Transition from Anomalous Hall Effect to Topological Hall Effect in Hexagonal Non-Collinear Magnet Mn3Ga

We report experimental observation of large anomalous Hall effect exhibited in non-collinear triangular antiferromagnet D019-type Mn3Ga with coplanar spin structure at temperatures higher than 100 K. The value of anomalous Hall resistivity increases with increasing temperature, which reaches 1.25 μΩ · cm at a low field of ~300 Oe at room temperature. The corresponding room-temperature anomalous Hall conductivity is about 17 (Ω · cm)−1. Most interestingly, as temperature falls below 100 K, a temperature-independent topological-like Hall effect was observed. The maximum peak value of topological Hall resistivity is about 0.255 μΩ · cm. The appearance of the topological Hall effect is attributed to the change of spin texture as a result of weak structural distortion from hexagonal to orthorhombic symmetry in Mn3Ga. Present study suggests that Mn3Ga shows promising possibility to be antiferromagnetic spintronics or topological Hall effect-based data storage devices.

effect (THE) 14 . THE has been proposed to appear in presence of non-coplanar spin configurations and therefore it may occur in antiferromagnetic materials with highly non-collinear and non-coplanar spin structure 15 . Onoda et al. pointed out that there are two mechanisms causing THE. One is the presence of inequivalent multiple loops in the unit cell, i.e. THE in Nd 2 Mo 2 O 7 16 , while other one is spin texture hosting the spin chirality, whose size is much larger than the lattice constant, i.e. THE in MnGe 17 , FeGe 18 , MnSi 19 with B20 crystal structure and MnNiGa with a layered Ni 2 In-type hexagonal structure 20 .
In this study, we report that besides the large AHE in non-collinear antiferromagnet Mn 3 Ga at room temperature, like in Mn 3 Sn and Mn 3 Ge 10, 11 , a large topological-like Hall effect appears at temperatures below 100 K accompanying with a weak structural transition. It is analyzed that THE is attributed to non-coplanar spin systems due to a small component of spin cant towards c axis in low temperature phase.

