Solid-state synthesis, magnetic and structural properties of interfacial B2-FeRh(001) layers in Rh/Fe(001) films

Here we first report results of the start of the solid-state reaction at the Rh/Fe(001) interface and the structural and magnetic phase transformations in 52Rh/48Fe(001), 45Rh/55Fe(001), 68Rh/32Fe(001) bilayers from room temperature to 800 °C. For all bilayers the non-magnetic nanocrystalline phase with a B2 structure (nfm-B2) is the first phase that is formed on the Rh/Fe(001) interface near 100 °C. Above 300 °C, without changing the nanocrystalline B2 structure, the phase grows into the low-magnetization modification αlʹ (MSl ~ 825 emu/cm3) of the ferromagnetic αʹ phase which has a reversible αlʹ ↔ αʺ transition. After annealing 52Rh/48Fe(001) bilayers above 600 °C the αlʹ phase increases in grain size and either develops into αhʹ with high magnetization (MSh ~ 1,220 emu/cm3) or remains in the αlʹ phase. In contrast to αlʹ, the αhʹ ↔ αʺ transition in the αhʹ films is completely suppressed. When the annealing temperature of the 45Rh/55Fe(001) samples is increased from 450 to 800 °C the low-magnetization nanocrystalline αlʹ films develop into high crystalline perfection epitaxial αhʹ(001) layers, which have a high magnetization of ~ 1,275 emu/cm3. αhʹ(001) films do not undergo a transition to an antiferromagnetic αʺ phase. In 68Rh/32Fe(001) samples above 500 °C non-magnetic epitaxial γ(001) layers grow on the Fe(001) interface as a result of the solid-state reaction between the epitaxial αlʹ(001) and polycrystalline Rh films. Our results demonstrate not only the complex nature of chemical interactions at the low-temperature synthesis of the nfm-B2 and αlʹ phases in Rh/Fe(001) bilayers, but also establish their continuous link with chemical mechanisms underlying reversible αlʹ ↔ αʺ transitions.

In this work, we describe the solid-state reactions between polycrystalline Rh with epitaxial Fe(001) films in 52Rh/48Fe(001), 45Rh/55Fe(001) and 68Rh/32Fe(001) bilayers with 52Rh:48Fe, 45Rh:55Fe and 68Rh:32Fe atomic ratios, respectively. Under these conditions, the reaction products of 52Rh/48Fe(001) fall into the (0.48 < x Rh < 056) concentration interval and the reaction products for 45Rh/55Fe(001) and 68Rh/32Fe(001) samples lie in Fe-rich and Rh-rich regions of the Fe-Rh system. The main purpose of this article is to show the complex and intricate nature of the B2-FeRh phases synthesis, which begins to form on the Rh/Fe interface at ~ 100 °C.

Results
Structural and magnetic phase transformations in 52Rh/48Fe(001) bilayer during annealing up 800 °C. Figure 1a shows a schematic diagram of the phase transformations consistently occurring in 52Rh/48Fe(001) bilayers on a MgO(001) substrate during annealing from room temperature to 800 °C which builds on the X-ray diffraction (XRD) analysis (Fig. 1b) and magnetic measurements (Fig. 1c,d). The transformations consist of the formation of a nonferromagnetic B2-FeRh phase (nfm-B2) thin layer at the Rh/Fe interface of the as-deposited sample, which above 300 °C turns into the α l ʹ phase. As will be shown below, the ferromagnetic αʹ phase may have two B2 modifications with similar or equal lattice parameters: a low-ferromagnetic α l ʹ having a magnetization ~ 825 emu/cm 3 and a fully reversible α l ʹ ↔ αʺ (AFM-FM) transition and a high-ferromagnetic α h ʹ with a magnetization ~ 1,220 emu/cm 3 and with a completely depressed α h ʹ → αʺ transition. As the annealing temperature increases above 600 °C the reaction products contain a mixture of epitaxial α l ʹ(001) and α h ʹ(001) grains. Figure 1b shows the XRD profiles of the as-deposited 52Rh/48Fe(001) film and after annealing at temperatures from room temperature to 800 °C. As-deposited samples show a strong Fe(002) peak, proving the epitaxial Fe(001) film growth on the MgO(001) substrate, and wide and very low diffraction peaks (001), (002) located at ~ 30° and ~ 62°, which are a signature of insignificant mixing, a reaction between the Rh and Fe(001) layers and the synthesis of a very thin epitaxial layer of nanocrystalline B2-ordered FeRh phase. These (001), (002) reflections were greatly broadened, split and their intensity did not change up to 600 °C. This strongly suggests that the reaction starts with the formation of (001)-textured nanograins containing B2-ordered FeRh phases with close lattice parameters and significant lattice distortions. After annealing above 600 °C the Fe(002) peak decreases significantly and practically disappears at 800 °C, which points to the complete termination of the reaction between the Fe and Rh layers. At the same time the (001), (002) peaks grow insignificantly, which is due to the annealing-induced coarsening of the B2-ordered FeRh nanograins. Using Scherrer's formula the average grain size was estimated to be ~ 10 nm and slightly increased to ~ 40 nm with an increase in temperature from 600 to 800 °C. This means that the final product is a low crystalline quality epitaxial B2-ordered FeRh (001) layer on Mg(001). The asymmetric XRD scans demonstrate the orientation relationship of the B2-FeRh (001)[001] || Fe(001)[001]||MgO(001)[011] (see Supplementary Fig. 1). The order parameter was estimated S = 0.90 ± 0.02 for the synthesized B2-FeRh samples at temperatures in the 600-800 °C range. Figure 1c shows the dependence of the in-plane relative magnetic anisotropy constant K 4 (T a )/K 4 0 and the M S (T a )/ M S 0 relative magnetization as a function of the annealing temperature T a {where for 52Rh/48Fe(001) samples K 4 0 = 2.4•10 5 erg cm 3 and M S 0 = 825 emu/cm 3 , see "Methods"}. With an increase in the annealing temperature T a the constant K 4 (T a ) monotonically decreases and becomes zero within experimental accuracy after annealing at 800 °C. This means that the first magnetic anisotropy constant K 1 of the B2-ordered FeRh phase is zero or less than the measurement error (0.2 × 10 4 erg/cm 3 ). A value of K 1 ~ 0 is consistent with the FeRh single films exhibiting an in-plane easy axis of magnetization with no measurable magnetocrystalline anisotropy 41 . Therefore, the K 4 (T a )/K 4 0 dependence can be used to find the thickness, magnetization and magnetic moment of the reacted Fe(001) layer after annealing at T a (Supplementary Note 1). The dependence of the relative magnetization M S / M S 0 as a function of annealing temperature T a (Fig. 1c) has an unusual shape and convincingly shows complex and intricate scenarios of various phase formation and their mutual transformations in the Rh/Fe(001) bilayer during annealing to 800 °C. Within experimental error the relative anisotropy constant K 4 (T a )/K 4 0 and the relative magnetization M S (T a )/M S 0 decrease identically as the annealing temperature increases up 300 °C. The synchronous decrease of the K 4 (T a )/K 4 0 and M S (T a )/M S 0 values clearly proves the onset of the slow mixing of the Rh and Fe layers and the synthesis of the nonferromagnetic B2-FeRh(001) phase (nfm-B2) on the Rh/Fe(001) interface, whose volume increases with an increase in annealing temperature to 300 °C. Above 300 °C the magnetization increases to M S /M S 0 ~ 1, which indicates a phase transformation of the nfm-B2 to the ferromagnetic α l ʹ phase. From Fig. 1c follows that the trilayer system Rh/α l ʹ/Fe (001) has the magnetization of the initial sample M S 0 = 825 emu/cm 3 (M S /M S 0 ~ 1) in the temperature range (350-500 °C), which means that only the Fe atoms contribute to the saturation magnetization of α l ʹ-FeRh. Surprisingly, after annealing at 550 °C, the saturation magnetization decreases to 660 emu/cm 3 (~ 20%), but the reaction product layer participates completely in the reversible α l ʹ ↔ αʺ transition (Fig. 1d). At annealing temperatures above 500 °C, the films begin to partially peel off from the substrate due to the strong stresses arising during the synthesis of the epitaxial α l ʹ-FeRh (001) film at the α l ʹ-FeRh(001)/Fe(001) interface. Therefore, a possible explanation is the deformation of some α l ʹ-grains with a loss of ferromagnetic order.  We hypothesize that the αʹ phase has two B2-ordered polymorphic modifications having similar lattice parameters, but different magnetic properties.
