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Emergence of the topological Hall effect in a tetragonal compensated ferrimagnet Mn2.3Pd0.7Ga

Topological spin textures such as magnetic skyrmions have attracted considerable interest due to their potential application in spintronic devices. However, there still remain several challenges to overcome before their practical application, for instance, achieving high scalability and thermal stability. Recent experiments have proposed a new class of skyrmion materials in the Heusler family, Mn1.4Pt0.9Pd0.1Sn and Mn2Rh0.95Ir0.05Sn, which possess noncollinear magnetic structures. Motivated by these experimental results, we suggest another Heusler compound hosted by Mn3Ga to overcome the above limitations. We fabricate Mn3-xPdxGa thin films, focusing on the magnetic compensation point. In Mn2.3Pd0.7Ga, we find a spin-reorientation transition around TSR = 320 K. Below the TSR, we observe the topological Hall effect and a positive magnetic entropy change, which are the hallmarks of a chiral noncollinear spin texture. By integrating all the data, we determine the magnetic phase diagram, displaying a wide chiral noncollinear spin phase even at room temperature. We believe that this compensated ferrimagnet shows promise for opening a new avenue toward chiral spin-based, high-density, and low-power devices. An alloy with room temperature properties useful in energy-efficient information processing has been developed by scientists in South Korea. Materials obtain their magnetic properties from an intrinsic property of fundamental particles called spin. Harnessing spin for information processing, known as spintronics, offers a low-power complement to conventional electronics but finding materials exhibiting appropriate stable magnetic properties at everyday temperatures is challenging. Myung-Hwa Jung and colleagues from Sogang University in Seoul have created a material in which the spins are arranged into a distinct pattern at room temperature. The material consisted of thin films of a gallium–manganese alloy which were then ‘doped’ with palladium to form Mn2.3Pd0.7Ga. The team observed that the spins formed chiral patterns useful for spintronics at temperatures up to approximately 47 °C. The tetragonal Mn3-xPdxGa becomes compensated ferrimagnet at x = 0.7. In the compensated ferrimagnet, Mn2.3Pd0.7Ga, we observed spin reorientation and topological Hall effect due to the strong spin-orbit coupling and inversion symmetry breaking by Pd atoms. We revealed that this additional Hall behavior is attributed to non-collinear spin configuration such as magnetic skyrmions. Our observations are expected that Mn-based compensated ferrimagnets are promising and will open a new avenue toward spintronic high-density and low-power devices.


Introduction
Topologically protected spin phases, such as magnetic skyrmions, show promise for future applications in nonvolatile memory and spintronic devices after being initially observed in MnSi bulk material [1][2][3][4] . To date, various mechanisms for generating this intriguing magnetic phase have been theoretically and experimentally identified, such as long-range magnetic dipolar interactions competing with perpendicular magnetic anisotropy [5][6][7] , Dzyaloshinskii-Moriya (DM) interactions 2 , the interplay of Ruderman-Kittel-Kasuya-Yosida (RKKY) and four-spin exchange interactions 8 , and geometrically frustrated spin systems 9 . These mechanisms operate separately or in tandem to generate skyrmion phases in many chiral magnets. An unconventional spin texture with scalar spin chirality acts as an effective magnetic field, resulting in the topological Hall effect (THE) 10,11 . Thus, the THE is often interpreted as a signature of a chiral spin texture, such as a magnetic skyrmion. Recently, in Mn-based tetragonal Heusler compounds such as Mn 1.4 Pt 0.9 Pd 0.1 Sn 12, 13 and Mn 2 Rh 0.95 Ir 0.05 Sn 14 , it has been reported that the other spin chirality of the antiskyrmion lattice is stabilized via strong spin-orbit coupling and structural symmetry breaking by Pd and Ir doping. However, despite the observation of a chiral spin texture in a variety of materials, there are some issues that must be overcome before their practical application. First, the spin chirality needs to be stabilized at room temperature so that it is not disturbed by thermal fluctuations 15 . Second, a low saturation magnetization is required to produce a small stray field for high-density devices 14 . For the above examples, the antiskyrmion state in Mn 2 Rh 0.95 Ir 0.05 Sn is stable up to 400 K, but the total magnetic moment is considerably high (~4 μ B /f.u.) 12 . On the other hand, the magnetization value of Mn 2 Rh 0.95 Ir 0.05 Sn is relatively low (~1 μ B /f.u.), but the antiskyrmion state emerges at lower temperatures up to~250 K 14 . As a potential candidate for designing stable skyrmions at room temperature together with a low saturation magnetization to overcome the aforementioned issues, we focus on a Mn 3 Ga host Heusler compound. More detailed comparisons with other materials hosting chiral spin textures are listed in Table S1 of the Supplementary Information.