Results and Discussion
Figure 2(a) shows XRD patterns measured at room temperature for Mn 3 Ga plate sample heat treated at 893 K. All diffraction peaks are indexed to be D0 19 type hexagonal structure with space group P63/mmc. The lattice parameters were calculated to be a = 5.4010 Å and c = 4.3945 Å, which are close to those reported previously 7 . Figure 2(b) shows field cooling (FC) and field heating (FH) curves measured at 100 Oe field from 350 K → 5 K → 350 K for hexagonal Mn 3 Ga. The magnetization gradually increases with decreasing temperature up to T t1 = 140 K, then followed by a great decrease with further cooling within 140~111 K. During heating, a reverse jump starting at T t2 = 100 K and finishing at 144 K can be clearly observed. The jump of M-T curve and existence of hysteresis between FC and FH jumps, together with the previous report that XRD confirmed hexagonal structure slightly distorts to an orthorhombic one at temperatures lower than 170 K in this alloy 7 , it is implied that a weak structural transition occurs in our alloy. AC susceptibility varying with temperature under different driving frequencies in the presence of 5 Oe ac field after zero field cooling to 5 K was measured. Inset of Fig. 2 shows the temperatre dependence of real part (χ′) of AC susceptibility. χ′-T curve shows one clear peak at 140 K, which does not present any frequency dispersion, meet with the feature of the structural transition 21 . Figure 3(a) and (b) show Hall resistivity ρ xy as a function of magnetic field at different temperatures. ρ xy increases rapidly with increasing magnetic field in very low fields exhibiting a clear hysteresis loop. Notably, at temperatures below 100 K, the shape and magnitude of ρ xy almost does not change with temperature, as shown in Fig. 3(a). ρ xy is negative for negative fields and positive for positive fields. At temperatures higher than 100 K, all the curves have similar shape. ρ xy increases rapidly initially followed by a great decrease with increasing field, peak value of ρ xy increases with increasing temperature, while at higher fields ρ xy decreases with increasing temperature. Furthermore, the sign of spontaneous Hall effect changes at temperatures higher than 100 K(see Fig. 3(b)). This temperature range for sign change is consistent with that of structural transition from hexagonal to orthorhombic phase. It was observed that one half of the curve of ρ xy at 100 K has the characteristic of lower temperature curves and another half has shape of high temperature curves, implying that the sample stays an intermediate transition state at 100 K. Figure 3(c) shows magnetic hysteresis curves (M-H) at different temperatures, exhibiting the same hysteresis behavior as Hall resistivity but with different curve shape, which is a striking feature for Hall effect of Mn 3 Ga. The magnitude of magnetization decreases with increasing temperature. The saturation magnetization decreases rapidly from 12 to 5 emu/g with temperature increasing from 125 K to 300 K. However, the peak value of ρ xy increases with decreasing saturation magnetization, which reaches 1.25 μΩ cm at a small field of ~300 Oe at room temperature. Since the shape of magnetization curves is different from that of Hall resistivity in this temperature range, ρ xy cannot be attributed to common AHE as observed in ferromagnets. Simultaneously, previous neutron diffraction measurements and theoretical analysis clarified inverse triangular spin structure of hexagonal Mn 3 Ga alloy with Mn moments lying in a-b plane 6 . Because of the in-plane coplanar magnetic spin structure, the shape deviation from the magnetization curves cannot attribute to THE, which stems from non-coplanar spin structure. Behavior of these curves for Mn 3 Ga is similar to that observed in Mn 3 Sn alloy 10 , which is considered to be arising from non-collinear antiferromagnetic spin structure. This additional contribution to the AHE, associated with non-vanishing Berry curvature due to non-collinear spin structure, results in the Hall resistivity features that do not resemble the magnetization curves. The value of anomalous Hall resistivity at room temperature is about 0.5~4 μΩ cm in Mn 3 Sn and Mn 3 Ge single crystal samples 10,11 , which is different in different crystallographic directions. Furthermore, the AHE present opposite sign in specified crystallographic directions (see Fig. 2 in both refs 10 and 11), showing strong anisotropic behavior. Our Mn 3 Ga sample is polycrystalline, the anomalous Hall resistivity is an average effect, thus the shape of curves is a little different from the single crystals of Mn 3 Sn and Mn 3 Ge.
Comparably, as temperature falls below 100 K, although magnetization decreases with increasing temperature, ρ xy -H curves almost do not change with temperature. Simultaneously, a hump-like anomaly can be clearly observed, which is considered as a unique symbol of THE 17 . These feathers indicate the appearance of THE in our Mn 3 Ga, as has been reported in MnSi 17 , FeGe 18 , MnGe 19 , and MnNiGa 20 alloys, which has been a distinction for the prominent non-planar magnetic configurations, i.e. spin chirality or magnetic winding. Hexagonal structure of Mn 3 Ga can slightly distort to an orthorhombic one at low temperatures, giving rise to a larger deviation of spin structure from the ideal triangular spin configuration compared with hexagonal structure 7 . This may result in a small component of spins canting towards the c axis at low temperature phase, as evidenced by increase of magnetization. This is necessary for the formation of scalar spin chirality. Thus, an interesting THE is observed.
The anomalous Hall conductivity (AHC) σ xy = −ρ xy /ρ xx 2 (satisfy ρ xx ≫ ρ xy ), where ρ xx is normal resistivity, has been calculated when temperature is higher than 100 K, as shown in Fig. 3(d). σ xy increases firstly, reaching a large value of ~17 (Ω · cm) −1 at a small field of ~300 Oe, and then followed by a great decrease. The absolute value of σ xy at 5 T increases with decreasing temperature, which is only 0.6 (Ω · cm) −1 at 300 K and nearly 15 (Ω · cm) −1 at 125 K. Theoretical calculations predicted that non-collinear antiferromagnet Mn 3 Ga exhibits the smallest AHC among Mn 3 Ge, Mn 3 Sn, and Mn 3 Ga 22 . Previous reports found that the AHC for Mn 3 Ge and Mn 3 Sn are 50, 20 (Ω · cm) −1 , respectively 10,11 . Both values are larger than the AHC for Mn 3 Ga, which has a value of 17 (Ω · cm) −1 . These experimental results are fully consistent with recent theoretical predication 22 .
To investigate low temperature THE deeply, the initial Hall resistivity ρ xy of Mn 3 Ga was measured at different temperatures, as shown in Fig. 4(a) , where R 0 is ordinary Hall coefficient, ρ S A xx 2 corresponds to AHE coefficient due to magnetization behavior and S A is H-independent parameter, H is magnetic field perpendicular to the sample plane, and M is the corresponding magnetization. To calculate ρ xy T , we must subtract both normal  Fig. 2(b) is temperature dependence of the real part (χ′) of AC susceptibility measured at different frequencies with an ac magnetic field of 5 Oe after zero field cooling to 5 K. and anomalous Hall resistivity from total Hall resistivity ρ xy . It should be pointed out that these equations are valid in weak magnetic field for which ω c τ ≪ 1, where ω c = eB/m is the cyclotron frequency, τ = m/ne 2 ρ xx is electron scattering time and m is electron mass 15 . Normal Hall coefficient R 0 , effective carrier density n, τ and calculated ω c τ up to the maximum applied field of 5 T at different temperatures are listed in Table 1. In the present study, we obtained ω c τ = BR 0 /ρ xx ~ 0.001, which satisfies the condition of ω c τ ≪ 1 15 . This indicates the feasibility of above method to obtain topological resistivity. Figure 4(b) shows magnetization curves at different temperatures with field perpendicular to the sample plane. Figure 4( in high magnetic field regions. Table 1 gives R 0 and S A at different temperatures. It is observed that R 0 is positive, ~10 −10 Ωm/T, suggesting hole-like conduction of the sample. The corresponding effective charge carrier density n is ~10 28 holes/m 3 . Simultaneously, R 0 increases with increasing temperature from 5 K to 70 K. The difference between total Hall resistivity ρ xy and fitting curve ρ at H < H c equals to topological resistivity ρ xy T . For instance, in Fig. 4 is in good agreement with experimental data. Figure 4(e) shows ρ xy T at different temperatures extracted from total Hall resistivity ρ xy . It was found that topological Hall resistivity is nearly temperature independent, which is in agreement with the feature of THE. Furthermore, the value of topological Hall resistivity increases initially and then decreases with further increasing field, showing a peak behavior. This hump-like anomaly is considered as a typical symbol of THE 19,23 . The peak value of ρ xy T for each temperature increases rather slowly with increasing temperature, as given in Table 1.
Maximum peak value of ρ xy T is about 0.255 μΩ · cm, which is larger than that for bulk MnNiGa (ρ xy T = 0.15 μΩ · cm) 20 and MnGe (ρ xy T = 0.16 μΩ · cm) 17 . Contour mapping of derived ρ xy T value is shown in Fig. 4(f). The magnitude of ρ xy T is nearly T-independent across a broad temperature range from 90 K to 5 K. It has been suggested that the THE is induced by fictitious magnetic field caused by non-vanishing Berry phase in non-collinear spin arrangment    Table 1. Normal Hall coefficient (R 0 ), effective carrier density (n), electron scattering time (τ), calculated ω c τ (ω c the cyclotron frequency), S A corresponds to AHE coefficient due to magnetization behavior, and the maximum value of ρ xy T at different temperatures. τ, ω c , ω c τ are calculated for the maximum applied field of 5 T.
antiferromagnet 12 . THE is generally considered as a hallmark of magnetic skyrmions that has topological spin textures, as observed in MnGe 17 , MnSi 19 and MnNiGa 20 alloys, so we can speculate that our sample may possess magnetic skyrmions, which are promising materials for technological applications in magnetic storage and other spintronic applications 24 . It would be amusing to confirm this possibility in future studies.

