Tunable topological Hall effects in noncollinear antiferromagnet Mn₃Sn/Pt bilayers

Noncollinear antiferromagnet (AFM) Mn₃Sn has drawn significant interest in spintronics research. As a possible Weyl semimetal, its topological band structure with non-zero Berry curvature has led to a series of novel magneto-transport properties, such as large anomalous Hall effect (AHE) and anomalous Nernst effect (ANE).^1–3 In addition, topological spin textures can be generated at temperatures (T) below 50 K where a phase transition turns Mn₃Sn from a triangular AFM configuration into spin-glass.^4–6 At T > 275 K, the energy favors the triangular AFM state in Mn₃Sn with a very small out-of-plane canting based on first-principle calculations, resulting in a small spin chirality at high temperatures.⁷ Recently, it was also reported that the topological Hall effect (THE) has been observed in Mn₃Sn crystals near room temperature, while the mechanism is not well understood.^8,9

It has been demonstrated that heavy metals (HMs), such as Pt, with large spin–orbit coupling can induce a sizable interfacial Dzyaloshinskii–Moriya interaction (DMI) in Pt/ferromagnet (FM) or Pt/AFM bilayers with an in-plane DMI vector, leading to the formation of topological spin textures.^10–12 For Mn₃Sn, the triangular AFM spins in the (0001) planes should only lead to the non-zero in-plane AHE.^1,7,13 However, in Mn₃Sn/Pt bilayers, the large spin–orbit coupling of Pt can break the out-of-plane mirror symmetry in Mn₃Sn when hybridizing with the neighboring Mn atoms across the interface.¹³ In this article, we report the detection of possible topological spin textures in Mn₃Sn/Pt bilayers using the topological Hall effect (THE) as well as the presence of the out-of-plane anomalous Hall effect. We observe a broad temperature range of THE from 210 to 365 K through tuning the thickness of the Mn₃Sn films.

For the epitaxial growth of c-axis-oriented Mn₃Sn films, we first grow a thin Pt at a substrate temperature of 260 °C as a buffer layer on the Al₂O₃ (0001) substrate, followed by the in situ growth of Mn₃Sn at 210 °C on Pt by off-axis sputtering.¹⁴ Pt is chosen as a buffer layer because its face-centered cubic (fcc) structure with a lattice constant of 3.912 Å can be grown epitaxially on Al₂O₃ (0001)¹⁵ with high crystalline quality. The resulting Pt (111) buffer layer has a hexagonal in-plane lattice constant of 5.532 Å, which is very close (∼1% lattice mismatch) to the in-plane lattice constant of 5.593 Å for Mn₃Sn (0001). Finally, a 3 nm Ta layer is deposited on Mn₃Sn at room temperature using off-axis sputtering to protect it from oxidation.

Figure 1(a) shows the 2θ/ω x-ray diffraction (XRD) scans of two Pt buffer layers with thicknesses of 3 and 20 nm grown on Al₂O₃ (0001) together with a Mn₃Sn(45 nm)/Pt(3 nm)/Al₂O₃ (0001) sample. The clear Laue oscillations in the XRD scan of Pt(20 nm)/Al₂O₃ indicate the high crystalline quality of the Pt buffer layer. The broad feature from 35° to 41° in both Pt(3 nm)/Al₂O₃ and Mn₃Sn(45 nm)/Pt(3 nm)/Al₂O₃ is due to the (111) peak of 3 nm Pt. From the Mn₃Sn (0002) XRD peak at 39.310°, we obtain the Mn₃Sn c-axis lattice constant of 4.580 Å, which is ∼1% larger than the bulk value due to the compressive strain of Mn₃Sn on Pt (111). Figure 1(b) shows the rocking curves of the Mn₃Sn (0002) and Pt (111) peaks of the Mn₃Sn(45 nm)/Pt(3 nm)/Al₂O₃ sample, which exhibit a full-width-at-half-maximum (FWHM) of 0.005° and 0.004°, respectively, indicating high crystalline quality. Figure 1(c) gives the x-ray reflectivity (XRR) scan of a Pt(3 nm)/Mn₃Sn(10 nm)/Pt(3 nm) trilayer on Al₂O₃ (0001). The fitting to the XRR curve reveals sharp interfaces with an interfacial roughness of 0.2 nm, which is corroborated by atomic force microscopy (AFM) imaging as shown in Fig. S1 in the supplementary material. The crystal ordering of a Mn₃Sn(45 nm) film is examined by cross-sectional scanning transmission electron microscopy (STEM) imaging using an aberration corrected FEI Titan 60/300 STEM at 300 kV. The STEM images in Fig. 1(d) confirm the epitaxial continuity of Mn₃Sn (0001) planes on Pt (111) grown on the Al₂O₃ (0001) substrate.

