Effect of epitaxial strain and lattice mismatch on magnetic and transport behaviors in metamagnetic FeRh thin films

We grew 80 nm FeRh films on different single crystals with various lattice constants. FeRh films on SrTiO3 (STO) and MgO substrates exhibit an epitaxial growth of 45° in-plane structure rotation. In contrast, FeRh on LaAlO3 (LAO) displays a mixed epitaxial growth of both 45° in-plane structure rotation and cube-on-cube relationships. Due to the different epitaxial growth strains and lattice mismatch values, the critical temperature for the magnetic phase transition of FeRh can be changed between 405 and 360 K. In addition, the external magnetic field can shift this critical temperature to low temperature in different rates for FeRh films grown on different substrates. The magnetoresistance appears a maximum value at different temperatures between 320 and 380 K for FeRh films grown on different substrates.


I. INTRODUCTION
FeRh alloy is an antiferromagnetic (AFM) material at room temperature, which has a CsCltype structure with lattice parameter of 2.997 Ǻ.2][3] This metamagnetic transition of FeRh is accompanied by an isotropic expansion in the unit cell volume, which indicates a strong coupling between magnetic and structural properties of FeRh. 3,4Consequently the magnetic and transport properties are changed during the metamagnetic transition of FeRh, for example a significant reduction in resistivity, 2 a large change in entropy, 5 a giant magnetoresistance (MR). 6,7Recently, FeRh in the form of thin films have attracted extensive attentions due to its potential in heat-assisted-magnetic recording (HAMR), micro-electrical-mechanical systems (MEMS), spintronic devices, etc. [8][9][10][11][12][13] In practical applications, the utilizations of FeRh metamagnetic transition are usually preformed at different temperatures, thus the magnetic transition need to be tuned to a required temperature for various applications.In this regard, Walter et al. reported that the addition of elements in FeRh with smaller atomic radius than Rh such as Ru, Os, and Ir could increase the transition temperature of FeRh up to 550 K, while the addition of elements with larger atomic radius such as Pd, V, and Au may decrease it to 150 K. 14 Wayne et al. found that a hydrostatic pressure could increase the transition temperature of FeRh at a rate of 5.75 K/kbar. 15Since most of magnetic devices utilize magnetic materials in thin film forms, it is critically important to realize the control of transition temperature in FeRh films.Recently, produced by ferroelectric BaTiO 3 (001) crystals to shift the transition temperature of epitaxially grown FeRh films about 25 K and to drive the magnetic transition between AFM and FM orders with a small electric field. 11Subsequently, Phillips et al. showed that a local strain driven by the rearrangement of ferroelastic domain in BaTiO 3 can also change both the magnetic order and the magnetic transition of FeRh films at the nanoscale. 13It is well known that a film epitaxially grown on single crystals have a compressive or tensile epitaxial strain due to the lattice mismatch between the substrate and the film grown on it.Therefore, the strain induced by epitaxial growth is an effective way to obtain FeRh films with different transition temperatures, which may satisfy the different requirements for various applications.In this study, in order to produce different epitaxial strains, we grew FeRh films on different single crystals including MgO, SrTiO 3 (STO), and LaAlO 3 (LAO).FeRh films can be grown on STO(001) and MgO(001) with the epitaxial relationship of 45 • in-plane structure rotation.
In contrast, FeRh grown on LAO(001) displays a mixed epitaxial growth with both 45 • in-plane rotation and cube-on-cube epitaxial relationships.The critical transition temperature for FeRh thin films grown on the three kinds of substrates is varied between 405 and 360 K.Moreover, the external magnetic field can lower the transition temperatures at different rates.As a result, the temperature at which the MR reaches maximum value can be tuned at 380, 340, and 320 K for FeRh films grown on STO, MgO and LAO substrates, respectively.

II. EXPERIMENT
FeRh thin films with a thickness of 80 nm were epitaxially deposited on commercial (001)oriented MgO, STO, and LAO single crystal in a magnetron sputtering system with a base pressure below 6.0×10 5 Pa.The substrates were annealed at 600 • C for 1 h in vacuum chamber, and then held at 650 • C during deposition.FeRh films were capped by a 3 nm Ta layer to avoid oxidation before taking it out from the vacuum chamber.The film thicknesses were controlled by the deposition time, which have been calibrated by X-ray reflectivity (XRR).The epitaxial growth of FeRh films was characterized by X-ray in-plane ϕ-scans using an X-ray diffractometer (XRD, Bruker).The temperature dependence of magnetization was characterized by using a magnetic properties measurement system (MPMS, Quantum Design).The magnetic field dependence of resistance was measured at various temperature on a homemade setup based on integrated cryogen free magnet with variable temperature insert (TeslatronPT, Oxford Instruments).

