function was 500 eV. The energy convergence criterion used was 0.1 meV. The ultrathin FeRh film on MgO(0 0 1) has been modeled by a (2 × 2 × 1) supercell as is shown in Fig. 1. The slab consists of five, seven or nine monolayers (ML) of FeRh containing in each ML two nonequivalent atoms per atomic species (Fe or Rh) and per unit cell 2

Journal of Magnetism and Magnetic Materials 502 (2020) 166488

M.J. Jiménez, et al.

Fig. 1. Scheme of construction of the supercell used to represent the epitaxial growth of the 5 ML of FeRh, for example, Fe-terminated (a) and Rh-terminated (b) supported on 3 ML of MgO. The superposition of FeRh monolayers grown on the substrate is indicated. Color online: Rh atoms are in gray, Fe atoms in gold (spin up), O atoms in red and Mg atoms in white. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

reported of 0.299 nm, for all calculations. A similar procedure was used to study the Fe(0 0 1)/MgO(0 0 1) epitaxy [38]. The in-plane FeRh lattice is initially fixed with the aMgO parameter. The initial out-of-plane lattice parameter is obtained as the height of the substrate plus that of the FeRh slab plus the vacuum. The thickness of the substrate corresponds to the value of cMgO. For the alloy, an initial value of the FeRh bulk parameter divided by 2 between layers was considered. This value is multiplied by the number of ML considered in the slab. For FeRh/ MgO interface separation we consider that the first metal layer is located as if it followed the packing of the MgO (~0.22 nm); finally, the vacuum was added to that value. In each interface configuration (-Rh and –Fe terminated), two magnetic structures (FM and AFM) have been also taken into account. With respect to the antiferromagnetic system, it has been experimentally observed that in the AFM structure the Fe moments have FM coupling in (1 1 1) planes and AFM coupling between the planes [39,40]. From this information and own results, we proceeded to assemble the different FeRh monolayers deposited over MgO following the stacking of the FeRh bulk alloy (type B2) with a magnetic configuration of up and down spins aligned according to the {1 1 1} family of planes. Previous DFT studies showed that both Fe and Rh atoms on top of O atoms of the MgO surface are stable and the interface with Fe-O bonding is the most energetically favorable [41].

located alternately, which are placed on top of the MgO slab of three ML (Fig. 1). Both terminations (–Fe (a) or –Rh (b)) have been considered. A vacuum region no less than 1.4 nm has been introduced to avoid interactions between the slab and its image created by the periodic boundary conditions. Other authors consider no less than 1.2 nm thick [24] and 1.5 nm thick [35]. The Brillouin zone (BZ) integration was performed on well-converged Monkhorst-Pack [36] k-point meshes of (3 × 3 × 1) for the FM and AFM bulk phases. The magnesium oxide bulk has a NaCl (B1) crystal structure with an equal number of atoms of Mg and O alternating according to a simple cubic structure and crystallizes with lattice parameter of a = 0.4211 nm [37] (a = 0.4216 nm [19]). Based on this structure the MgO (0 0 1) surface is modeled using a slab of 3 ML and the cell parameters (aMgO, cMgO) obtained after optimization are 0.4133 nm and 0.4303 nm. In order to obtain an epitaxial growth of the Fe-Rh multilayers over the substrate, we consider the alloy surface whose cell parameter is best fitted to reduce the interface tensions. In particular the FeRh(1 1 0) is equivalent to rotating 45° the cell of the alloy with respect to the MgO substrate being √2.aFeRh-bulk = aMgO (Fig. 2). This ratio would give us a close aFeRh-bulk value than the experimentally

3. Results and discussion To facilitate the analysis, the results together with the discussion of them are presented in subsections according to the properties and in particular whether the surface is terminated in Rh or in Fe. The physical properties of a material are strongly dependent on the atomic distribution and relaxation at surfaces and interfaces. The results obtained are detailed in the next section. 3.1. Structural and magnetic properties The cell parameters obtained from the optimization of the twelve configurations studied considering the FM and AFM couplings are summarized in Table 1. In the process of relaxation, two layers of the bottom of the substrate were left fixed. The MgO surface layer together with the different layers of the substrate film, were allowed to relax completely (relaxation along the x-axis, y-axis and z-axis). The changes in the position of the atoms in the coordinates of the plane (x, y) depend on the systems and do not exceed ± 2%. The corresponding strain percentages for the twelve systems are presented in Supplementary material (Table A1). Only changes in the coordinate perpendicular to

aMgO: 0.413 nm Fig. 2. Top view of the tetragonal structure of FeRh rotated 45° with respect to the MgO(0 0 1) substrate. Example of the Fe-terminated FeRh/MgO heterostructure where the O atoms (in red) are placed on top of the Fe atoms (in gold). Color online: Rh atoms are in gray, Fe atoms in gold and Mg atoms in white. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) 3