We measure the magnetization hysteresis loops of the Mn₃Sn(45 nm)/Pt(3 nm)/Al₂O₃(0001) sample at 300 K using a superconducting quantum interference device (SQUID) magnetometer (see Fig. S1 in the supplementary material for more details). The Mn₃Sn film exhibits a small magnetic moment of ∼5 emu/cm³ when the field is in-plane along the [11$2̄$0] and [1$1̄$00] directions, which increases to ∼13 emu/cm³ when the field is out-of-plane along [0001]. The measured magnetization is larger than the theoretical predication of 2–3 emu/cm³, possibly due to off-stoichiometry, such as excess Mn or defects in the epitaxial Mn₃Sn film.^1,3

For magnetotransport measurements, we first grow a Mn₃Sn(5 nm)/Pt(1.5 nm) bilayer on Al₂O₃ (0001), which is patterned into a Hall bar with a current channel width of 100 μm. Figure 2(a) shows a schematic of the Hall measurement on the bilayer with an out-of-plane magnetic field. Figures 2(b) and 2(c) show the longitudinal magnetoresistance MR = ρ_xx/ρ₀ (ρ₀ is the zero-field resistivity) and the Hall resistivity (ρ_xy), respectively, as a function of the out-of-plane magnetic field, H//Mn₃Sn[0001]. The ordinary Hall effect (OHE) contribution, ρ_OHE, with a linear field dependence has been subtracted in Fig. 2(c). The calculation of the Hall resistivity has already considered the shunting effect from Pt and the capping layer. At T = 300 K, a large anomalous Hall resistivity ρ_AHE = 43 nΩ cm is observed. The non-ferromagnetic origin of the AHE is confirmed by the longitudinal MR as shown in Fig. 2(b), which is non-hysteretic with a magnitude of only <0.05% up to 14 T.⁴ 

Surprisingly, as temperature increases, the magnitude of ρ_AHE decreases and changes sign at around 330 K [see Fig. 2(c)], while the longitudinal MR has essentially no change [Fig. 2(b)]. Because the observed AHE in Mn₃Sn is not ferromagnetic in origin, we fit the ρ_AHE loops using the Langevin equation as shown in Fig. 2(c). After subtracting the fitted ρ_AHE contribution from ρ_xy, we obtain an additional Hall signal (other than OHE and AHE) in Fig. 2(d). It is generally believed that the detected Hall resistivity includes three contributions: ρ_xy = ρ_OHE + ρ_AHE + ρ_THE where the last term arises from the topological Hall effect. The topological Hall signal has a pair of antisymmetric peaks at corresponding positive and negative magnetic fields, which is typically attributed to the formation of topological spin textures. This is consistent with our experimental results in Fig. 2(d). The maximum magnitude of ρ_THE occurs near the temperature where ρ_AHE reserves its sign, which is similar to the previous reports of SrRuO₃/SrIrO₃ bilayers and SrRuO₃ single layers.^16,17

To further exclude the possibility of spurious signals, we measure the longitudinal and Hall resistivities of the Mn₃Sn(5 nm)/Pt(1.5 nm) bilayer on Al₂O₃ (0001) with an in-plane magnetic field H//[11$2̄$0], as shown in Figs. 2(e)–2(g). Non-zero in-plane ρ_AHE is detected with similar temperature dependence as the out-of-plane Hall resistivity. However, the magnitude of in-plane ρ_AHE is approximately an order of magnitude smaller than that of out-of-plane ρ_AHE. Meanwhile, the in-plane longitudinal MR [Fig. 2(f)] also shows a weak temperature dependence, but its magnitude is about half of the out-of-plane MR. Such an AHE-like signal under the in-plane field was reported before in Mn₃Sn,³ which was attributed to its noncollinear spin structure. Compared with previous reports on Mn₃Sn bulk single crystals and thin films, our Pt/Mn₃Sn bilayer has a larger ρ_AHE when the field is out-of-plane.^1,3 Figure 2(h) shows the Hall resistivity after subtracting the fitted ρ_AHE contribution in Fig. 2(d), which shows no detectable THE signal.

After observing the anomalous Hall and topological Hall effect in the Mn₃Sn(5 nm)/Pt(1.5 nm) bilayer, we perform similar measurements on different Mn₃Sn thicknesses ranging from 3 to 15 nm. Figure 3(a) shows the ρ_THE hysteresis loops in an out-of-plane field for the 3, 5, and 15 nm Mn₃Sn samples at the temperature where the magnitude of ρ_THE reaches the maximum. The 3 nm Mn₃Sn sample shows zero coercivity and two antisymmetric THE peaks in each branch (e.g., from +14 to −14 T) of the hysteresis loop. For the 5 nm Mn₃Sn sample, there is a small coercivity and two antisymmetric THE peaks in each branch. However, for the 15 nm sample, there is only one THE peak in each branch with a sizable coercivity. Thus, both the coercivity and hysteresis behavior of the topological Hall effect exhibit clear dependence on the thickness of the Mn₃Sn film.

