The anomalous Hall effect is allowed by symmetry in some non-collinear antiferromagnets and is associated with Bloch-band topological features. This topological anomalous Hall effect is of interest in the development of low-power electronic devices, but such devices are likely to demand electrical control over the effect. Here we report the observation of the anomalous Hall effect in high-quality thin films of the cubic non-collinear antiferromagnet Mn3Pt epitaxially grown on ferroelectric BaTiO3 substrates. We demonstrate that epitaxial strain can alter the anomalous Hall conductivity of the Mn3Pt films by more than an order of magnitude. Furthermore, we show that the anomalous Hall effect can be turned on and off by applying a small electric field to the BaTiO3 substrate when the heterostructure is at a temperature of around 360 K and the Mn3Pt is close to the phase transition between a low-temperature non-collinear antiferromagnetic state and a high-temperature collinear antiferromagnetic state. The switching effect is due to piezoelectric strain transferred from the BaTiO3 substrate to the Mn3Pt film by interfacial strain mediation.
Soon after Edwin Hall discovered the Hall effect in nonmagnetic metals1—an electric voltage transverse to mutually orthogonal electric currents and magnetic fields—he observed a larger effect in ferromagnetic metals2. This became known as the anomalous Hall effect (AHE), because it is apparently independent of the Lorentz force and can be non-zero even in the absence of an external magnetic field. Of all the electrical transport properties of crystals, the AHE has been the most difficult to understand, and its theory has often been a topic of intense debate3. In recent years, a consensus has emerged that in many magnetic materials it has dominant contributions from the interband mixing of Bloch electrons induced by electric fields4,5, and spin-dependent scattering effects due to spin–orbit coupling. It is now understood that the former contribution can be represented as an integral of the Berry curvature5,6,7 over occupied Bloch bands and has an intimate relation to the current interest in topology in condensed matter systems8.
Criteria for the existence of the AHE can be simply formulated based on symmetry arguments, even when microscopic mechanisms are imperfectly understood. This line of thought has led to the recent theoretical prediction9,10 and experimental demonstration11,12,13,14 of an AHE in a number of non-collinear antiferromagnets, countering the conventional wisdom that the AHE is proportional to total magnetization. This development adds electrical detectability to the well-known advantages of antiferromagnets in spintronic devices, such as insensitivity to external magnetic fields and fast spin dynamics15. Because of their AHE, the order parameter directions of these non-collinear antiferromagnets can be revealed by a voltage measurement. For applications in spintronics it is, however, highly desirable to be able to demonstrate the AHE in thin films and to show that it can be manipulated by electric-field control16,17. In this Article, we report the realization of this important step in the development of antiferromagnetic spintronics.
Topological AHE in epitaxial Mn3Pt films
Mn3Pt is a cubic antiferromagnetic intermetallic compound with a0 = 3.833 Å and Néel temperature T N ~ 475 K. At room temperature, the magnetic moments on the Mn atoms establish normal triangular magnetic order18,19,20, identical to that in Mn3Ir (ref. 9). Both the structure and magnetic order of Mn3Pt are in sharp contrast to previous experimental examples of non-collinear antiferromagnets having non-zero AHE, which all have a hexagonal structure and the inverse triangular magnetic order that breaks the three-fold rotation symmetry with respect to the c axis11,12,13,14. Moreover, at ~360 K, Mn3Pt exhibits a convenient first-order magnetic phase transition between a low-temperature non-collinear triangular state (D phase) and a high-temperature collinear antiferromagnetic state (F phase)18,19,20. The transition is accompanied by an abrupt ~0.8% lattice expansion19,20. Provided that high-quality single-crystal Mn3Pt films can be epitaxially integrated on ferroelectric substrates, this strong spin–lattice correlation is ideal for electric control of spin structure via piezoelectric-strain-mediated magnetoelectric coupling21,22,23. However, epitaxial thin-film growth of intermetallic compounds such as Mn3Pt on oxide substrates has been a challenging task due to potential non-wetting and interfacial oxidation issues. Epitaxially strained intermetallic alloy films are even more challenging to realize.