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the surface (z) are analyzed in detail. In Table 2 the corresponding optimized structures are shown. To be able to compare with data from the literature we calculate the values of the parameters of the FeRh bulk unit cell identified as a′, b′ and c′. According to what it is explained in Section 2, a′ = b′ = a/√2. To estimate a value of the c parameter that would have the bulk cell of the alloy (c′), we divide the thickness of the FeRh film by the number of unit cells. The results are shown in Table 1. In general terms, after the optimization, the cell parameters are increased in percentages that go from 1.2, 1.3 and 1.6% (-Rh terminated) and 0.4, 0.6 and 1.0% (-Fe terminated) when the thickness of the film grows from 5 to 9 ML and the magnetic coupling is FM. The thickness of the film tends to a slight reduction of the order of hundredths of nm in the case of films -Rh terminated and undergoes an increase of about 0.02 nm in the case of films -Fe terminated. In the case of AFM coupling, the trend is different if both terminations -Rh or -Fe are considered. When the films finish in Rh the cell parameters increase with percentages of 0.5, 0.7 and 0.7% as the thickness of the film grows from 5 ML to 9 ML. But when the films end in Fe the cell parameters are contracted. It deserves special attention the cell of 7 ML whose parameter suffers the greatest contraction of all the evaluated systems (−1.98%). Regarding the c′/a′ relation it is observed that in the case of the films -Rh terminated the value close to 1 indicates a cubic structure

Table 1 Lattice parameters calculated for the different ML of FeRh deposited on MgO. Both terminations (–Rh or –Fe) are considered for both magnetic couplings (FM and AFM). The optimized values of a, b and c (includes the vacuum, film and substrate) correspond to those of the supercell of the film. The values of the parameters of the FeRh unit cell identified as a′, b′ and c′ were obtained as indicated in the text. ML thickness

5 ~ 0.6 nm

7 ~ 0.9 nm

9 ~ 1.2 nm

Cell parameters (nm)

a=b c a′ = b′ c′/a′ a=b c a′ = b′ c′/a′ a=b c a′ = b′ c′/a′

FM

AFM

-Rh

-Fe

-Rh

-Fe

0.418 2.507 0.296 1.00 0.419 2.810 0.296 1.01 0.420 3.316 0.297 1.01

0.415 2.527 0.293 1.05 0.416 2.833 0.294 1.04 0.417 3.331 0.295 1.03

0.415 2.505 0.294 1.01 0.416 2.808 0.294 1.02 0.416 3.320 0.294 1.02

0.412 2.529 0.291 1.05 0.405 2.881 0.286 1.12 0.409 3.416 0.289 1.13

Table 2 Structures obtained after optimization for the different configurations studied whose parameters are summarized in Table 1. Below each configuration the calculated value of the total energy per atom is presented. Color online: Rh atoms are in gray, Fe atoms in gold, O atoms in red and Mg atoms in white. Fe atoms with spin down are in blue. The figures are aligned according to MgO(0 0 1) axes and the FeRh multilayers are rotated 45° according to Fig. 2 (see text).

4

Journal of Magnetism and Magnetic Materials 502 (2020) 166488

M.J. Jiménez, et al.

5.0

substrate

3.5

FeRh/MgO - Rh terminated

vacuum mm per layer ( B/at)

