Anomalous and topological Hall effects in epitaxial thin films of the noncollinear antiferromagnet Mn$_{3}$Sn

Noncollinear antiferromagnets with a D0$_{19}$ (space group = 194, P6$_{3}$/mmc) hexagonal structure have garnered much attention for their potential applications in topological spintronics. Here, we report the deposition of continuous epitaxial thin films of such a material, Mn$_{3}$Sn, and characterize their crystal structure using a combination of x-ray diffraction and transmission electron microscopy. Growth of Mn$_{3}$Sn films with both (0001) c-axis orientation and (40$\bar{4}$3) texture is achieved. In the latter case, the thin films exhibit a small uncompensated Mn moment in the basal plane, quantified via magnetometry and x-ray magnetic circular dichroism experiments. This cannot account for the large anomalous Hall effect simultaneously observed in these films, even at room temperature, with magnitude $\sigma_{\mathrm{xy}}$ ($\mu_{0}H$ = 0 T) = 21 $\mathrm{\Omega}^{-1}\mathrm{cm}^{-1}$ and coercive field $\mu_{0}H_{\mathrm{C}}$ = 1.3 T. We attribute the origin of this anomalous Hall effect to momentum-space Berry curvature arising from the symmetry-breaking inverse triangular spin structure of Mn$_{3}$Sn. Upon cooling through the transition to a glassy ferromagnetic state at around 50 K, a peak in the Hall resistivity close to the coercive field indicates the onset of a topological Hall effect contribution, due to the emergence of a scalar spin chirality generating a real-space Berry phase. We demonstrate that the polarity of this topological Hall effect, and hence the chiral-nature of the noncoplanar magnetic structure driving it, can be controlled using different field cooling conditions.