The undoped compound Mn 3 Ga is ferrimagnetic with a Curie temperature of T C = 820 K and crystallizes in a D0 22 tetragonal structure with perpendicular magnetic anisotropy (PMA) 16 . Two inequivalent Mn sublattices, Mn I and Mn II, possess different magnetic moments of 3.1 μ B /f.u. and 4.2 μ B /f.u., which are coupled antiferromagnetically and lead to a total magnetization of 1.1 μ B /f.u. 17 . Interestingly, a recent neutron scattering experiment revealed that tetragonal Mn 3 Ga has an inplane tilted spin structure ( Fig. 1a) 17 , where the magnetic moment at the Mn II site is fixed along the c-axis and the direction of the magnetic moment at the Mn I site is tilted in the ab plane, leading to an in-plane magnetic component at low magnetic fields. Additionally, there is oscillatory exchange coupling from the first and second nearest neighbors depending on the distance between the Mn sublattices 17 . Moreover, previous studies reported that the magnetic properties of Mn 3 Ga can be tuned by substituting a transition metal for Mn II in Mn 3-x Y x Ga, such as Y = Pt, Pd, Co, and Ni, and can be fully compensated with a zero net magnetic moment 18 . A typical example of magnetic compensation is when Y = Pt 18,19 . The net magnetization changes from ferrimagnetic to completely compensated at x = 0.65 in Mn 3-x Pt x Ga, demonstrating a fully compensated ferrimagnetic state. However, there has been no report on the THE being observed at the magnetic compensation point in Mn 3- x Pt x Ga, where the noncollinear spin texture is maximally expected 19 . This is compared to Mn 1.4 Pt 0.9 Pd 0.1 Sn, in which they reported a spin-reorientation transition from a collinear ferromagnetic to a noncollinear configuration below T SR = 135 K, accompanied by the topological Hall effect but with no magnetic compensation 20 . Among the magnetic interactions mentioned above, the role of DM interactions is essential to lead to scalar spin chirality. The crucial elements of DM interactions are strong spin-orbit coupling and structural symmetry breaking 21 . Thus, we deduce the possibility of forming scalar spin chirality through heavy metal substitution in Mn 3 Ga. Heavy metals can act as crucial elements of DM interactions for strong spin-orbit coupling and structural symmetry breaking. Recently, the observation of positive magnetic entropy was proposed to be additional evidence of skyrmion formation 22 . The magnetic entropy change is interpreted as a transition from magnetic order to disorder states. For example, when a system in an external field transits from an ordered spin state such as a fully saturated ferromagnetic phase (low entropy) to a highly disordered spin state such as a skyrmion phase (high entropy), the change in magnetic entropy becomes positive 22 . The magnetic entropy change can be measured using isothermal magnetization with a constant temperature interval 22,23 .