й reůadžaƟŽn

3.0 2.0 1.0

vacuum

2.5 2.0 1.5 1.0 0.5 0.0

0.0 Rh

Fe +/-

Rh Fe +/Rh 5 ML - FM 7 ML - FM

Fe +/Rh 9 ML - FM

Fe +/-

Rh 5 ML - FM

Rh

(a) substrate

FeRh/MgO - Rh terminated

thicknesses. The most noticeable difference with respect to the FM coupling is that the net magnetic moment of the Rh atoms is zero (Fig. 4) while those of the Fe acquire values close to those they had in the FM phase. Initially a value of 1 μB for the mm of the Rh atoms was assigned, however after optimization the magnetic moments go to zero. In particular, for the cases of films of 0.6 nm and 0.9 nm, half of the Rh atoms have spin up and the other half spin down of the order of hundredths averaging equally to zero. The magnetic moment values of the Fe atoms are around +/−3.1μB for the three systems. However, if we consider the net magnetic moment per layer, also the Fe layer gives zero. Our results are in agreement with the values obtained for the magnetic moments of the same system reported by Bordel [23]. Another point of interest is to study how the tensions of the films affect their magnetic properties. To facilitate the analysis in Fig. A1 and Fig. A2 (Supplementary material), the relaxation is plotted together with the magnetic moments for FM and AFM coupling. There is not much more to add to what has already been commented. Only that the percentages of relaxation between layers are relatively low so the relationship c′/a′ tends to one. With respect to the films terminated in Fe, the percentage of relaxation with respect to the original separation of layers as well as their corresponding values of the magnetic moments of the atoms (Fe, Rh) of each layer are plotted for a better visualization in Fig. 5, Fig. 6 and Fig. A2 (Supplementary material). In the three presented systems of 5, 7 and 9 ML the tendency of values of magnetic moments for the FM coupling is around 3.2 μB for the case of Fe and around 1.0 μB for the case of Rh, similar to the Rhterminated films with a slight decrease in the case of the Rh atoms of the last layer unlike the Rh-terminated systems. Regarding the relaxation, the first layer of Fe that is in contact with the substrate tends to separate but in a lower percentage than in the case of Rh. When the thickness of the film is ultrathin (0.6 nm) the layers tend to separate. As the film grows (0.9 nm) the relaxations are practically twice larger than those corresponding to the cases of films terminated in Rh. In particular, Rh layers away from the substrate are the ones that relax most. A similar trend is observed for the 1.2 nm film, unlike the first layer of Rh which has the lowest percentage of relaxation (0.2%) slightly approaching that of the Fe layer. We now turn to the results corresponding to AFM coupling. Undoubtedly the highest relaxation percentages are observed in Feterminated films. In particular, in the 7-layer system the Fe atoms in contact with the substrate undergo the least relaxation and their magnetic moments are parallel and equal to −1 μB. From the third layer there is a marked growth to reach 5% relaxation (Fig. 5b). The results obtained allow us to affirm that there is a tendency for greater relaxation in the case of –Fe terminated films for both magnetic couplings. In the interface, the trend already noted in the previously analyzed systems with significant relaxation and decrease in the second layer is observed.

2.0 1.0 0.0 Fe +/Rh Fe +/Rh 5 ML - AFM 7 ML - AFM

Fe +/Rh 9 ML - AFM

Rh Fe +/Rh Fe +/Rh 7 ML - AFM 9 ML - FM 9 ML - AFM

vacuum

3.0

Rh

Fe +/Rh Fe +/5 ML - AFM 7 ML - FM

Fig. 4. Calculated magnetic moments (mm) per layer in μB/at for AFM and FM couplings of the films terminated in Rh.

4.0 й reůadžaƟŽn

FeRh/MgO - Rh terminated

3.0

4.0

5.0

substrate

Fe +/-

Rh

(b) Fig. 3. Calculated relaxations (%) of the interatomic planes in the direction perpendicular to the surface for FM (a) and AFM (b) couplings of the films terminated in Rh.

(type B2 ClCs) independent of the thickness of the film or the magnetic configuration. In contrast, the -Fe terminated films tend to have a centered tetragonal structure (bct), which is accentuated in AFM cases. Similar first-principles calculations for FeRh/MgO surfaces are presented in [35], where tetragonal distortions of the lattice are observed due to the presence of the substrate and the magnetic order is strongly depend on the FeRh/vacuum or FeRh/MgO interface termination. Experimental results are a′ = 0.2984 nm and c′ = 0.3021 nm for films of ~100 nm, respectively [18,19]. Let us first comment the results corresponding to the relaxation/ contraction percentages for both couplings (FM-AFM) of the films terminated in Rh presented in Fig. 3. The percent relaxation values were calculated considering the difference between the final positions of the atoms after the optimization, with respect to the original positions that were the same for all the evaluated systems, based on the initial positions. We will start with the analysis of the results for the FM configurations (Fig. 3a). With regard to relaxation, the first Rh layer that is in contact with the substrate tends to separate more in the three cases studied a tendency that diminishes when approaching the surface except for the last layer of Fe that increases its relaxation with respect to the previous layers (~1.3%) coincident with a slight decrease in the magnetic moment (Fig. 4) of about 0.2 μB. In particular is observed for the 0.9 nm and 1.2 nm films the almost zero relaxation of the first layer of Fe increasing its corresponding moment to 3.22 μB (Fig. 4). With respect to magnetic properties, in the three presented systems of Rh/Fe alternating layers, the tendency of magnetic moments values is maintained at around 3.2 μB for the case of Fe and 1.0 μB for the case of Rh (Fig. 4) with a slight increase in the case of the Rh atoms of the last layer (1.13 μB, 1.11 μB and 1.14 μB for 5, 7 and 9 ML respectively). With regard to the relaxation percentage for the AFM coupling (Fig. 3) the values are slightly lower compared to those obtained for the FM particularly for the layer in contact with the substrate (Rh) and the last layer of Fe (subsurface); this behavior is maintained for all three 5

