Observation of topological Hall effect in Mn2RhSn films

Recently non-collinear magnetic structures have attracted renewed attention due to the novel Hall effects that they display. In earlier work evidence for a non-collinear magnetic structure has been reported for the ferromagnetic Heusler compound Mn2RhSn. Using sputtering techniques we have prepared high quality epitaxial thin films of Mn2RhSn by high temperature growth on MgO (001) substrates. The films are tetragonally distorted with an easy magnetization axis along the c-axis. Moreover, we find evidence for an anomalous Hall effect whose magnitude increases strongly below the Curie temperature that is near room temperature. Consistent with theoretical calculations of the anomalous Hall conductivity that we have carried out by deriving the Berry curvature from the electronic structure of perfectly ordered Mn2RhSn, the sign of the anomalous Hall conductivity is negative, although the measured value is considerably smaller than the calculated value. We attribute this difference to small deviations in stoichiometry and chemical ordering. We also find evidence for a topological Hall resistivity of about 50 nΩ cm, which is ∼5% of the anomalous Hall effect, for temperatures below 100 K. The topological Hall effect signifies the presence of a chiral magnetic structure that evolves from the non-collinear magnetic structure that Mn2RhSn is known to exhibit.


Introduction
Magnetic non-collinear spin textures, such as magnetic bubbles and skyrmions [1][2][3][4][5][6][7][8][9][10], have recently attracted much attention, both from a fundamental as well as a technological perspective. Whilst magnetic bubbles were extensively studied several decades ago as non-volatile magnetic bits in magnetic bubble memory devices, renewed interest in bubbles and related skyrmions arises from the possibility of manipulating these magnetic nano-objects using electrical currents via spin transfer torques [9,[11][12][13][14]. Skyrmions, predicted theoretically many years ago [3,15], have recently been experimentally detected in various materials including single crystals of MnSi via small angle neutron scattering [11], and FeGe via Lorentz transmission electron microscopy (TEM) [6]. In these systems lattices of skyrmion are formed when there is a sufficiently large Dzyaloshinskii-Moriya indirect exchange interaction (DMI) compared to the direct Heisenberg exchange [16,17]. A DMI exchange requires an absence of inversion symmetry, which can also take place at interfaces: recently skymions have been observed in various magnetic thin films deposited on underlayers with sufficiently large DMI [18], but in most cases magnetic fields are required to stabilize skyrmions or the skyrmions are found only at low temperatures. Heusler compounds are a large family of compounds that offer tunability in many key parameters that are needed to engineer novel magnetic states [19]. Heuslers have the general chemical formula X 2 YZ, where X and Y are transition metals, and Z is a main group element. Heuslers with X=Mn have high Curie temperatures. These compounds crystallize in either an inverse cubic or a tetragonal structure when Y is a late transition metal element. Since the DMI interaction originates from spin-orbit coupling, the DMI interaction is typically larger for heavy elements. Thus, the Mn 2 RhSn system [20,21]  moments are fixed and oriented along the c axis but the Mn II moments face competing nearest and next nearest neighbor antiparallel coupling that can lead to canted moments [20].
Neutron diffraction studies of bulk polycrystalline Mn 2 RhSn have revealed a canting of Mn II moments below a spin reorientation transition near ∼80 K [20]. Electronic properties, studied by hard x-ray photoelectron spectroscopy, and the temperature dependence of magnetoresistance in thin films of Mn 2 RhSn have been studied by Meshcheriakova et al [21]. In this work, we report the observation of a temperature dependent topological Hall effect (THE) in thin films of Mn 2 RhSn. The origin of THE is discussed in terms of an additional component to the Berry phase caused by the non-collinear spin arrangement in the Mn 2 RhSn. Our study is relevant for stabilizing magnetic sub-structures such as skyrmions in Heusler thin films, where T C can be tuned to well above room temperature.