Conclusion
In summary, we report an experimental observation that a large anomalous Hall effect exhibits in non-collinear triangular antiferromagnet Mn 3 Ga at temperatures above 100 K. The value of anomalous Hall resistivity increases with increasing temperature. As the temperature is lower than 100 K, a topological-like Hall effect up to 0.255 μΩ · cm is observed due to the spin texture change resulting from the weak structural distortion from hexagonal to orthorhombic phase in Mn 3 Ga. The present study provides a possible candidate material for magnetic skyrmions, which will have great potential applications in future high-performance spintronic devices.

Methods
Sample preparation and structure characterization. Polycrystalline Mn 3 Ga button ingot was prepared using an arc melting furnace in argon atmosphere from high purity (99.99 %) elemental metals. The ingot (~5 g) was heat-treated at 893 K for 3 days in vacuum followed by quenching into ice water. The structure of the sample was characterized by X-ray diffraction (XRD) technique using a Philips X'Pert MPD instrument with Cu Kα radiation.
Magnetic and transport measurements. To measure magneto-transport properties, the polycrystalline crystal was milled into a bar-shape with a typical size of about 3.0 × 1.0 × 0.04 mm 3 . The longitudinal and Hall resistivities were measured using a standard four probe method on the same sample with Physical Properties Measurement System (PPMS, Quantum Design, Inc.). Field dependence of Hall resistivity was obtained by subtracting the longitudinal resistivity component, while the field dependence of the longitudinal resistivity was obtained by subtracting the Hall resistivity component. The zero-field remanent magnetization, M, was also measured using same field-cooling procedures as used in both longitudinal and Hall resistivity measurements using PPMS. Magnetization hysteresis curves and AC susceptibility were also measured for the same bar sample with PPMS system.