Journal of Magnetism and Magnetic Materials 502 (2020) 166488

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FeRh/MgO - Fe terminated 5.0

[17] observed experimentally that the transition to the AFM phase is incomplete, indicating the presence of an FM signal below the transition temperature. This can be interpreted as coming from the mismatch of the crystal lattices in the direction normal to the plane of the interface FeRh/MgO(0 0 1) that can change the magnetic order in the regions close to the deformation. Experimental data from Han and coworkers [22] indicate residual ferromagnetism in ultrathin films deposited on Si, where the antiferromagnetic phase becomes more unstable as the film becomes thinner. They indicate that the FM phase could be stabilized by a magnetic field when the thickness of the film is less than 10 nm. Due to the effect of the structural relaxation from bulk positions, the surface planes undergo a sizeable displacement, confirming that the surface properties in FeRh can be expected to resemble from the bulk, as has been recently published by our group [42]. It is for this reason that from the results obtained from the relaxed films, an attempt was made to obtain a value of the unit cell parameters of the alloy itself, in order to relate it with the observations of other authors presented in the introduction, referring to c/a relationship. In this sense in the Table 1 it can be seen that the ć/á ratio is greater for AFM systems indicating a tetragonal bct structure. A stability of the tetragonal cell with respect to the cubic one was also obtained for the AFM phase in the FeRh bulk alloy [42] [and the references mentioned therein]. This suggests that this distortion observed in the bulk is also feasible in films and the strain-induced martensitic transformation. This asymmetry could be an example of a distortion of Jahn-Teller, as previously mentioned by other authors [15,43], phenomenon interpreted as a deformation of the lattice by anisotropic electronic clouds of the d electrons, both of the Fe atoms (3d) and of the Rh atoms (4d). According to the aforementioned analyzes, it is clear that structural relaxations are strongly linked to magnetic behavior. To verify it, we plot the % relaxation obtained for the same systems but without considering the spin polarization (NSP). The corresponding curves are shown in Fig. A3 (Supplementary material). It is interesting to highlight the influence on the consideration of spin polarization. For both films terminations (-Rh, -Fe) relaxation percentages of practically almost twice those obtained previously are observed. In particular, the changes in the case of –Rh terminated films are more noticeable, where these percentages triple those obtained for FM and AFM couplings. In order to find explanations for this behavior, both the charge transfers and the density of states curves (DOS) were analyzed. The results are presented in Section 3.3.

vacuum

substrate

й reladžaƟŽn

4.0 3.0 2.0 1.0 0.0 Fe +/-

Rh

Fe +/-

5 ML - FM

Rh

Fe +/-

Rh

7 ML - FM

Fe +/-

Rh

Fe +/-

9 ML - FM

(a) FeRh/MgO - Fe terminated 5.0

vacuum

substrate

й reladžaƟŽn

4.0 3.0 2.0 1.0 0.0 Fe +/-

Rh

Fe +/-

5 ML- AFM

Rh

Fe +/-

Rh

7 ML - AFM

Fe +/-

Rh

Fe +/-

9 ML - AFM

(b) Fig. 5. Calculated relaxations (%) of the interatomic planes in the direction perpendicular to the surface for FM (a) and FM (b) couplings of the films terminated in Fe. For simplicity in the graph the average values were considered.

FeRh/MgO - Fe terminated 3.5

substrate

vacuum

3.0 mm per layer ( B/at)

2.5

3.2. Energetic properties

2.0 1.5

We will now proceed to analyze the energetic properties. Regarding the energy per atom values presented in Table 2 it can be said that it increases as the ultra-thin film grows, of the order of 0.2 eV/at for both terminations (-Rh, -Fe) being slightly more favorable those -Fe terminated. Another important data for experimentalists is the value of the adhesion energy involved in these systems. The ideal adhesion or separation energy Eadhesion is defined as the reversible work needed to separate an interface into two free surfaces [44], assuming no plastic or diffusional modifications. It can be given by the difference in total energy between the interface and their isolated components. The corresponding adhesion energies have been calculated as:

1.0 0.5 0.0 -0.5

Fe +/-

Rh

Fe +/-

Rh

Fe +/-

Rh

Fe +/-

Rh

Fe +/-

-1.0 -1.5 5 ML - FM

5 ML- AFM

7 ML - FM

Fig. 6. Calculated magnetic moments (mm) per layer in μB/at for AFM and FM couplings of the films terminated in Fe.