Experimental details
Thin films of Mn 2 RhSn were grown on MgO (001) substrates at 350°C using DC magnetron co-sputtering from Mn, Rh and Sn sputter targets. To improve chemical ordering, the films were annealed at the growth temperature for 30 min The annealed films were capped in situ with ∼3 nm thick MgO films that were deposited at room temperature. The film composition was characterized using energy-dispersive x-ray (EDX) microscopy. Structural characterization was carried out using standard x-ray diffractometry using CuK α radiation (λ=1.5406 Å). Magnetization measurements were performed with a vibrating sample magnetometer (MPMS 3, Quantum Design). Transport measurements were carried out in a Quantum Design Dynacool system.

Results and discussions
3.1. Structural characterization Figure 1(a) shows x-ray diffraction patterns for a 40 nm thick Mn 2 RhSn film grown on an MgO (001) substrate and post-annealed at 350°C. A tetragonal structure is confirmed from the diffraction peak positions. As shown in the schematic diagram of the unit cell in the inset to figure 1(a), the Mn atoms occupy two different lattice sites. Mn I have a tetragonal coordination and occupy 2b (0, 0, 1/2) Wyckoff positions. Mn II have an octahedral coordination and occupy 2c (0, 1/2, 1/4) Wyckoff positions. Rh atoms occupy 2d (0, 1/2, 3/4) and Sn atoms occupy 2a (0, 0, 0) Wyckoff positions [22]. 2θ-ω scans were obtained to find (00n) and (112) peaks by an appropriate sample alignment: typical scans are shown in figure 1(a) and its inset, respectively. The out-of-plane (OP) (c) and the in-plane (IP) (a) lattice parameters are thereby determined to be 6.50±0.01 Å and 4.30±0.01 Å, respectively. Thus the c/a ratio is found to be 1.51 which is consistent with a tetragonal structure. These values compare with those of 6.62 Å and 4.29 Å found for bulk material [22]. Strain due to lattice mismatch of the thin films with the MgO (001) substrate (4.21 Å) likely accounts for the difference in values between the thin films and bulk, although small differences in composition and in the chemical ordering could also be responsible. The surface topography of the thin films was analyzed by atomic force microscopy (AFM). Figure 1(b) shows an AFM scan for an area of 3 μm×3 μm of a 40 nm thick film: a r.m.s roughness of 0.6 nm is obtained. TEM was performed to evaluate the film quality at the nanoscale.  figure 2(a). The Curie temperature (T C ) is determined to be 293±4 K by taking the first derivative of the temperature dependence of the magnetization curve. The resulting T C is close to that of 270 K reported earlier for stoichiometric bulk polycrystalline samples [22]: the T C in these earlier studies was found to depend sensitively on the composition of the material so the slightly higher T C that we find in our thin films is likely due to small variations away from the nominal stoichiometry, as indicated by EDX analysis mentioned above.
The magnetization measurements were performed in zero field cooled (ZFC, black solid curve) and field cooled (FC, red solid curve) conditions. The difference in the ZFC and FC curves at low temperatures presumably arises due to the unsaturated magnetic state in the ZFC curve as a result of the high magnetic anisotropy of the tetragonal phase. As expected, the (IP ZFC and FC M versus T curves exhibit a smaller magnetization than that of the OP curves due to the higher magnetic fields required to saturate the magnetization IP. This is confirmed by magnetic hysteresis loops that were obtained at various temperatures after zero field cooling the samples from a temperature above T C . The OP and IP hysteresis loops measured at 50 K are shown in figure 2(b). It can be clearly seen that the easy axis of magnetization is along the c-axis. The saturation field along the c axis is much smaller The coercivities for the OP and IP hysteresis loops are ≈0.06 T and ≈0.026 T at 50 K, respectively. The coercivities vanish near T C .