2 Antiferromagnets (AF) are of interest for spintronic applications [1], in particular topological materials [2], that can provide the large read-out signals required through electrical signatures such as the intrinsic anomalous Hall effect (AHE) [3]. Mn3Sn is a noncollinear AF with Mn moments arranged in hexagonal crystal planes [4], which exhibits an inverse triangular spin structure resulting from a combination of exchange and Dzyaloshinskii-Moriya (DM) interactions [5]. The inverse triangular AF order breaks time-reversal symmetry, thus introducing a fictitious magnetic field generated by momentum-space Berry phase, which has been theoretically predicted [6] to drive a highly anisotropic AHE [7]. This was subsequently experimentally measured in single crystals of Mn3Sn [8] (as well as in Mn3Ge [9]). Berry curvature is connected with the presence in Mn3Sn of Weyl quasiparticles [10][11][12], which generate an anomalous Nernst effect [13][14][15]. Further enhancement of the attractiveness of Mn3Sn for spintronics stems from its hosting of an intrinsic spin Hall effect [16][17][18] (originally discovered in the cubic noncollinear AF Mn3Ir [19]).
The inverse triangular spin texture also gives rise to a magneto-optical Kerr effect [20][21][22], which reveals that Mn3Sn contains AF domains possessing opposite chiralities of a cluster octupole order parameter [23] and, hence, opposite polarity of magnetotransport effects [24]. These chiral domains can be propagated [22] by coupling an external magnetic field to the small uncompensated magnetic moment [25] that is created in Mn3Sn by spins canting slightly towards magnetocrystalline easy axes [26]. This weak magnetization can freely rotate within the basal plane [5], acting to orient the entire inverse triangular spin structure into a single chiral domain state.
As Mn3Sn is cooled, its magnetic order changes depending on microstructure [27]. At 275 K, Mn-deficient samples transition to a helical magnetic phase [28]. Around 50 K, the magnetic structure changes to a 'glassy' ferromagnetic (FM) (or spin glass) state Recently, AHE has been measured in polycrystalline Mn3Sn films [35][36][37], as has a planar Hall effect in epitaxial films [38]. In this Rapid Communication, we extend these results by demonstrating both AHE and THE in epitaxial thin films of Mn3Sn.
We previously grew Mn3Sn films that were epitaxial but discontinuous [39]. By changing substrate and optimizing post-annealing temperature, we succeeded in fabricating continuous Mn3Sn films (details in the Supplemental Material). Fig. 1(a) shows 2θ-θ x-ray diffraction (XRD) patterns measured for films deposited on SrTiO3 (111) and MgO (001) substrates. In both cases, a 5 nm Ru buffer layer was used We studied film structure at the nanoscale using transmission electron microscopy (TEM). Fig. 1(b) shows a cross-section scanning-TEM micrograph from a 70 nm film deposited on SrTiO3 (111), which demonstrates explicitly the epitaxial growth of (0001) oriented Mn3Sn on a Ru (0001) buffer. The inset of Fig. 1(b) displays a wideview scanning-TEM image of the same lamella, confirming the preparation of continuous films.  Fig. 1 wide-view TEM images, an example of which is shown in the inset of Fig. 1(e).
Finally, we used atomic force microscopy to quantify the roughness of Mn3Sn. An example topographic map is shown in the inset of Fig. 1(d), which yields an average roughness of ≈ 0.5 nm over a 1 µm 2 region of a 50 nm Mn3Sn (404 ̅ 3) film capped with 2 nm Ru. With magnetic field applied along one of two orthogonal IP directions, a similar hysteretic behavior is observed, but with a smaller magnitude and an isotropic response. This is because magnetization is averaged over many crystallites, which can be four-fold symmetrically oriented with either [011 ̅ 0] (in the plane where 5 uncompensated moment freely rotates) or partially IP [0001] (hard axis) directions parallel to the magnetic field. The inset of Fig. 2(a) plots magnetization response to magnetic field at different temperatures (T). At 5 K, a significant enhancement of magnetization demonstrates the appearance of the glassy FM phase [29].
X-ray magnetic circular dichroism (XMCD) was measured at the BESSY synchrotron facility [40], using negative, σ-, polarized x-rays in an OP magnetic field of µ0H± = ± 8 T. Non-zero XMCD around the Mn L2,3 edges at 100 K, displayed in Fig. 2 confirms the presence of a net Mn moment that is reversible by external magnetic field. Using XMCD sum rule analysis [41], an uncompensated magnetic moment of ms+l = 0.279 µB/f.u. was calculated, comprising of spin, ms = 0.273 µB/f.u., and orbital, ml = 0.006 µB/f.u., moments respectively. Measured ml is of the same order of magnitude as that simulated [25], whilst ms is found to be substantially larger than the theoretically predicted value for zero-field weak magnetization.
We explain this by considering the inset of Fig. 2(b), showing the magnetic field dependence of XMCD, measured as in Ref. [42]. XMCD increases approximately linearly, because of Mn spins tilting out of the film plane in response to strong applied magnetic fields [42]. This therefore enhances ms, whose magnitude is in agreement with that determined from SQUID-VSM, which indicates similar paramagnetic behavior after the closing of the hysteresis loop. In addition, such SQUID-VSM measurements reveal that the remnant uncompensated moment within the basal plane is enhanced compared with bulk crystals. This may be exacerbated by structural defects and chemical disorder acting to modify the balance of AF exchange, DMI interactions and magnetocrystalline anisotropy that governs the spontaneous canting of Mn spins [39].
The inset of Fig. 2(b) also presents XMCD measured in a -8 T magnetic field at different temperatures. XMCD is reduced at 300 K, whilst its enhancement at 5 K evidences an increased net moment after transition to the spin glass state.
We now report on magnetotransport measurements in Mn3Sn thin films lithographically patterned into 75 × 25 µm 2 Hall bar devices. Fig. 3(a) shows the variation in longitudinal resistivity (ρxx) for a 70 nm thick Mn3Sn (0001) film as a 6 function of temperature, during either zero-field cooling (ZFC) or cooling in a 7 T OP magnetic field (FC), followed in both cases by zero-field warming (ZFW). A background contribution from the 5 nm Ru buffer layer has been subtracted (see Supplemental Fig. S2). On cooling, a deviation from metallic behavior below 100 K, down to a bump in resistivity close to 50 K, provides evidence for the transition to the glassy FM phase. No change is observed between ZFC and FC protocols, as expected with cooling field parallel to the [0001] hard axis.
During subsequent ZFW, a thermal hysteresis is seen, with resistivity dipping between 50 K and 100 K. The resulting drop in resistivity is maintained until the film is warmed above room temperature. This may indicate that the transition from the inverse triangular to glassy FM state during cooling is not fully reversible until close to the Néel temperature (TN = 420 K [4]), for example due to pinning of the magnetic structure at AF domain walls discussed below.  Hall effect in Mn3Sn single crystals, attributed to domain walls whose internal moment configuration is maintained during forward and reverse field sweeps (but whose sense of rotation is inverted). They also observe a dependence of the planar Hall effect polarity on applied field history.
We measure a similar magnetic state history in Mn3Sn (404 ̅ 3) films. The inset of Fig.   4(b) shows that, when the thin film is ZFC after saturation in a -9 T OP magnetic field, the polarities of both symmetric THE peaks invert. This represents a sign change of real-space Berry phase, corresponding to an opposite sign of the finite scalar spin chirality generating it. We propose, therefore, that the handedness of the inverse triangular spin texture set at room temperature favors a certain chirality of domain wall formed during low temperature magnetization reversal.
Furthermore, the THE bumps with either negative or positive polarity are enhanced after cooling in a +9 T or -9 T OP magnetic field respectively. This may be explained by the external field further stabilizing the preferred domain wall moment configuration during cooling. We thus demonstrate a memory effect in noncollinear AF thin films, that can be controlled by setting the orientation of the inverse triangular spin texture from which the chirality of domain walls evolves, which may find applications in neuromorphic computing.
In conclusion, we have grown epitaxial thin films of Mn3Sn with both (0001) c-axis orientation and (404 ̅ 3) crystallographic structure. In the latter case, Berry curvature driven AHE is observed at room temperature. Upon cooling through the magnetic phase transition at 50 K, a peak in the Hall resistivity indicates the appearance of a THE. The sign of this THE signal, and hence the chirality of the noncoplanar spin texture generating it, can be manipulated through cooling field conditions, thus furthering the potential of Mn3Sn in chiralitronic devices.    sweeps respectively). Inset shows magnetization as a function of out-of-plane magnetic field, measured at different temperatures. (b) XAS and XMCD spectra for a 70 nm Mn3Sn (404 ̅ 3) film, recorded using σpolarized x-rays in µ0H± = ± 8 T magnetic fields applied out-of-plane, at 100 K. Inset shows XMCD, calculated as the difference between spectra recorded with σ± polarized x-rays, measured in different out-of-plane magnetic fields at 100 K, as well as that measured in -8 T at 300 K and 5 K.