In the case of 5-layer films the main difference with the FM coupling is the cancellation of the magnetic moment of the Rh atoms. The Fe atoms maintain their ± 3 μB. In the other two cases studied, the values for Rh are between 0.1 and 0.2 μB. A different situation is found for the Fe atoms. The Fe atoms of the other layers recover their values of ± 3 μB. The behavior of the film of 9 layers is different; the Rh atoms acquire magnetization, of the order of one tenth of μB, in increasing order as they approach to the free surface. In the same way Barton et al.

Eadhesion = EFeRh / MgO − EMgO − EFeRh where EFeRh/MgO corresponds to the total energy of the FeRh/MgO optimized heterostructure, EMgO corresponds to the total energy of the MgO slab and EFeRh corresponds to the total energy obtained from the FeRh slab calculation. It is necessary to take into account that in this calculation, from the relaxed FeRh/MgO system, the energies of both the MgO-substrate and the FeRh slab were calculated without relaxing, that is, maintaining the same cell of the FeRh/MgO system. The 6

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analyze the most atypical cases of 7 ML and 9 ML. As previously mentioned in the case of 7 ML, the Fe of the first layer have all spin down and an approach to the substrate is observed with average values of Fe-O distances of 0.209 nm. In contrast, in the case of 9 ML, the distances between O atoms and Fe with spin up are larger (0.222 nm); if we measure the O-Fe distances along the b-axis, particularly in the line where the Fe atoms alternate the spins, the values are 0.219 nm (spin up) and 0.215 nm (spin down). That is, in general, the Fe atoms with spin down approach the substrate and those of spin up tend to move away from the surface. Finally, it should be mentioned that at present we have no knowledge of experimental data to compare with our simulations.

AFM

Eadh (J/m2)

1.5

1.0

0.5

0.0 5 ML-Fe

5 ML-Rh

7 ML-Fe

7 ML-Rh

9 ML-Fe

3.3. Electronic properties

9 ML-Rh

Fig. 7. Comparative graph of adhesion energies calculated for FM and AFM coupling corresponding to both terminated surfaces -Rh and –Fe.

In order to complete the analysis, the corresponding electronic structures are presented in this section. The total DOS for the two magnetic configurations FM (Fig. 8) and AFM (Fig. 9) are plotted. We also include the LDOS corresponding to Fe-3d and Rh-4d bands to complete the analysis of the changes observed in the magnetic properties of this system. The electronic properties at the Fermi level play an essential role in the understanding of the magnetic properties of materials. The qualitative form of the DOS curves for the FM configurations is similar in all three configurations with the strong presence of Fe states at approximately 1 eV above the Fermi level. In particular, we found a large spin-down DOS compared to the spin-up component at the Fermi level implying that all the structures exhibit ferromagnetic properties. One way to quantify this difference is by evaluating spin polarization at the Fermi level by using the expression:

objective is to be able to evaluate the energy put into play in the adhesion metal/oxide. To compare with experimental results, the values were calculated in J/m2 considering the corresponding areas obtained after optimization. The results corresponding to both terminated surfaces (-Rh and -Fe) for FM and AFM coupling are presented in Fig. 7. Looking at Fig. 7 we can say that the difference in the adhesion energies depends, considering the same thickness, on whether the surface of the film ends with Rh or Fe atoms. A lower adhesion energy value indicates that the system is more stable; the film is more adhered complicating the removal or separation from the substrate. We emphasize two general facts, on the one hand, the adhesion energy tends to an average value of the order of 1.5 J/m2 being slightly higher in the case of AFM coupling i.e., the AFM coupling facilitates the takeoff compared to the FM coupling; on the other hand, the adhesion energy tends to decrease as the thickness of the film grows. In particular, we can mention for example, the system of 7 ML -Fe terminated (AFM) surface has a highest adhesion energy value of 1.6 J/ m2 and the lowest percentage of relaxation of 1.10% (Fig. 5 – Table A3 Supplementary material), referring to the first layer of the film in contact with the substrate. Analyzing in particular the spin configuration of both systems (7 ML and 9ML -Fe terminated, Table 2 – fourth column) it is observed that in the case of the 9 ML film, the Fe layer in contact with the substrate undergoes a spin change in some of the atoms that should have spin up (indicated in blue in the row that should have been golden). A different situation is that of the case of 7 ML whose interface Fe layer has a configuration of spin down and not alternated as in the case of 5 ML. It is important to note that the metal-oxide interface has Fe/Rh atoms in the plane in contact with the substrate oxygen atoms. In particular, the average distance O-Rh in the Rh-terminated is 0.224 nm. However, in the case of surfaces –Fe terminated, the Fe-O average distance varies according to the thickness of the film, in particular we