In the first modification the α l ʹ phase has a low magnetization about 825 emu/cm 3 , which is defined only by the Fe atoms with the Rh atoms not contributing to the magnetization, and the α l ʹ undergoes a complete reversible α l ʹ ↔ αʺ transition ( Supplementary Fig. 3a). In contrast, in the second α h ʹ modification, which is primarily in the (B) samples, the Fe atoms supposedly polarize the Rh and the Rh atoms make the contribution to the saturation magnetization 1,220 emu/cm 3 and in the α h ʹ phase the α h ʹ ↔ αʺ transition is completely suppressed (Supplementary Fig. 3b). Under such conditions, with an increase in temperature above 650-800 °C, some low-magnetic α l ʹ nanograins turn into high-magnetic α h ʹ and therefore, the samples have a magnetization between 825 and 1,220 emu/cm 3 and exhibit an imperfect reversible transition with a residual magnetization. To summarize, the chemical reaction between Fe and Rh arises on the Fe/Rh interface at a low annealing temperature (~ 100 °C) and with an increase in annealing temperature the phase sequence 52Rh/48Fe → (~ 100 °C) nfm-B2 → (300 °C) α l ʹ → (600 °C) α l ʹ or α h ʹ is formed as shown in Fig. 1a.
The phase and magnetic evolution in the 45Rh/55Fe(001) bilayer during annealing up 800 °C. The schematic diagram in Fig. 2a is based on the results presented in Fig. 2b-d and shows the same www.nature.com/scientificreports/ nonferromagnetic nfm-B2 phase which was formed in the 45Rh/55Fe and 52Rh/48Fe bilayers during annealing from room temperature to 300 °C. Above 300 °C the nfm-B2 phase consistently turns into ferromagnetic lowmagnetization α l ʹ, which above 450 °C grows into the high-magnetization α h ʹ phases. As shown in Fig. 2b after annealing above 400 °C the (001) and (002) peaks start to grow and become very strong above 500 °C, which indicates the formation of high structural quality epitaxial α h ʹ(001) layers on the MgO(001) surface. The K 4 (T a )/ K 4 0 and M S /M S 0 dependencies (where for 45Rh/55Fe(001) samples K 4 0 = 2.5 × 10 5 erg cm 3 and M S 0 = 875 emu/ cm 3 , see "Methods") presented in Fig. 2c show that the nanocrystalline phase α l ʹ (001) with low magnetization (M S /M S 0 ~ 1.0) grows into the high quality epitaxial phase α h ʹ(001) with high magnetization (M S /M S 0 ~ 1.47) above 450 °C. The high quality of the chemical ordering of the α h ʹ(001) films after annealing at 500 °C and 800 °C supports the order parameter S = 0.96 ± 0.02, which is more than the S = 0.90 ± 0.02 for α l ʹ in 52Rh/48Fe films. This result is unexpected, since the α l ʹ exists in a narrow composition range of nearly equiatomic concentration and must have a more complete B2 order than the Fe-rich α h ʹ phase. The α h ʹ(001) and α l ʹ(001) films have the same orientation relationship with the substrate MgO(001) (Supplementary Fig. 1). Above 500 °C the Fe has completely reacted with the Rh as evidenced by the K 4 (Ta)/K 4 0 dependence (Fig. 2c). As can be seen from Fig. 2d the degree of the AFM-FM transition η ~ 0.9, which means the α l ʹ phase exists in a narrow temperature range (300-450 °C) and the AFM-FM transition has a relatively low residual magnetization (see Supplementary Fig. 4). Figure 2d shows the absence of the AFM-FM transition (η = 0), which indicates the formation of a α h ʹ phase from the α l ʹ phase after annealing above 450 °C (see also Supplementary Fig. 5). From these facts it transpires that the Fe-rich α h ʹ phase formed from the equiatomic α l ʹ compound above 450 °C by the solid-state reaction α l ʹ + Fe → (~ 450 °C) α h ʹ. Finally, we proved that even a slight Fe doping of α l ʹ causes a chemical reaction between Fe and α l ʹ and the start of the synthesis of the α h ʹ phase. This suggests that the high magnetization α h ʹ phase occurring in the 52Rh/48Fe(001) bilayer (B samples) also has more Fe content than α l ʹ and explains the compositional heterogeneity arising as a result of the nonequilibrium reaction processes. Thus, we show the phase evolution 45Rh/55Fe → (~ 100 °C) nfm-B2 → (300 °C) α l ʹ → (450 °C) α h ʹ is induced by the solid-statereaction method and the final reaction product is a highly B2-ordered phase α h ʹ, which has a high magnetization of 1,270 emu/cm 3 and in which the reversible α h ʹ ↔ αʺ transition is completely suppressed.
Kinetic growth of the nanocrystalline nfm-B2 layer during thermal aging at 110 °C. To gain a better understanding of the origin and formation of the very thin nanocrystalline nfm-B2 layer at the Rh/ Fe(001) interface at the temperature of the α l ʹ → αʺ transition, the synthesis kinetics of the nfm-B2 layer during isothermal aging at 110 °C was investigated. As stated above, deposition of Rh on Fe(001) at room temperature at any ratio of thicknesses between Rh and Fe leads to the formation of a thin interfacial nanocrystalline nfm-B2 layer. However, slight heating to 100 °C during sputtering cannot be excluded, therefore, aging of as-deposited samples was investigated at 110 °C. XRD data from the as-deposited Rh/Fe(001) bilayer and after aging up to 360 h shows a small broadened (001) superlattice and the fundamental (002) peaks of the nfm-B2 phase which did not change from aging time to 360 h (Fig. 4a). This means that long-time aging does not lead to the nfm-B2 grains coarsening and clearly demonstrates the inherent nanocrystalline nature of nfm-B2, which is also inherited by the α l ʹ phase. Figure 4b shows the TEM image and EDX line scan results of the Rh/Fe(001) bilayer aged at 110 °C for 360 h. The elemental profile obtained by the EDX line scan across the Rh/nfm-B2/Fe(001) trilayer shows an interfacial nfm-B2 thin film beside the initial Rh and Fe layers. The TEM image displays a compositional contrast that is proportional to the difference in the average atomic number of the respective areas. As a consequence, the reaction product nfm-B2 can be easily distinguished in the interfacial region from the initial Rh and Fe(001) areas. This allows one to estimate the thickness of the interfacial nfm-B2 h nfm-B2 ~ 15 nm (Fig. 4b). Figure 4c shows the thickness d Fe of the Fe(001) layer, which entered into a reaction with Rh at 110 °C, as a function of aging time. There is a large experimental error in the thickness d Fe measurements and therefore the dependence d Fe (t) is impossible to describe by an unambiguous kinetic equation, which suggests a possible growth mechanism. As shown in Fig. 4c the thickness d Fe after aging for 360 h at 110 °C is ~ 8 nm, which corresponds to the thickness d nfm-B2 ~ 17 nm of the nfm-B2 layer (Supplementary Fig. 8a). This value agrees well with the estimated d nfm-B2 ~ 15 nm obtained from TEM-EDX analysis. These findings are in good agreement with Scientific RepoRtS | (2020) 10:10807 | https://doi.org/10.1038/s41598-020-67837-2 www.nature.com/scientificreports/ a previous report 42 which showed and discussed the tendency towards intermixing and interfacial Rh-Fe alloy formation at the Rh/Fe interface at room temperature.