Hall effect measurements
Non-collinear magnetic structures can give rise to an additional Hall resistance [10]. Hall resistivity ( ) r xy was measured for several Mn 2 RhSn thin films for temperatures between 2 and 290 K using the experimental setup shown schematically in figure 3(a). An IP current was applied along the x-axis, the magnetic field was applied parallel to the z-axis (c) and the Hall voltage (V H ) was measured along the y-axis using fields up to 5 T. Since the dependence of R xx on magnetic field is negligible ( figure 3(a)), so to eliminate the R xx contribution, we have offset the raw R xy at zero field to zero at each temperature. Typical data are shown in figure 3(b). Each measurement was performed after ZFC. r xy is found to be ∼−1 μΩ cm at 2 K which is considerably higher than found in earlier studies on similarly prepared films although these earlier films were protected by a 5 nm thick Rh layer which would shunt current [21]. r xy increases nonlinearly for low fields and linearly for m The low field nonlinear behavior is enhanced for T<100 K. To determine the origin of this nonlinear part of r xy we have used the following relationship where R H, o r , AHE and r THE correspond to the ordinary, anomalous (AHE) and topological Hall effects, respectively. R H o is obtained by a linear fit of r xy between 1 and 5 T as shown in the inset of figure 3(c). The AHE has contributions from intrinsic and extrinsic scattering mechanisms as follows where, r xx is the longitudinal resistivity and the term with α corresponds to intrinsic and side-jump scattering whereas the term with β corresponds to skew scattering. At a fixed T, r xx has a very weak dependence on the magnetic field (shown in figure 3(a)), hence r AHE effectively depends linearly on M. r THE is the contribution from any chiral spin texture present in the material and for > H H , C r THE is expected to be zero. Hence, for and the red solid curve is r AHE obtained at T=2 K. A non-zero value of r THE is obtained at low fields ( ) < H H , C and is shown by the blue solid curve. A maximum of r THE at 2 K is about 50 nΩ cm and is nearly 5% of the total AHE. We have performed a similar analysis for all measured temperatures and found that r THE almost disappears for temperatures above 100 K. The magnitude of r THE observed in Mn 2 RhSn is slightly higher than that found in MnSi [10]. The topological Hall component observed in the present case indicates the presence of a non-collinear spin structure below 100 K which is also observed by neutron diffraction experiments [20]. The finding of such a THE in other materials has been attributed to the presence of chiral magnetic structures such as skyrmions [10]. Thus the observation of a THE in Mn 2 RhSn thin films is evidence for the presence of a chiral magnetic structure. We have observed similar results in similarly grown samples, however a further systematic investigation on thickness and stoichiometry is suggested.

AHE calculation
The band-structure and the Berry-curvature of Mn 2 RhSn was computed using the ASW (LMTO) method [23,24]. The standard local spin-density functional approximation was used. The magnetic structure considered in these calculations was a non-collinear ferromagnetic, as described before [20]. The results obtained are interesting in the details of the Berry-curvature pattern [24]. In figure 4 this is shown in two planes symmetric with respect to the plane through k=0. One recognizes a rotation of the pattern by π/2; this rotation does not lead to canceling contributions in opposite parts of the Brillouin zone but is summed up to give the anomalous Hall conductivity having a value of σ xy =−184 (Ωcm) −1 . To obtain the Hall resistivity one needs the longitudinal resistivity r xx for which we measured a value of ∼470 μΩ cm at 2 K. An experimental value of s xy is which is valid for  r r .
xx xy However, the measured value is much smaller than the calculated value, presumably because of the rather large value of the longitudinal resistivity (see the significantly smaller r xx in [21]). In a similar way as for s , xy we also calculate values of s yz and s zx which are found to be around −8 (Ωcm) −1 , and much smaller than s . xy The anomalous Hall conductivity calculation is performed for a perfect single crystal, perfectly ordered and at 0 K. From the x-ray diffraction, discussed above, we find a FWHM of ∼0.96°for the rocking curve obtained from the (004) peak, indicating the degree mosaicity in the films. Furthermore, the possibility of stoichiometric variations in our films cannot be completely ignored. These factors might account for the low values of the measured Hall conductivities. But the rather high value of the longitudinal resistivity could also be a result of these factors.

Conclusion
We find evidence of a significant anomalous Hall conductivity in thin single crystalline films of the Heusler compound Mn 2 RhSn below its Curie temperature, whose sign is consistent with theoretical calculations. Below ∼100 K evidence for a small THE is found that is indicative of a chiral or helical magnetic ordering beyond a simple non-collinear magnetic ordering.