P=

ρ↑ − ρ↓ ρ↑ + ρ↓

here ρ↑ and ρ↓ are the total density of states of the spin-up and spindown bands at the Fermi level, respectively. The values of the spin polarizations are negative in the six systems studied: −0.240 (5 ML), −0.654 (7 ML), −0.795 (9 ML) for the films –Rh terminated and −0.903 (5 ML), −0.725 (7 ML), −0.756 (9 ML) for the films –Fe terminated. The biggest difference in the P value depending on whether it is terminated in Fe or Rh is observed in the thinnest film. However, as the films grow, the values of P are equating. Similar behaviors have been reported both theoretically and experimentally by Pressaco et al. [45]. Comparing the DOS curves for AFM films of 5 ML and 7 ML, there is a small shift of the curves of the Rh-terminated systems towards higher energies, with respect to the curves of the systems terminated in Fe. In contrast, for the 9 ML systems, this difference is not perceived. However, there are other important features to mention. We will focus more on the analysis of AFM curves for 9 ML systems because we are interested in analyzing the different behavior observed in films terminated in Fe with respect to those terminated in Rh. The first observation

Fig. 8. Total DOS for FM films of 5 ML (a), 7 ML (b) and 9 ML (c) terminated in Fe (orange curve) and terminated in Rh (gray curve). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) 7

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Fig. 9. Total DOS for AFM films of 5 ML (a) and 7 ML (b) terminated in Fe (orange curve) and terminated in Rh (gray curve). In (c) and (d) the total DOS for AFM films of 9 ML (black curve) and LDOS curves corresponding to Fe-3d (orange) and Rh-4d (gray) are presented to complete the analysis of the changes observed in the magnetic properties of this system (Table 2). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

of 9 ML there is a greater interaction between the atomic layers of the film (lower adhesion energy), a situation that is not recognized in films -Rh terminated.

to make is that although the calculation is made by setting an antiferromagnetic configuration, in Fig. 9d it is observed an asymmetry between the spin up and spin down curves that is not present in Fig. 9c. If we also measure the occupation of majority and minority states in both cases, we find that there are notorious differences in the occupation values at the Fermi level. In the case of the film terminated in Rh (9 ML) the occupation of both states (up and down) are practically identical and the P value is 4.10-4. On the other hand, if we analyze the same difference for the case of films terminated in Fe the P value is −0.08. This would indicate that this structure exhibits remnant ferromagnetism. These figures show that the spin-up and spin-down components are not equally distributed with respect to the energy. The states near and above the Fermi level are assigned mainly to those of the Fe atoms. In order to complete the analysis, we investigate the possibility of charge transfer between the film and the substrate. First we calculate the Bader charges [46]. The charge values for all the systems studied are summarized in Table A2 (Supplementary material). The table shows the net charge values of the substrate (MgO) and the charge average of each species of film (Fe and Rh). We observe that in all systems the Fe atoms are positively charged, going from an approximate value of +0.6 e/Fe-at in the case of the –Rh terminated film to +0.5 e/Fe-at for the -Fe terminated film. In the case of the Bader charge analysis for the Rh atoms, the Rh atoms increase its negative charge going from an approximate value of −0.5 e/Rh-at (–Rh terminated film) to −0.7 e/Rhat for the case of the film –Fe terminated. In the case of the substrate (MgO) the net charge of Bader in the case of the –Rh terminated film, is higher than the charge in the case of -Fe terminated film. With the aim to complete the visualization of the charge transfer effect on the local metal-surface interaction observed, the corresponding differences in charge densities were performed (Fig. 10) limiting us to 7 ML and 9 ML AFM systems terminated in Rh (a and c) and in Fe (b and d). Again the most marked differences are in the systems shown in Fig. 10 b) and d). It is observed that in the case of 7 ML the interaction with the substrate is greater (in accordance with greater adhesion energy) than with the layer of Rh atoms that is on top, whereas in the case

4. Conclusions In order to improve the knowledge of bimetallic systems properties, theoretical calculations have been carried out. Among the main objectives proposed in this work we can conclude that the results obtained are mostly influenced by the surface termination (-Rh or -Fe). That is why the main conclusions can be summarized in the following items depending on the termination: -Rh terminated:

