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 material1,2,3,4. 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 anisotropy5,6,7, Dzyaloshinskii-Moriya (DM) interactions2, the interplay of Ruderman-Kittel-Kasuya-Yosida (RKKY) and four-spin exchange interactions8, and geometrically frustrated spin systems9. 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 Mn1.4Pt0.9Pd0.1Sn12,13 and Mn2Rh0.95Ir0.05Sn14, 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 fluctuations15. Second, a low saturation magnetization is required to produce a small stray field for high-density devices14. For the above examples, the antiskyrmion state in Mn2Rh0.95Ir0.05Sn is stable up to 400 K, but the total magnetic moment is considerably high (~4 μB/f.u.)12. On the other hand, the magnetization value of Mn2Rh0.95Ir0.05Sn is relatively low (~1 μB/f.u.), but the antiskyrmion state emerges at lower temperatures up to ~250 K14. 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 Mn3Ga 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 Mn3Ga is ferrimagnetic with a Curie temperature of TC = 820 K and crystallizes in a D022 tetragonal structure with perpendicular magnetic anisotropy (PMA)16. Two inequivalent Mn sublattices, Mn I and Mn II, possess different magnetic moments of 3.1 μB/f.u. and 4.2 μB/f.u., which are coupled antiferromagnetically and lead to a total magnetization of ~1.1 μB/f.u.17. Interestingly, a recent neutron scattering experiment revealed that tetragonal Mn3Ga has an in-plane 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 sublattices17. Moreover, previous studies reported that the magnetic properties of Mn3Ga can be tuned by substituting a transition metal for Mn II in Mn3-xYxGa, such as Y = Pt, Pd, Co, and Ni, and can be fully compensated with a zero net magnetic moment18. A typical example of magnetic compensation is when Y = Pt18,19. The net magnetization changes from ferrimagnetic to completely compensated at x = 0.65 in Mn3-xPtxGa, demonstrating a fully compensated ferrimagnetic state. However, there has been no report on the THE being observed at the magnetic compensation point in Mn3-xPtxGa, where the noncollinear spin texture is maximally expected19. This is compared to Mn1.4Pt0.9Pd0.1Sn, in which they reported a spin-reorientation transition from a collinear ferromagnetic to a noncollinear configuration below TSR = 135 K, accompanied by the topological Hall effect but with no magnetic compensation20. 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 breaking21. Thus, we deduce the possibility of forming scalar spin chirality through heavy metal substitution in Mn3Ga. 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 formation22. 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 positive22. The magnetic entropy change can be measured using isothermal magnetization with a constant temperature interval22,23.

Fig. 1: Structural and magnetic properties of Mn3-xPdxGa.
figure 1

a Crystal structure for tetragonal Mn3Ga with the direction of the magnetic moment. b Crystal structure for tetragonal Mn3-xPdxGa with the direction of the magnetic moment. Mn II atoms are partially replaced by Pd atoms. The Mn I, Mn II, Ga, and Pd atoms are displayed as blue, red, green, and yellow spheres. c, d Out-of-plane (H//c) and in-plane (H⊥c) magnetization curves measured at 340 K as a function of the magnetic field for Mn3-xPdxGa films; x = 0.6 (black), 0.65 (red), 0.7 (blue), 0.75 (green), and 0.8 (purple). e, f Out-of-plane (H//c) and in-plane (H⊥c) magnetization data measured after cooling in a field of 1 kOe as a function of temperature for Mn3-xPdxGa films; x = 0.6 (black), 0.65 (red), 0.7 (blue), 0.75 (green), and 0.8 (purple). The arrows show the temperature of spin reorientation.