Phase transition from nfm-B2 to α l ′ at 300 °C. For a further understanding of the reactivity of Fe and Rh during the transition from nfm-B2 to α l ʹ around 300 °C, we investigated the evolution of the temperature dependencies of the magnetization and the thickness of the interfacial h B2-FeRh layer in the 52Rh/ B2-FeRh/48Fe(001) trilayer after annealing at 280 °C, 300 °C and 350 °C. Figure 5a shows the M-T curves for the 52Rh/nfm-B2/48Fe(001) trilayer after annealing at 280 °C which do not contain changes in either the forward or the reverse direction. This clearly demonstrates that the B2-FeRh interlayer remains a non-ferromagnetic nanocrystalline nfm-B2 layer after annealing in the 110-280 °C temperature interval. From the crosssectional TEM image and the EDS line-scan (Fig. 5a), it can be seen that the d nfm-B2 interlayer in the 48Rh/nfm-B2/52Fe(001) trilayer increases to a thickness around d nfm-B2 ~ 30 nm after annealing at 280 °C. ( Supplementary  Fig. 8b). As shown in Fig. 5a,b slight increase in the annealing temperature to 300 °C leads to the appearance a road FM-AFM transition with a temperature hysteresis of magnetization about 80 K and a small increase in the d B2-FeRh thickness of the B2-FeRh interlayer to ~ 40 nm (Supplementary Fig. 8c). The change in magnetization at the AFM-FM transition gives a rough estimate of the thickness d(α l ʹ) ~ 20 nm of the α l ʹ layer in the B2-FeRh interlayer. This clearly proves that after annealing at 300 °C the B2-FeRh interlayer contains a mixture of 50%  Figure 5c shows that the thickness d B2-FeRh grows quickly to 135 nm as the annealing temperature increases to 350 °C ( Supplementary Fig. 8d). This value is in good agreement with the estimate obtained from the K 4 (T a )/K 4 0 dependence (Fig. 1c, see Supplementary Note 3). EDS anal-  Figure 5c shows the M-T curve having a road FM-AFM transition with large thermal hysteresis width about 100 K, which often occurs in thin film system. This may be due to inhomogeneities of composition, stresses and nanocrystalline growth as a result of non-equilibrium synthesis of the B2-FeRh phases. Thus, this is proof that the reactivity of Fe and Rh is very low at 110 °C and begins to increase greatly during the transition nfm-B2 → α l ʹ above 300 °C. This causes strong temperature dependencies up to 500 °C of the relative magnetic anisotropy constant K 4 (T a )/K 4 0 (Figs. 1, 2, 3) and electrical resistance ( Supplementary Fig. 9).