In our study, we chose the 4d element Pd as the substitution atom because, compared to the 5d element Pt, Pd is well magnetized and is expected to contribute to the complex spin configuration (Fig. 1b) 24 . We fabricated Mn 3-x Pd x Ga (x = 0.6, 0.65, 0.7, 0.75, and 0.8) thin films (see Supplementary Figs. S1 and S2). The compensation point, theoretically reported as x~0.65 18 , was experimentally confirmed by the minimized magnetization point at x = 0.7 with a fairly low saturation magnetization (=0.14 μ B /f.u.) at 340 K. In addition to the ferromagnetic behavior well above room temperature, Mn 2.3 Pd 0.7 Ga exhibited a transition to a state with a higher magnetic moment below T SR = 320 K, which was assigned to a spinreorientation transition. The low magnetic moment at the compensation point could be accounted for by considering a noncollinear spin alignment. In the Mn 2.3 Pd 0.7 Ga thin film, we observed a considerable topological Hall effect and positive magnetic entropy change at temperatures up to 320 K, which was the spin-reorientation transition of Mn 2.3 Pd 0.7 Ga. We also determined the magnetic phase diagram from the topological Hall effect and magnetic entropy data, suggesting that a chiral noncollinear spin structure such as skyrmions was present in the tetragonal compensated ferrimagnet Mn 2.3 Pd 0.7 Ga. This Heusler-based compensated ferrimagnet is a potential candidate for use in high-density and low-power data storage memory devices by replacing conventional magnetic materials.

Results and discussion
A series of Mn 3-x Pd x Ga (x = 0.6, 0.65, 0.7, 0.75, and 0.8) thin films were prepared on a clean MgO substrate to investigate the magnetic compensation point. Figure 1c, d show the magnetic field dependence of magnetization and M-H curves measured at 340 K. The magnetic fields were applied perpendicular (H//c) and parallel (H⊥c) to the film plane. Regarding H//c, the Mn 3-x Pd x Ga films exhibit clear hysteresis loops, indicating that the ferrimagnetic state persists well above room temperature with perpendicular magnetic anisotropy even after Pd substitution. The coercive fields are approximately H C = 30 kOe, except H C = 15 kOe for x = 0.7. With increasing Pd concentration, the saturation magnetization decreases and becomes the minimum (M S = 0.14 μ B /f.u.) at x = 0.7. This result demonstrates the compensated ferrimagnetic state of Mn 2.3 Pd 0.7 Ga, which is consistent with the theoretical report 18 . Here, there are discontinuous steps around the zero field in the M-H curves, which can be attributed to the existence of secondary magnetic phases such as D0 19 hexagonal Mn 3 Ga, L2 1 cubic Mn 3 Ga, or D0 22 tetragonal Mn 2 Ga. However, in the Supplementary Information, we describe the reasons why the coexistence of two magnetic phases can be ruled out. On the other hand, regarding H⊥c, there exists an in-plane magnetic component caused by the canted Mn I moment, as previously mentioned in Fig. 1a, b. For further study on the magnetic properties that depend on the Pd concentration, we measured the temperature dependence of the magnetization M-T curves. The data were taken after cooling in a 1 kOe field for the H//c and H⊥c configurations. As shown in Fig. 1e, f, only the x = 0.7 sample undergoes a transition to a state with a higher magnetic moment at T SR = 320 K, while the other samples show nearly temperature-independent behavior. We assign the magnetic ordering at T SR to a spin reorientation transition, which is an additional magnetic state probably caused by the chiral noncollinear spin texture in the compensated ferrimagnet of Mn 2.3 Pd 0.7 Ga.