Anomalous and topological Hall effects in epitaxial thin films of the noncollinear antiferromagnet Mn3Sn
James M.

I -Thin film growth and structural characterization
The epitaxial thin films samples of Mn3Sn utilized in this study were deposited using magnetron sputtering following the procedure described in Ref.
[39] of the Main Text.
However, in this case single crystal substrates of either (111) cut SrTiO3 or (001) cut MgO were used to seed either (0001) c-axis texture or (404 ̅ 3) orientation respectively. In order to achieve continuous films, we made modifications to the temperatures during growth and post-annealing of the different layers. The Ru buffer layer was grown at 400°C, and allowed to cool to room temperature. Mn and Sn were then co-sputtered at room temperature, and the films post-annealed by heating to 300°C at a rate of 10°C / minute, holding for 10 minutes, then allowing to cool back to room temperature over a period of approximately 60 minutes.
Stacks were subsequently capped with 2.5 nm Al, which partially oxidizes, thus protecting the Mn3Sn without shorting too much current during transport measurements. Since the surface of the resulting Al(Ox) is rough, samples used for AFM measurements were capped with 2 nm Ru, which follows the topography of the underlying Mn3Sn closely, thus allowing an accurate quantification of its roughness.
Additional reference samples, consisting of either 30 nm or 5 nm Ru buffer layers alone, grown on MgO (001) and MgO (111) substrates respectively, were also prepared. Due to the proximity of the sets of peaks in 2θ-θ position, the pole figure scans of the Ru 〈0002〉 reflections shown in Fig. 1(d) of the Main Text were measured from the 30 nm Ru buffer reference film. Meanwhile, the 5 nm reference sample was used to measure the contribution of the Ru to electrical transport, discussed below, and to record the background magnetization contribution from the substrate and buffer layer (subtracted from the total signal measured by SQUID-VSM, as explained in the discussion around Fig. 2(a) of the Main Text).
The composition of the thin film stacks was quantified, by energy dispersive x-ray spectroscopy measured in a scanning electron microscope, as Mn0.76Sn0.24. We denote this as Mn3Sn, although we point out that the films grow with a slightly Mn-rich composition (and are thus not expected to show a first-order phase transition to a helical magnetic state below 275 K).  By setting the diffractometer to the 2θ-θ position of each of these partially IP peaks and scanning the rotational angle, ϕ, the azimuthal scans in the inset of Fig. 1(a)

II -Contribution of Ru buffer layer to electrical transport properties
The metallic Ru buffer layer will act to short some electric current during transport Mn3Sn films), means that the buffer layer will make a minimum contribution to the overall magnetotransport behavior of the full stack.

III -Thickness dependence of AHE in Mn3Sn (404 ̅ 3) thin films
To demonstrate the negligible magnetotransport contribution of the Ru layer Text. Although the magnitude of Hall resistivity decreases as thickness decreases, we otherwise observe no qualitative change in the AHE generated by the topology of the noncollinear AF structure. In particular, the coercive field, which reflects the reversal of the handedness of the inverse triangular AF spin texture through a mechanism of chiral domain nucleation and propagation (and is enhanced by the 6 pinning of AF domain walls at crystallite grain boundaries as discussed above), remains the same across the thickness series.
In order to compare this thickness dependence of AHE directly with previous studies, we calculate Hall conductivity (σxy = ρxy / ρxx 2 ) for the Mn3Sn (404 ̅ 3) films of different thickness, using their simultaneously measured longitudinal resistivity, as plotted in the right-hand panel of Supplemental Fig. S3. The Hall conductivity remains broadly the same across the thickness series, with a small decrease observed for the 30 nm film, which may reflect a reduction in crystal structure quality at such low thickness.
We extract a typical remnant Hall conductivity of σxy (µ0H = 0 T) = 21 Ω -1 cm -1 , which, whilst small than that measured for bulk single crystals [8], is larger than the planar of equal magnitude and with the same coercive field, is observed in devices down to

Figure Captions
Supplemental