Discussion
Numerous experiments have proved that as temperature rises, only one phase appears on the interface of bilayer film systems, which is called the first phase [43][44][45] . The initiation temperatures T in of the first phase for most bilayers lie below 400 °C. However, many thin-film reactions are initiated near room temperature and even occur at cryogenic temperatures. At such low temperatures diffusion is extremely small and cannot provide atomic transfer in a solid state [46][47][48] . This suggests an alternative view, in which not diffusion, but chemical interactions play a crucial role in the initiation and kinetics of solid state interfacial reactions. Under the influence of chemical interactions that arise above the initiation temperature T in , the chemical bonds break in the reactants, and the reacting atoms migrate into the reaction zone to synthesize new compounds. Previously, it was shown that the initiation temperatures T in are close to or coincide with the solid-state transformation temperatures T k of several reagent-based binary systems, such as order-disorder transitions, the superionic transition, the spinodal decomposition, martensitic transformations and others [46][47][48] . This suggests that the same chemical interactions underlie and control both the solid-state thin-film reactions and the corresponding solid-state transformations. The equality T in = T k indicates that low-temperature solid-state thin-film reactions in A/B bilayers occur only in A-B binary systems, which have corresponding low-temperature solid-state transformations. Therefore, the study of reactions in A/B bilayers with different layer ratios is a study of the low-temperature part of the A-B phase diagram. It is well established that ordered B2 alloys, such as NiTi, AuCd, NiAl have reversible low-temperature martensitic transformations, in which the high-temperature austenite B2-phase develops into a low-temperature martensitic phase through a complex process of the formation of intermediate phases. We have shown earlier the initiation temperatures T in (Ti/Ni) < 150 °C 49   www.nature.com/scientificreports/ induced by the application of stress 19,20,24,25,[37][38][39][40] and magnetic field 1,9,10 , has martensitic instabilities 36,54 and the α l ʹ and αʺ lattices have a cube-on-cube orientation relationship. According to the phase diagram, the transition α l ʹ ↔ αʺ has a minimum temperature T k ~ 100 °C among other structural transformations in the Fe-Rh system. From the above, we have concluded that the initiation temperature of the reaction T in (Rh/Fe) in the Rh/Fe bilayer coincides with the martensitic-like transition temperature T K ~ 100 °C in B2-FeRh. The coincidence of the starting temperature of the reaction between Fe and Rh and the temperature of the magnetostructural AFM-FM transition suggests common chemical mechanisms behind both phenomena, but that connection remains to be confirmed by additional experimentation. As mentioned above, the formation of compounds at the Rh/Fe interface starts in the temperature range 100-300 °C from the synthesis of the non-ferromagnetic nfm-B2 phase. Since this phase has only (001) and (002) B2-FeRh reflections, this means that nfm-B2 is either a martensitic-like antiferromagnetic αʺ-phase or a nonferromagnetic martensitic variant which is stabilized by strains resulting from the non-equilibrium synthesis of the nfm-B2 phase. B2-FeRh, similar to other B2 phases of NiTi, AuCd, NiAl alloys, experiences premartensitic instabilities with the subsequent formation of the different structural variants of martensite. Our hypothesis is the amorphous phase appears above 100 °C at the Rh/Fe interface, which is then transformed into a nanocrystalline state containing B2 nanograins of martensite variants with lattice parameters close to αʺ martensite. This is consistent with the possible existence of various structural phases of FeRh, predicted by ab initio calculations 54,55 and found in the experimental study 36 . Competition between the α l ʹ and αʺ phases during the partial crystallization suppresses grain growth and stabilizes the nano-grained B2 structures in an amorphous matrix. The formation of an amorphous phase is a quite common phenomenon in the initial stage of solid-state reactions in bilayers and multilayers, although the nature of this phenomenon is still a subject of dispute 57,58 . It is interesting to note the general features of the initial stage of the synthesis of B2 phases in Ti/Ni and Rh/Fe thin films. In Ti/Ni multilayers the amorphous phase starts near the martensitic transition temperature (~ 100 °C), which turns into B2-NiTi 59,60 at annealing temperatures above 350 °C. Similar to Ti/Ni, the reaction in the Rh/Fe(001) bilayer starts at ~ 100 °C with the formation of the interfacial amorphous phase, which partially crystallizes. From this point the as-deposited films consist of nanocrystalline B2 grains dispersed in the amorphous matrix. This strongly suggests that both amorphous phases are amorphous martensite, which may be a universal phenomena of the solid-state synthesis of martensitic phases 61 . This scenario is different from the synthesis of B2-NiAl and B2-AuCd, which begin to form in Al/Ni 50  Our approach assumes ~ 100 °C is the starting temperature of the formation of the B2 phase, which is associated with the reversible AFM-FM transition, and the synthesis temperatures T in (α h ʹ) = ~ 450 °C and T in (γ) = ~ 500 °C of the α h ʹ and γ phases coincide with the phase transition temperatures in the Fe-rich and Rh-rich regions of the Fe-Rh system, respectively. Such an approach is justified by us for the well-studied Fe-Ni system 62 and made it possible to predict phase transformations in other binary metallic systems [46][47][48] . Therefore, further study of solidstate reactions in Rh/Fe films, depending on the composition, will make it possible to specify the low-temperature part of the Fe-Rh phase diagram, which still remains unknown 63 .