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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 Mn3-xPdxGa (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 ~ 0.6518, was experimentally confirmed by the minimized magnetization point at x = 0.7 with a fairly low saturation magnetization (=0.14 μB/f.u.) at 340 K. In addition to the ferromagnetic behavior well above room temperature, Mn2.3Pd0.7Ga exhibited a transition to a state with a higher magnetic moment below TSR = 320 K, which was assigned to a spin-reorientation transition. The low magnetic moment at the compensation point could be accounted for by considering a noncollinear spin alignment. In the Mn2.3Pd0.7Ga 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 Mn2.3Pd0.7Ga. 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 Mn2.3Pd0.7Ga. 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 Mn3-xPdxGa (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 Mn3-xPdxGa 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 HC = 30 kOe, except HC = 15 kOe for x = 0.7. With increasing Pd concentration, the saturation magnetization decreases and becomes the minimum (MS = 0.14 μB/f.u.) at x = 0.7. This result demonstrates the compensated ferrimagnetic state of Mn2.3Pd0.7Ga, which is consistent with the theoretical report18. 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 D019 hexagonal Mn3Ga, L21 cubic Mn3Ga, or D022 tetragonal Mn2Ga. 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 TSR = 320 K, while the other samples show nearly temperature-independent behavior. We assign the magnetic ordering at TSR to a spin reorientation transition, which is an additional magnetic state probably caused by the chiral noncollinear spin texture in the compensated ferrimagnet of Mn2.3Pd0.7Ga.

To unveil the origin of the spin reorientation transition of the compensated ferrimagnet Mn2.3Pd0.7Ga, we carried out detailed magnetic and electrical measurements at various temperatures above and below the TSR. The comparison of Mn3-xPdxGa films with different x values is displayed in Fig. S3 in the Supplementary Information. Remarkably, unusual magnetic properties are observed only in the compensated ferrimagnet when x = 0.7. In Fig. 2a, we depict the M–H curve results of x = 0.7 measured at T = 150 K, 300 K, 320 K, and 340 K in both the H//c and H⊥c configurations. The MS values at all temperatures are lower than those reported in undoped Mn3Ga17. It is apparent that Mn2.3Pd0.7Ga exhibits dramatic changes in the M–H curves at T < TSR, while being ferrimagnetic with perpendicular anisotropy. As the temperature decreases, the MS values of H//c and H⊥c increase to approximately 0.75 μB/f.u. and 0.5 μB/f.u., respectively. The HC value of H//c gradually decreases with decreasing temperature and becomes nearly zero at room temperature; then, it increases again to HC ~3.5 kOe at 150 K. The most striking feature is that at 300 K, HC approaches zero, but the hysteresis loop is maintained in the high-field regime. This unconventional form of the magnetic hysteresis loop just below the TSR 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 Mn3Ga tetragonal ferrimagnet phase, is observed at 150 K. These results imply that the spin configuration of the compensated ferrimagnet, Mn2.3Pd0.7Ga, is not a typical form below TSR, thus changing the magnetic anisotropy. As reported earlier17, the tetragonal ferrimagnet of Mn3Ga 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 Mn2.3Pd0.7Ga from the reported value of c ~ 7.11 Å of Mn3Ga16, 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 Mn2.3Pd0.7Ga provides the possible existence of DM interactions, which were theoretically proposed18. 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, Mn2.3Pd0.7Ga is a candidate to realize the DM interactions that lead to the formation of a chiral noncollinear spin texture.

Fig. 2: Results of M-H curve and ρxy-H curve for Mn2.3Pd0.7Ga film.
figure 2

a M–H curves of the Mn2.3Pd0.7Ga film measured at various temperatures, T = 150, 300, 320, and 340 K in the H//c (red) and H⊥c (blue) directions. b ρxy–H curves of the Mn2.3Pd0.7Ga film measured at various temperatures, T = 150, 300, 320, and 340 K. The normal Hall contribution is eliminated by a linear term in the high-field regime. The arrows represent the positions of the maximum magnitude of the hump.