• With regard to the out-of-plane relaxation percentage for the AFM

•

• • 8

coupling, lower values are observed compared to those obtained for the FM coupling. The highest percentages are for the layer in contact with the substrate (Rh) and the last subsurface layer of Fe; this behavior is maintained for all three thicknesses (0.6 nm, 0.9 nm and 1.2 nm). With respect to magnetic properties, in the three presented systems of Rh/Fe alternating layers, the tendency of magnetic moments values for the FM coupling is maintained in around 3.2 μB/at for the case of Fe and 1.0 μB/at for the case of Rh. For AFM the most noticeable difference is the cancellation of the magnetic moments of Rh. The magnetic moment values of the Fe atoms are around +/−3.1 μB/at for the three systems. However, if we consider the net magnetic moment per layer, also the Fe layer gives zero. The adhesion energy tends to an average value of the order of 1.5 J/ m2; on the other hand, the AFM coupling facilitates the takeoff compared to the FM coupling. Moreover, regarding the difference between FM and AFM results for different thicknesses, the percentages are slightly lower for –Rh terminated films. Regarding the c′/a′ relation, it is observed that the films -Rh terminated maintain a cubic structure (type B2) independent of the thickness of the film or the magnetic configuration.

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Fig. 10. Charge density differences of AFM films of 7 ML and 9 ML terminated in -Rh (a,c) and terminated in -Fe (b,d) to visualize the effects of support (MgO) in the electronic structure of the film. The yellow and blue light represent the positive and negative level isosurfaces, respectively, obtained using VESTA [47,48]. The corresponding level value is 0.005 e/Å3. Reference color: Rh atoms are in gray, Fe atoms in gold, O atoms in red and Mg atoms in white. For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

-Fe terminated:

• Regarding the out-of-plane relaxation percentage, they depend on

•

the thickness of the film and the magnetic coupling. The first layer of Fe that is in contact with the substrate tends to separate in a lower percentage than in the case of –Rh terminated being greater in the case of the AFM coupling (9 ML > 5 ML > 7 ML) than in the FM one (5 ML > 7 ML > 9 ML). As the film grows (0.9 nm) the relaxations are practically double than those corresponding to the cases of films terminated in Rh. In particular, Rh layers away from the substrate are the ones that relax most. A similar trend is observed for the 1.2 nm film, unlike the first layer of Rh, which has the lowest percentage of relaxation (0.2%) and is slightly closer to the Fe layer, the rest of the layers relax. The results corresponding to AFM coupling are the ones that differ most from the rest of the cases studied. In the case of 0.6 nm films the main difference with the FM coupling is the cancellation of the magnetic moment of the Rh atoms. However, the Fe atoms maintain their ± 3 μB/at. As the film grows the magnetic moment values for Rh are between 0.1 and 0.2 μB/at. The situation is different for the Fe atoms. In particular, in the 0.9 nm system the Fe atoms in contact with the substrate undergo the least relaxation and their magnetic moments are parallel and equal to −1 μB/at. The Fe atoms of the

•

•

9

other layers recovered their values of ± 3 μB/at. The behavior of the film of 1.2 nm is different; the Rh atoms acquire magnetization, of the order of one tenth of μB/at, in increasing order as they approach to the free surface. The presence of residual ferromagnetism at the interfaces of the FeRh films deposited on MgO(0 0 1) has also been observed experimentally by Fan et al [28]. In particular, the systems with the lowest value of adhesion energy (AFM) coincide with those with the highest percentage of relaxation referring to the first layer of the film in contact with the substrate. On the other hand, the 7 ML (AFM) system is the only one with highest adhesion energy value (1.6 J/m2) and the lowest percentage of relaxation (0.45%). Analyzing in particular the spin configuration of both systems it is observed that in the case of the 9 ML film, the Fe layer in contact with the substrate undergoes a spin change in some of the atoms that should have spin up. A different situation is that of the case of 7 ML whose interfacial Fe layer has a configuration of spin down (remnant ferromagnetism) and it is not alternated, as in the case of 5 ML. With respect to the analysis of the isosurface figures, the most marked differences are in the systems -Fe terminated. It is observed that in the case of 0.9 nm the interaction with the substrate is greater (in accordance with greater adhesion energy) than with the layer of Rh atoms that is on top, whereas in the case of 1.2 nm there

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•

is a greater interaction between the atomic layers of the film (lower adhesion energy), a situation that is not recognized in films -Rh terminated. In contrast with the films -Rh terminated, the films -Fe terminated tend to have a centered tetragonal structure (bct), which is accentuated in AFM cases.