In conclusion, we have uncovered that regardless of the Rh and Fe thicknesses the thin nonmagnetic nanocrystalline B2-FeRh layer starts to form at ~ 100 °C and grows up to 300 °C on the Rh/Fe interface. Above 300 °C the nonmagnetic phase is converted into a low-ferromagnetic B2 α l ʹ modification of the α ʹ phase with a magnetization ~ 825 emu/cm 3 without changing the nanocrystalline structure. Above 500 °C the α l ʹ reacted with Fe and formed B2 α h ʹ with a magnetization ~ 1,270 emu/cm 3 in the 45Rh/55Fe(001) samples and the α l ʹ reacted with Ph and formed the non-ferromagnetic γ phase in the 68Rh/32Fe(001)samples. Magnetic analysis has revealed that only the α l ʹ undergoes the complete reversible α l ʹ ↔ αʺ transition and there's no transition in the α h ʹ samples. Thus, our work not only provides an idea of how phase sequences start and develop depending on the composition of the Fe/Rh bilayers, but also suggests the interesting possibility that a similar chemical mechanism may be at play behind the low-temperature reaction of Fe and Rh and the AFM-FM transition in B2-FeRh.

Methods
52Rh/48Fe(001), 45Rh/55Fe(001) and 68Rh/32Fe(001) bilayers preparation and characterization. At first the epitaxial Fe(001)/MgO(001) films were grown on single-crystal MgO(001) substrates by a thermal evaporation method in a vacuum chamber at a pressure of 10-6 mbar. To obtain high-quality Fe(001) films, the substrates was previously outgassed at 300 °C for 1 h and the Fe layers were deposited at 250 °C. Epitaxial Fe (001) films had the orientation ratio Fe(001),[100]||MgO(001), [110] with the MgO(001) substrate and the magnetocrystalline anisotropy constant K 4 , which coincided with the value of bulk iron K 1 = 4.9 × 105 erg/ cm 3 . The constant K 4 in the (001) plane was determined by a torque magnetometer in a magnetic field H = 12 kOe. The torque curve L || (φ) in the (001) plane was determined according to the equation 2L || (φ) = K 4 Vsin4φ + 2 K u VSin(2φ + γ), in which, in addition to the dominant 4φ-term, there is a minor 2φ-term K u term due to the surface roughness of the MgO(001) substrate and a slight misorientation of the Fe(001) grains. In the equation K u is uniaxial anisotropy constant, V is the volume of the film, φ is the angle between the easy axis of fourfold anisotropy and the magnetization MS, γ is the angle between the easy axis of fourfold anisotropy and the axis of the uniaxial anisotropy. The K 4 V value was calculated from the torque curve L || (φ) at the maximum of the 4φ-term: 2L max = K 4 V. High quality epitaxial Fe(001)/MgO(001) films also can be obtained by various other methods as reported in the literature.
The starting Rh/Fe(001) bilayers were obtained by the evaporation of the Rh layers on Fe(001)/MgO(001) samples using dc sputtering in a magnetron sputtering system. The base pressure of the chamber was less The saturation magnetization M S 0 and the magnetic fourfold anisotropy constants K 4 0 were determined for the total volume of the 52Rh/48Fe, 45Rh/55Fe and 68Rh/32Fe bilayers, which turned out to be M S 0 = 825 emu/cm 3 , K 4 0 = 2.2 × 10 5 erg/cm 3 for the 52Rh/48Fe bilayers, M S 0 = 875 emu/cm 3 , K 4 0 = 2.4 × 10 5 erg/cm 3 for the 45Rh/55Fe bilayers and M S 0 = 450 emu/cm 3 , K 4 0 = 1.25 × 10 5 erg/cm 3 for the 68Rh/32Fe bilayers. The reversible AFM-FM phase transitions were checked using a superconducting quantum interference device (SQUID) magnetometer. Magnetic fields of H = 1.0 kOe were applied along the in-plane [100] MgO direction, which coincides with the easy axis of the Rh/Fe (001) bilayers, at all measurements in the 77-400 K temperature interval. The saturation magnetization M S and the coercivity H C were measured with a vibration magnetometer in magnetic fields up to 22 kOe. All saturation magnetization measurements were monitored using the torque method 64 .