We have successfully grown high-quality epitaxial thin films of Mn3Pt on (001) BaTiO3 (BTO) single-crystal substrates. Figure 1a–c shows reflection high-energy electron diffraction (RHEED) patterns of a (001)-oriented BTO single-crystal substrate before deposition, a 20-nm-thick Mn3Pt film deposited on the BTO substrate, and the Mn3Pt film after annealing in vacuum for 1 h, respectively. The streaky peaks after the thin-film deposition in Fig. 1b suggest epitaxial growth with a smooth film surface. After vacuum annealing at a higher temperature to improve chemical ordering, the streaky peaks remain (Fig. 1c). The out-of-plane X-ray diffraction (XRD) θ–2θ scan in Fig. 1d indicates that the Mn3Pt film is (001)-oriented and single-crystalline and the 360° ϕ scans around the (111) peaks of Mn3Pt and BTO confirm the epitaxial growth (Fig. 1e), which is schematized in Fig. 1f. The scanning transmission electron microscopy (STEM) image in Fig. 1g reveals high-quality epitaxy with a clear interface between the intermetallic Mn3Pt film and the BTO substrate. The film composition was determined to be Mn75.3Pt24.7 (±2 at%) by energy-dispersive X-ray spectroscopy. Compared with bulk Mn3Pt, which is cubic with a = 3.833 Å, a 20-nm-thick Mn3Pt film under tensile strain becomes tetragonal with a = 3.852 Å and c = 3.813 Å.
The room-temperature crystal structure and magnetic order of cubic Mn3Pt is illustrated in Fig. 2a. Above 300 K, the temperature-dependent resistivity (ρ–T) curve of a 20 nm Mn3Pt film exhibits a broad hysteresis loop between 325 and 360 K (Fig. 2b). The sharp resistivity jump at 348 K during warm-up and the abrupt drop at 335 K during cool-down reflect the first-order magnetic phase transition of the Mn3Pt (ref. 24). Moreover, the slope of the ρ–T curve changes abruptly across the phase transition, which can be due to distinct spin scattering and/or band structures in the two phases. Temperature-dependent lattice constant measurements of the Mn3Pt film reveal a similar hysteresis loop (Fig. 2c) as in the ρ–T curves, confirming the first-order transition of the Mn3Pt film. On heating up, c changes from 3.819 Å at 350 K to 3.849 Å at 360 K. The 0.78% lattice constant variation across the phase transition is rather comparable to that seen in bulk Mn3Pt (refs 19,20).
As shown in Fig. 2d, the AHE is strong in the low-temperature non-collinear antiferromagnetic phase of the Mn3Pt film, but absent in the high-temperature collinear state. The zero-field anomalous Hall resistivity ρH reaches ~5 μΩ cm at 10 K and decreases to ~3 μΩ cm at 300 K. The temperature-dependent zero-field anomalous Hall resistivity (Fig. 2e) displays a similar hysteresis loop on warming up and cooling down, which confirms the nature of the first-order phase transition again and, more importantly, establishes that the AHE exists only in the low-temperature non-collinear phase. A rather weak remanent magnetization (~ 4.5 mμB/Mn) can be detected along the (001) direction of the Mn3Pt film in the non-collinear state due to symmetry-allowed spin canting (Fig. 2f). This weak moment per Mn atom has a similar size to that in Mn3Sn (ref. 11), but its direction is not parallel with the kagome planes as in the latter case. In contrast, no weak ferromagnetism could be detected in the high-temperature collinear phase.
Strain dependence of the AHE
Armed with these observations, it is then interesting to explore how the AHE in Mn3Pt films changes with strain (or lattice symmetry). Remarkably, residual epitaxial strain is preserved in our Mn3Pt thin films up to large thicknesses due to their high-quality epitaxy. As illustrated in Fig. 3a, a and c of our Mn3Pt films change with thickness d, significantly but continuously, and only approach the bulk cubic lattice constant 3.833 Å at d ~ 100 nm. Below 50 nm, the tetragonality factor c/a of the Mn3Pt films changes sharply with decreasing d, from 0.999 at 50 nm to 0.986 at 10 nm (Fig. 3b). The room-temperature resistivity strongly depends on d below 30 nm due to increased interface scattering in ultrathin films (Fig. 3c). Below 10 nm, the films are not continuous as a result of island formation and growth, and consequently lack macroscopic percolation in electrical measurements.
Interestingly, we found the room-temperature AHE to be strongly dependent on d (Fig. 3d); larger d yields larger coercive fields μ0Hc (Fig. 3e) and smaller ρH (Fig. 3f). For a 200 nm film, the magnetic field for switching the AHE reaches ~0.3 T, which is more than one order of magnitude larger than that of a 10 nm film (~26 mT). In addition, the room-temperature remanent magnetic moment Mr decreases with d, in a manner similar to ρH (Fig. 3g). The similar trend of μ0Hc, Mr and ρH versus d indicates that the epitaxial strain field, which decreases with increasing d as shown in Fig. 3a, can be treated as a perturbation, and in this perturbative regime all ground-state properties and response coefficients are expected to follow simple power laws in the strength of the perturbation. We also note that there are other possible mechanisms contributing to the variations of these physical quantities with d, for example, the decreasing surface/bulk ratio with increasing d, and the different film morphology at different thicknesses as discussed above. As a result of competition between these mechanisms, the anomalous Hall conductivity (AHC) estimated using |σH| = |ρH|/ρ2 peaks at 20 nm and reaches ~98 ± 13 Ω−1 cm−1 (Fig. 3h). This value is much larger than that in bulk samples of Mn3Sn (ref. 11) and Mn3Ge (refs 12,13) at room temperature, and is ~10 times larger than that in thick films (>200 nm) of Mn3Pt, suggesting significant potential to control the size of the AHC in thin films of non-collinear antiferromagnets.