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Figure 2b shows the Hall resistivity, ρxy, 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 ρxy 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 MS; notably, this is different from what is commonly known. Regarding Mn2.3Pd0.7Ga, 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 texture8,9,25. Here, it is noteworthy that there is an unexpected hump-like anomaly in the low-magnetic-field regime of the ρxy data below 320 K, which is the spin-reorientation temperature, TSR. In addition, note that this hump is only present in the Mn2.3Pd0.7Ga sample (see Supplementary Fig. S6). The black arrow represents the position of the maximum value of the hump. At temperatures below the TSR, 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 materials10,26.

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 field2,7,13. 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 direction24. Thus, we measured the MR of Mn2.3Pd0.7Ga at the same temperatures for comparison. In Fig. 3a, b, we plot the magnified data of ∣ρxy∣ 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.

Fig. 3: Electrical properties of Mn2.3Pd0.7Ga film.
figure 3

a ρxy–H curves magnified in the low-field region ranging from −10 to 10 kOe measured at T = 150, 300, 320, and 340 K. The y-axis is expressed as an absolute value for comparison. The arrows show the direction of magnetic field sweep. b Perpendicular MR ratio, (R(H)−R(0))/R(0), measured at T = 150, 300, 320, and 340 K. The arrows show the direction of magnetic field sweep. The dashed lines represent the position of the maximum value of MR, which is well matched with the position of the emerging point of THE.

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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 Mn2.3Pd0.7Ga. This is because the stray field is locally canceled by antiparallel spins27. An alternative approach to provide a hint for the possible presence of a noncollinear spin state is the magnetic entropy change22. We calculated the magnetic entropy change, ΔSM, by using the relation \(\Delta S_{{{\mathrm{M}}}} = \frac{1}{{\Delta T}}\left[ {{\int}_0^H {\left( {M_1} \right)dH}\, - \,{\int}_0^H {\left( {M_2} \right)dH} } \right]\) from the isothermal magnetization curves for constant temperature intervals22,23. Figure 4a shows the temperature dependence of ΔSM. The temperature interval is ΔT = 5 K, and each line represents the different field range of integration, ΔH = 0.4 kOe. The ΔSM 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 Mn2.3Pd0.7Ga film.

Fig. 4: Magnetic phase diagram for the Mn2.3Pd0.7Ga film.
figure 4

a Temperature dependence of the magnetic entropy change, ΔSM. The temperature interval is used as ΔT = 5 K. Each line represents the different field range of integration, ΔH = 0.4 kOe. The top line depicts the integrated field range, H = 1 kOe, and the bottom line depicts the integrated field range, H = 15 kOe. b H–T magnetic phase diagram derived from the positive ΔSM (red-shaded area) and the maximum THE (open square symbols).

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As we expected, a positive ΔSM (red and black areas) starts to emerge at temperatures below the TSR. 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 ΔSM with the THE, we take the field values of the maximum magnitude of the hump from the ρxy-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 ρxy 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 GdRu2Si2 hosting noncollinear spin textures by four-spin exchange interactions8. In Fig. 4b, we plot the position of the maximum values of the THE, together with the area of the positive ΔSM. It is remarkable that the two data points, namely, the THE maximum and the positive ΔSM, considerably overlap. Furthermore, as the range of positive ΔSM 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 Mn2.3Pd0.7Ga with relatively low magnetization.

Conclusion

In summary, we experimentally confirmed the magnetic compensation point of Mn3-xPdxGa (0.6 ≤ x ≤ 0.8) to be x = 0.7. Tetragonal Mn3Ga 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 TSR = 320 K, which is above room temperature. Below TSR, we observed the topological Hall effect and a positive magnetic entropy change, originating from the chiral noncollinear spins of Mn2.3Pd0.7Ga. 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

Mn3-xPdxGa (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, Mn2Ga, 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 Mn3Ga thin films reported elsewhere16,28. 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 SiO2 capping layer was deposited by in situ sputtering in the same chamber at room temperature to prevent oxidation. The chemical composition of Mn3-xPdxGa 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.