III. RESULTS AND DISCUSSIONS
The X-ray ϕ-scans with a fixed 2θ value at the (011) reflection display a 90 o interval of four peaks.The FeRh peaks are observed at 45 o with respect to the MgO or STO peaks, as respectively shown in Figs.1(a) and 1(b).These features indicate that the FeRh films are grown epitaxially with 45 • in-plane structure rotation on MgO(001) and STO(001) substrates, i.e., the epitaxial relationships of FeRh(001)<110>//STO(001)<100> and FeRh(001)<110>//MgO(001)<100>, as schematically shown in Fig. 1(d).According the lattice constants a, the lattice mismatch values ε are theoretically calculated as -0.53% and -7.8% for FeRh epitaxially grown on MgO (a=4.216Å) and on STO (a=3.905Å), respectively.Due to the rather small lattice mismatch, FeRh/MgO films can be coherently strained throughout the thickness.In contrast, the lattice mismatch in FeRh/STO films is much higher, which cannot stabilize coherent epitaxial growth within the whole film thickness.As a consequence, only a part of FeRh film close to the FeRh/STO interface can be grown according to the relationship of 45 • in-plane structure rotation.Thus, the epitaxial strain in FeRh/STO relaxes with increase in the thickness.The X-ray ϕ-scan performed on FeRh/LAO(001) exhibits two series of FeRh peaks as shown in Fig. 1(c).The four weak reflections are shifted by 45 • with respect to the LAO peaks while the other four strong reflections overlap with the LAO peaks, indicating that there are two types of crystallites grown with both 45 • in-plane structure rotation and cube-on-cube epitaxial relationships in FeRh/LAO films.The theoretical lattice mismatch for FeRh grown on LAO (a=3.792Å) according to the 45 • in-plane structure rotation is -10.5%, which is much larger than that of FeRh/STO.Consequently, the growth of 45 • in-plane structure rotation becomes very unstable because of the accumulation of strain energy.Previously, J. Narayan et al. have shown that in large lattice mismatch systems, the epitaxial growth is possible by matching of domains where the integral multiples of major lattice planes match across the interface. 16In FeRh/LAO(001) film, the majority of epitaxial growth adopts the cube-on-cube relationship with five FeRh unit cells matching four LAO unit cells, the lattice mismatch can be reduced to 1.2%, which is much less than that in the epitaxial grown with 45 o in-plane structure rotation.Therefore a mixed epitaxial growth in FeRh/LAO is observed with minor FeRh(001)<110>//LAO(001)<100> and major FeRh(001)<100>//LAO(001)<100> epitaxial relationships to reduce the strain energy, as schematically shown in Fig. 1(e).Figure 2(a) shows the temperature dependent magnetization of FeRh films grown on STO, MgO, and LAO substrates measured with an in-plane magnetic field of 0.2 T. The magnetization of FeRh films is rather small at room temperature, and then gradually increases in the heating process, indicating a typical AFM-FM phase transition of FeRh.In contrast, the magnetization of FeRh films gradually decreases in the cooling process.A temperature hysteresis of the magnetization can be observed, indicating the first order phase transition of FeRh. 17The transition temperature can be determined from the differential of M-T curves.The critical phase transition temperatures T AFM-FM and T FM-AFM of FeRh/MgO films are obtained at 398 and 382 K for the heating and cooling processes, respectively.Due to a compressive strain of 0.53% imposed by MgO substrate, the AFM-FM phase  transition induced by lattice expansion is shifted to a higher temperature.Similarly, T AFM-FM and T FM-AFM for FeRh/STO film are enhanced to 405 and 383 K, respectively, because of a higher compressive epitaxial strain of 7.8%.In contrast, the transition temperatures of FeRh/LAO film reduce to T AFM-FM = 360 K and T FM-AFM = 310 K due to the tensile strain.The effect of epitaxial strain in FeRh thin films on T AFM-FM and T FM-AFM are summarized in Fig. 2 (b).These experimental results demonstrate clearly that the compressive and tensile epitaxial strains can lead to the increase and decrease of magnetic transition temperature respectively, which is in good agreement with the first-principles calculations in the framework of density-functional theory as reported by the previous work, 11 and indicates that the AFM FeRh phase is favored by a compressive strain.Figure 3 displays the M-T curves for FeRh films on different substrates measured under various external magnetic fields.Upon increasing the magnetic fields from 1 to 7 T, T FM-AFM decreases from 375 to 322 K, from 370 to 328 K, and from 319 to 261 K for FeRh/MgO, FeRh/STO, and FeRh/LAO films, respectively, as shown in Figs.3(a) to 3(c).The magnetic field dependent T AFM-FM and T FM-AFM follow the identical slopes.The calculated slopes from linear fitting are -8.5, -7.1 and -9.7 K/T for FeRh films grown on MgO, STO, and LAO respectively, as shown in Fig. 3(d).The different effects of magnetic field on metamagnetic transition are mainly due to the different epitaxial strains of FeRh films grown on various substrates.Our experimental observations indicate that both the magnetic field and the epitaxial strain can affect the transition temperature.A compressive epitaxial strain, for instance FeRh/STO, could slow the decrease of T AFM-FM and T FM-AFM with magnetic field, while a tensile epitaxial strain, for example FeRh/LAO, could accelerate the decrease of T AFM-FM and T FM-AFM with magnetic field.
In FeRh alloys, the high resistance AFM state is obtained at room temperature, which can be transformed to the low resistance FM state by applying a magnetic field, leading to a large MR effect of about -50%. 18Since the epitaxial strain has a significant influence on the metamagnetic transition temperature, the MR of FeRh films should be different on various substrates.The MR behaviors of FeRh films grown on MgO, STO, and LAO substrates were measured with an in-plane magnetic field up to 10 T in the temperature range from 250 to 400 K.It should be noted that the magnetic field at which the resistance of FeRh film gets saturated is dependent on the epitaxial strain.For example, the resistance of FeRh/LAO film reaches the saturation value at 4.6 T, but for FeRh/MgO not even saturated up to 10 T at the same temperature of 340 K.This phenomenon can be attributed to the different metamagnetic transition temperatures for FeRh on different substrates.The resistance of FeRh/LAO film at 340 K reaches the saturation because majority of FM state is detected due to the low metamagnetic transition temperature.In contrast, the majority magnetic state of FeRh/MgO and FeRh/STO films at 340 K is in AFM state because of the high metamagnetic transition temperature, thus the resistance is hard to get saturation.The MR ratio measured in this work is given by (R H=10 T R 0 )/R 0 , where 10 T was used the maximum magnetic field applied.The MR of FeRh/MgO films increases with increase in temperature, and a maximum value of about -46% appears at 340 K, as shown in Fig. 4(a).Then, the MR value is decreased with further increasing temperature.The MR of FeRh/STO and FeRh/LAO films display the similar temperature dependence, as respectively shown in Figs.4(b) and 4(c).They reach the maximum values of about -40% and -45% at 380 and 320 K, respectively.The temperature dependent MR of FeRh thin films are summarized in Fig. 4 (d).
Obviously, the MR reaches the maximum value at a relative low temperature due to the tensile epitaxial strain in FeRh/LAO films, but in the case of FeRh/MgO and FeRh/STO films the MR value appears at a higher temperature due to the compressive strain.