To unveil the origin of the spin reorientation transition of the compensated ferrimagnet Mn 2.3 Pd 0.7 Ga, we carried out detailed magnetic and electrical measurements at various temperatures above and below the T SR . The comparison of Mn 3-x Pd x Ga films with different x values is displayed in Fig. S3  The H C value of H//c gradually decreases with decreasing temperature and becomes nearly zero at room temperature; then, it increases again to H C~3 .5 kOe at 150 K. The most striking feature is that at 300 K, H C approaches zero, but the hysteresis loop is maintained in the high-field regime. This unconventional form of the magnetic hysteresis loop just below the T SR is not an M-H curve commonly observed in a ferromagnet or ferrimagnet. Furthermore, an apparent hysteresis loop of H⊥c, which is not expected in the undoped Mn 3 Ga tetragonal ferrimagnet phase, is observed at 150 K. These results imply that the spin configuration of the compensated ferrimagnet, Mn 2.3 Pd 0.7 Ga, is not a typical form below T SR , thus changing the magnetic anisotropy. As reported earlier 17 , the tetragonal ferrimagnet of Mn 3 Ga has an oscillatory exchange interaction depending on the distance between Mn moments along with the uniaxial anisotropy energy; thus, the strength of exchange coupling at each Mn site can be tuned by changing the lattice parameter. In this study, we observed a lattice expansion of c = 7.15 Å for the c-axis parameter of Mn 2.3 Pd 0.7 Ga from the reported value of c~7.11 Å of Mn 3 Ga 16 , which can cause a more canted Mn I moment. Therefore, the in-plane magnetization component enhanced by Pd substitution can be interpreted as being due to the weakened antiferromagnetic interaction between Mn moments. Furthermore, a careful look at the M-H curve of Mn 2.3 Pd 0.7 Ga provides the possible existence of DM interactions, which were theoretically proposed 18 . The DM interactions can be supported by inversion symmetry breaking and strong spin-orbit coupling due to the substitution of the 4d element Pd. In this regard, Mn 2.3 Pd 0.7 Ga is a candidate to realize the DM interactions that lead to the formation of a chiral noncollinear spin texture. Figure 2b shows the Hall resistivity, ρ xy , taken at the same temperatures as the magnetic measurements above. There is no temperature dependence of the normal Hall effect (see Supplementary Fig. S4), and we subtract the normal Hall contribution using the linear slope in the high-field regime. The ρ xy data clearly show the anomalous Hall effect at all temperatures. It is clearly seen that the anomalous Hall resistivity values at H = 70 kOe are nearly temperature independent compared to the strong temperature dependence of M S ; notably, this is different from what is commonly known. Regarding Mn 2.3 Pd 0.7 Ga, we observe a nonlinear relation between the magnetization and anomalous Hall resistivity (see Supplementary  Fig. S5), which cannot be described by the ferromagnetic component alone and can be attributed to the noncollinear spin texture 8,9,25 . Here, it is noteworthy that there is an unexpected hump-like anomaly in the low-magneticfield regime of the ρ xy data below 320 K, which is the spinreorientation temperature, T SR . In addition, note that this hump is only present in the Mn 2.3 Pd 0.7 Ga sample (see Supplementary Fig. S6). The black arrow represents the position of the maximum value of the hump. At temperatures below the T SR , a hump-like anomaly starts to appear and moves to higher fields as the temperature is decreased. The overall shape of the anomaly is similar to the topological Hall effect (THE) reported in various skyrmion materials 10,26 .
Typically, a noncollinear spin state such as a magnetic skyrmion emerges in the low-field region immediately after which the aligned spins generate magnetic stripe domains around the zero field 2,7,13 . Therefore, we predict that if the skyrmion state emerges, the magnetoresistance (MR) becomes a maximum at the stripe domain state due to the anisotropic magnetoresistance (AMR), which exhibits a low (high) resistance when the direction of magnetization is perpendicular (parallel) to the current direction 24 . Thus, we measured the MR of Mn 2.3 Pd 0.7 Ga at the same temperatures for comparison. In Fig. 3a, b, we plot the magnified data of |ρ xy | and MR in the low-field regime ranging from −10 kOe to 10 kOe. It is apparent that the position of the emerging point of the THE is well matched with the maximum position of MR, as predicted above. Moreover, we observe the signature of weak (anti) localization in both the longitudinal and perpendicular MR curves (see Supplementary Fig. S7), indicating the strong spin-orbit coupling required for the realization of DM interactions that give rise to the formation of skyrmions. This result also supports our hypothesis for the Pd substitution effect, which plays an important role in strong spin-orbit coupling and structural symmetry breaking.