We define ρ_THE−max as the maximum THE resistivity [labeled in Fig. 3(a) for the 5 nm sample] observed at T = T_THE−max, which is 330 K as shown in Fig. 2(d). Figure 3(b) plots the Mn₃Sn thickness dependencies of ρ_THE−max and T_THE−max. The magnitude of ρ_THE−max decreases from 5 to 15 nm and vanishes at 45 nm (see the supplementary material for more results). This agrees with the behavior expected from the interfacial DMI due to the broken inversion symmetry at the Mn₃Sn/Pt interface as the origin of the THE. However, values of ρ_THE−max for the 3 and 4 nm samples are smaller than that of the 5 nm sample, which deviates from the mechanism of interfacial DMI induced topological spin textures. This may be due to the lower quality of the Mn₃Sn film at thicknesses below 5 nm, although we have no direct evidence. Meanwhile, T_THE−max initially increases quickly from 3 to 5 nm Mn₃Sn and then reaches a plateau at 10–15 nm. Bulk Mn₃Sn has a Néel temperature (T_N) of ∼420 K, which generally decreases in thin films.¹⁸ Thus, the tunability of the topological Hall effect is correlated with the change in T_N of Mn₃Sn thin films through thickness control. This is consistent with a previously reported phase diagram in ferromagnetic systems as the topological Hall effect emerges near the Curie temperature (T_C).¹⁹ 

To summarize our results, Fig. 4 shows the field-temperature phase diagrams of ρ_THE for the 3, 5, 10, and 15 nm Mn₃Sn films for both the decreasing and increasing field branches of the hysteresis loops, indicating the phase space of topological spin texture. As the thickness of Mn₃Sn increases, the temperature range of ρ_THE increases from 210 to 225 K for 3 nm Mn₃Sn to 345–365 K for 15 nm Mn₃Sn. Previously, the THE in Mn₃Sn was observed only at temperatures below 50 K, where the triangular spin state transitions into a glassy ferromagnetic state. For the triangular spin state of Mn₃Sn, the small intrinsic DMI vector is perpendicular to the in-plane (0001), which makes it serve as an in-plane anisotropy.²⁰ Thus, it is predicted that the spin chirality of Mn₃Sn is small. However, heavy metal Pt provides a strong interfacial DMI in Mn₃Sn/Pt bilayers, which potentially generates topological spin textures in Mn₃Sn. The emergence of the skyrmion phase in frustrated triangular AFM with DMI has been theoretically predicted by Monte-Carlo simulations.²¹ The observation of the topological Hall effect offers evidence for the existence of chiral spin textures in the Mn₃Sn/Pt bilayers.

Previously,²² positive AHE was reported in Pt/Mn₃Sn (0001) bilayers with 60 nm Mn₃Sn at temperatures from 2 to 300 K, where the observed AHE was explained as the topological Hall resistivity induced by real space spin chirality under an out-of-plane magnetic field. Similar positive AHE is also observed in our 45 nm Mn₃Sn sample with a comparable magnitude and temperature range. However, for thinner Mn₃Sn, we observe a sign reversal of the AHE. This is similar to the AHE and THE shown in a well studied SrIrO₃/SrRuO₃ bilayer system.¹⁷ 

Recently, it was proposed that the THE-like signal observed in some systems, such as single layer SrRuO₃, could be due to the superposition of different AHE contributions with opposite signs.²³ However, it is not likely to be the case here. AHE sign change occurs in our 5 nm Mn₃Sn sample with both out-of-plane and in-plane fields. If the THE-like signal originates from the superposition of two opposite AHE signals, it should appear in both field orientations. However, we only detect THE when the field is out-of-plane, which is consistent with the prediction that the interfacial DMI tilts the noncollinear spins toward out-of-plane, resulting in non-zero topological charges. To fully confirm the existence of topological spin textures in Mn₃Sn/Pt bilayers, direct imaging is required; however, imaging of noncollinear AFM spin structures remains a challenging task.

In summary, we observe the topological Hall effect in Mn₃Sn/Pt bilayers within a broad Mn₃Sn thickness and temperature range. The high tunability of spin textures in Mn₃Sn/Pt bilayers through thickness control of the Mn₃Sn layer offers potential for spintronic applications and provides insights into the underlying physics of the topological band structure in the Weyl semimetal Mn₃Sn.

See the supplementary material for epitaxy and magnetic properties of Mn₃Sn/Pt films, Hall measurements with different Hall bar channel widths, and Hall measurements of different Mn₃Sn film thicknesses.

This work was primarily supported by the Department of Energy (DOE), Office of Science, Basic Energy Sciences, under Grant No. DE-SC0001304. M.Z. and J.H. acknowledge partial support for the STEM work by the Center for Emergent Materials, an NSF-funded MRSEC, under Grant No. DMR-2011876.

The data that support the findings of this study are available within the article and its supplementary material.