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CRediT authorship contribution statement M. Julia Jiménez: Conceptualization, Methodology, Writing - original draft. Alejandro Butera: Validation. Gabriela F. Cabeza: Conceptualization, Methodology, Validation, Supervision, Writing review & editing. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments The authors thank the financial support from the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) and the Universidad Nacional del Sur (UNS) (PGI: 24/F068). GFC and ABS are Members of CONICET and MJJ is Doctoral Research Fellow. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.jmmm.2020.166488. References [1] M. Fallot, Les alliages du fer avec les métaux de la famille du platine, Ann. Phys. (Paris) 11 (1938) 291–332, https://doi.org/10.1051/anphys/193811100291. [2] T. Moriyama, N. Matsuzaki, K.J. Kim, I. Suzuki, T. Taniyama, T. Ono, Sequential write-read operations in FeRh antiferromagnetic memory, Appl. Phys. Lett. 107 (2015) 1–5, https://doi.org/10.1063/1.4931567. [3] V.L. Moruzzi, P.M. Marcus, Antiferromagnetic-ferromagnetic transition in FeRh, Phys. Rev. B. 46 (1992) 409–457, https://doi.org/10.1007/978-3-7091-6294-1_13. [4] S. Maat, J.U. Thiele, E.E. Fullerton, Temperature and field hysteresis of the antiferromagnetic-to-ferromagnetic phase transition in epitaxial FeRh films, Phys. Rev. B - Condens. Matter Mater. Phys. 72 (2005) 1–10, https://doi.org/10.1103/ PhysRevB.72.214432. [5] J. Kim, R. Ramesh, N. Kioussis, Revealing the hidden structural phases of FeRh, Phys. Rev. B. 94 (2016) 1–5, https://doi.org/10.1103/PhysRevB.94.180407. [6] Z. Feng, H. Yan, Z. Liu, Electric-field control of magnetic order: from FeRh to topological antiferromagnetic spintronics, Adv. Electron. Mater. 5 (2019) 1–14, https://doi.org/10.1002/aelm.201800466. [7] N.A. Zarkevich, D.D. Johnson, FeRh ground state and martensitic transformation, Phys. Rev. B. 97 (2018) 1–5, https://doi.org/10.1103/PhysRevB.97.014202. [8] M. Wolloch, M.E. Gruner, W. Keune, P. Mohn, J. Redinger, F. Hofer, D. Suess, R. Podloucky, J. Landers, S. Salamon, F. Scheibel, D. Spoddig, R. Witte, B. Roldan Cuenya, O. Gutfleisch, M.Y. Hu, J. Zhao, T. Toellner, E.E. Alp, M. Siewert, P. Entel, R. Pentcheva, H. Wende, Impact of lattice dynamics on the phase stability of metamagnetic FeRh: Bulk and thin films, Phys. Rev. B. 94 (2016) 1–17, https://doi. org/10.1103/PhysRevB.94.174435. [9] J.A. Arregi, M. Horký, K. Fabianová, R. Tolley, E.E. Fullerton, V. Uhlíř, M. Horký, K. Fabianová, J.A. Arregi, R. Tolley, Magnetization reversal and confinement effects across the metamagnetic phase transition in mesoscale FeRh structures, J. Phys. D. Appl. Phys. 51 (2018) 105001, , https://doi.org/10.1088/1361-6463/aaaa5a. [10] L.M. Sandratskii, P. Mavropoulos, Magnetic excitations and femtomagnetism of FeRh: A first-principles study, Phys. Rev. B - Condens. Matter Mater. Phys. 83 (2011) 1–13, https://doi.org/10.1103/PhysRevB.83.174408. [11] S. Lounis, M. Benakki, C. Demangeat, Ferromagnetic stabilization of ordered B2 FeRh thin films, Phys. Rev. B – Condens. Matter Mater. Phys. 67 (2003) 1–5, https://doi.org/10.1103/PhysRevB.67.094432. [12] M. Sharma, H.M. Aarbogh, J.U. Thiele, S. Maat, E.E. Fullerton, C. Leighton, Magnetotransport properties of epitaxial MgO(001)/FeRh films across the antiferromagnet to ferromagnet transition, J. Appl. Phys. 109 (2011), https://doi.org/ 10.1063/1.3573503. [13] J.-U. Thiele, S. Maat, E.E. Fullerton, FeRh/FePt exchange spring films for thermally assisted magnetic recording media, Appl. Phys. Lett. 82 (2003) 2859–2861, https:// doi.org/10.1063/1.1571232.

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