The formed phases were identified with a DRON-4-07 diffractometer (CuKa radiation). The epitaxial relationships between MgO(001) and the B2, γ layers that formed in the reaction products were X-ray studied with a PANalytikal X'Pert PRO diffractometer with a PIXctl detector. CuKa radiation monochromatized by a secondary graphite monochromator was used in the instrument. The order parameter for the synthesized samples at temperatures in the 600-800 °C range was estimated using the equation S = (I 001 /I 002 ) 1/2 /1.07, where I 001 and I 002 are experimental integrated intensities of superstructural (001) and fundamental (002) reflections 65 .
The cross-sectional samples for TEM studies were prepared by a focused ion beam (single-beam FIB, Hitachi FB2100) at 40 kV. In order to protect the surface of interest from milling by the Ga + ion beam during sample preparation, a Ge layer was deposited onto the Fe-Rh film before cross-sectional sample preparation by FIB. TEM studies were carried out using a Hitachi HT7700 TEM (acceleration voltage 100 kV, W source) equipped with a STEM system and a Bruker Nano XFlash 6T/60 energy dispersive X-ray (EDX) spectrometer. The imaging and EDX spectroscopy line scans and mapping were carried out in STEM mode with an electron probe of diameter ~ 30 nm. characterization of solid-state phase transformations. The starting 52Rh/48Fe, 45Rh/55Fe and 68Rh/32Fe bilayers were annealed at temperatures ranging from 50 to 800 °C in increments of 50 °C. The samples were held at each temperature at a pressure of 10 −6 Torr for 1 h. To characterize the phase transformations the crystal structure, the magnetic moments m 0 (T a ) (where m 0 (300 K) = M S 0 V), the magnetic fourfold anisotropy constants K 4 (T a ) and the degree of the αʹ → αʺ transition η(T a ) were determined for all bilayers after annealing at each temperature T a . In order to fully characterize the phase transformations, cross-sectional SEM images and an elemental analysis of the phases of several samples using EDX were carried out.
Measurement of the α l ′ → α″ transition degree. In experiments, the degree η(T a ) of the FM-AFM phase transition was determined for all 52Rh/48Fe, 45Rh/55Fe and68Rh/32Fe samples after annealing at each temperature in the range of 100-800 °C . The magnetic moments m 0 (T a ) were measured by the torque method 64 , after annealing at temperature T a and cooling in liquid nitrogen m N (T a ), to find the value of the degree η(T a ). The magnetic moment m(T a ) of the synthesized α l ʹ-FeRh layer in the Rh/α l ʹ-FeRh/Fe(001) trilayer after annealing at temperature T a is equal to the difference m(T a ) = m 0 (T a )-K 4 (T a )m 0 /K 4 0 of the magnetic moments of the m 0 (T a ) film and the K 4 (T a )m 0 /K 4 0 unreacted layer of the Fe(001) layer, where K 4 (T a )m 0 /K 4 0 is the magnetic moments of the unreacted Fe(001) layer. After placing the sample in liquid nitrogen, only the ferromagnetic α l ʹ-FeRh phase in the Rh/α l ʹ-FeRh/Fe(001) trilayer is subjected to the transition into the antiferromagnetic αʺ phase and the magnetic moment m(T a ) is reduced to m N (T a ). The quantity η = 1 − m N (T a )/m(T a ) is a quantitative characteristic of the degree of the α l ʹ → αʺ transition, where η = 0 and η = 1 mean the absence of and the complete FM → AFM transition (residual magnetization is zero), respectively.