IV. CONCLUSIONS
In summary, we have studied the epitaxial growth of FeRh films on different single crystals and the influence of epitaxial strain on the metamagnetic transition between AFM and FM phases.For FeRh films on STO and MgO substrates, the epitaxial growth shows a 45 • in-plane structure rotation relationship.In contrast, FeRh on LAO displays a mixed epitaxial growth of both 45 • inplane structure rotation and cube-on-cube relationship.The critical temperature for the magnetic phase transition of FeRh can be changed between 405 and 360 K due to the different growth strains.Upon applying a magnetic field, these critical temperatures decrease at a rate of -8.5, -7.1 and -9.7 K/T for FeRh films grown on MgO, STO and LAO, respectively.The MR reaches a maximum value at 380, 340, and 320 K for FeRh films grown on STO, MgO and LAO substrates, respectively.

FIG. 2 .
FIG. 2. (a) Temperature dependent magnetization for various epitaxial FeRh films in an applied magnetic field of 0.2 T. (b) Epitaxial strain dependent T AFM-FM and T FM-AFM of FeRh thin films on heating and cooling processes.

FIG. 3 . 5 Xie
FIG. 3. Temperature dependent magnetization for FeRh films grown on (a) MgO, (b) STO, and (c) LAO under different magnetic fields.(d) Summary of the magnetic field dependent T AFM-FM and T FM-AFM for different epitaxial FeRh thin films.