Direct magnetic imaging is available using real-space measurements such as Lorentz transmission electron microscopy and magnetic force microscopy (MFM) 2,13 . Therefore, we carried out MFM measurements by varying the temperature from one sample to another in many different positions. However, we could not observe any magnetic domain structure in the compensated ferrimagnet of Mn 2.3 Pd 0.7 Ga. This is because the stray field is locally canceled by antiparallel spins 27 . An alternative approach to provide a hint for the possible presence of a noncollinear spin state is the magnetic entropy change 22 . We calculated the magnetic entropy change, ΔS M , by from the isothermal magnetization curves for constant temperature intervals 22,23 . Figure 4a shows the temperature dependence of ΔS M . The temperature interval is ΔT = 5 K, and each line represents the different field range of integration, ΔH = 0.4 kOe. The ΔS M data reveal positive values starting at room temperature. Using the broad scan of the magnetic entropy change ranging from 100 K to 350 K with the integrated external field ranging from 0.1 kOe to 20 kOe, we plot a contour map in Fig. 4b, where the x-axis is the temperature, the y-axis is the magnetic field, and the z-axis is the magnetic entropy change. Thus, we determined the H-T magnetic phase diagram of the Mn 2.3 Pd 0.7 Ga film.
As we expected, a positive ΔS M (red and black areas) starts to emerge at temperatures below the T SR . The noncollinear spin phase expands as the temperature is decreased down to~130 K, and then it begins to contract again. For the comparison of ΔS M with the THE, we take the field values of the maximum magnitude of the hump from the ρ xy -H plots in Fig. 2b, which are marked with open square symbols in Fig. 4b. Note that the pure topological Hall signals could not be directly extracted from the measured ρ xy data. This is presumably due to complex exchange interactions caused by geometrically frustrated spins at the magnetic compensation point, as reported earlier in regard to GdRu 2 Si 2 hosting noncollinear spin textures by four-spin exchange interactions 8 . In Fig. 4b, we plot the position of the maximum values of the THE, together with the area of the positive ΔS M . It is remarkable that the two data points, namely, the THE maximum and the positive ΔS M , considerably overlap. Furthermore, as the range of positive ΔS M begins to contract, the magnitude of the THE also starts to decrease and finally becomes zero at T = 100 K. From this figure, it is clear that the noncollinear spin phase is stable over a wide range of temperatures above room temperature. In addition, note that there is a high possibility of a skyrmion phase that occurs in the compensated ferrimagnet Mn 2.3 Pd 0.7 Ga with relatively low magnetization.

Conclusion
In summary, we experimentally confirmed the magnetic compensation point of Mn 3-x Pd x Ga (0.6 ≤ x ≤ 0.8) to be x = 0.7. Tetragonal Mn 3 Ga with a noncollinear spin configuration could be tuned by introducing the heavy metal element Pd for substitution, giving rise to structural symmetry breaking and strong spin-orbit coupling. We found a spin-reorientation transition at T SR = 320 K, which is above room temperature. Below T SR , we observed the topological Hall effect and a positive magnetic entropy change, originating from the chiral noncollinear spins of Mn 2.3 Pd 0.7 Ga. Currently, the application of chiral spin-based spintronics is a very important issue. Therefore, we hope that our findings of a compensated ferrimagnet phase emerging above room temperature with a quite low magnetization will open the possibility for new chiral spin devices.

Experimental method
Mn 3-x Pd x Ga (0.6 ≤ x ≤ 0.8) thin films with a thickness of 100 nm were deposited on a MgO (001) substrate by DC and RF magnetron sputtering systems at a base pressure on the order of 10 −6 Torr. Using three targets, namely, Mn 2 Ga, Mn, and Pd, the films were cosputtered at 400°C with an Ar pressure of 2 mTorr during deposition. We basically followed the detailed growth conditions for Mn 3 Ga thin films reported elsewhere 16,28 . To change the substitution rate of Pd for Mn, the working current of the Pd target gun was varied from 16 mA to 20 mA while maintaining the other growth conditions. After deposition, a 2-nm-thick SiO 2 capping layer was deposited by in situ sputtering in the same chamber at room temperature to prevent oxidation. The chemical composition of Mn 3-x Pd x Ga was determined by energy dispersive X-ray (EDX) spectroscopy. The crystal structure was investigated using X-ray diffraction (XRD) with a Cu Kα radiation source. The magnetic and electrical properties were measured with a superconducting quantum interference device-vibrating sample magnetometer (SQUID-VSM) in magnetic fields up to 70 kOe and at temperatures down to 2 K. The electrical measurements were carried out with the van der Pauw method. To avoid the possible discrepancy caused by shape anisotropy, the same films were used for all measurements.