Electrical switching of the AHE
We now turn to the effect of piezoelectric strain triggered by an electric field E applied to the ferroelectric BTO substrate, as illustrated schematically in Fig. 4a on the AHE of a 20 nm Mn3Pt film. As shown in Fig. 4b, the warm-up transition temperature of a 20-nm-thick Mn3Pt film is shifted up by ~28.5 K to 376.5 K after an E of 4 kV cm−1 is applied perpendicular to the BTO substrate. At ~360 K a Mn3Pt film originally in the collinear state can be switched to the non-collinear state by applying E = 4 kV cm−1. Accordingly, the AHE is switched on by E = 4 kV cm−1 at 360 K (Fig. 4c). Extensive measurements of the AHE versus E applied to the BTO substrate demonstrate that the AHE can be switched on by |E| > 2 kV cm−1, and subsequently switched off by reducing |E| to less than 0.5 kV cm−1 (Fig. 4d). Unlike previous reports on E control of the AHE, which require a magnetic field of 0.1 T or higher to be sustained25, the present work has realized electric switching between zero and finite AHE at zero magnetic field.
In addition, the E dependence of the zero-field |ρH| in Fig. 4d indicates that the switching effect is due to piezoelectric strain transferred from BTO to the Mn3Pt film by interfacial strain mediation. The piezoelectric strain generated by BTO is controlled by a to c domain switching on applying an out-of-plane E, as evidenced in Fig. 4e. To quantitatively determine the lattice change of the Mn3Pt film, both a and c were measured versus E applied to BTO at 360 K. As seen in Fig. 4f,g, the Mn3Pt film is compressed in-plane but stretched out-of-plane as a consequence of the compressive piezoelectric strain from BTO. The in-plane strain ε a is as large as approximately −0.35% at E = −4 kV cm−1. Plotting ε a versus the out-of-plane strain ε c of the Mn3Pt film yields a linear curve (Fig. 4h), and the fitted Poisson ratio is ν ≈ 0.35.
The AHE in the non-collinear phase of Mn3Pt originates from its 120° magnetic order, which breaks the cubic symmetry of the nonmagnetic structure. In the intrinsic contribution to the AHE, this is reflected by the non-zero momentum-space Berry curvature of the Bloch bands of Mn3Pt and its non-zero integral over filled bands, as shown in Fig. 5. We calculated the intrinsic contribution to the AHE of the non-collinear phase of Mn3Pt using the lattice parameters of the 20 nm film measured at 360 K with a 4 kV cm−1 electric field, and obtained σH = 81 Ω−1 cm−1, which is very close to the experimental value of 74.2 Ω−1 cm−1. The good agreement between the intrinsic contribution to AHE and the measured value is consistent with the expected suppression of scattering contributions to the AHE at higher temperatures and in moderately dirty samples. We note that the magnetic order of the high-temperature collinear phase of Mn3Pt is still not completely understood26, but the absence of both AHE and weak magnetization is consistent and suggests a magnetic symmetry that forbids quantities described by time-reversal-odd pseudovectors.
Using experimentally determined lattice parameters, we also calculated the thickness dependence of the intrinsic contribution to the AHC of Mn3Pt thin films. The results are shown in Fig. 5c. The qualitative trend is consistent with the experimental result in Fig. 3h for films thicker than 20 nm, below which the films exhibit high surface roughness and lack continuity. Note that although it is expected purely from symmetry considerations that the AHC vector along the film normal will scale with the amount of lattice strain (see Supplementary Fig. 1 and relevant discussion in Supplementary Note 1) and hence vary with film thickness, the sign of the effect depends on details of the electronic structure at energies near the Fermi level. Quantitatively, the AHE in the experiment increases more rapidly with decreasing film thickness than expected on the basis of these theoretical results. The discrepancy might be related to enhanced surface scattering contributions to the AHE in thinner films, which have larger surface to volume ratios and rougher surfaces.
We have observed a large AHE in high-quality epitaxial single-crystalline films of cubic Mn3Pt with a normal triangular spin structure on BTO substrates. The AHC is found to be very sensitive to epitaxial strain and it changes with film thickness by an order of magnitude. The capability of electrically switching the AHE on and off implies new possibilities for information storage and processing based on all-electrical operations in antiferromagnets: switching it electrically with a voltage and reading it with a sense current in the same layer. Moreover, the successful demonstration of thickness-tunable strain in the intermetallic Mn3Pt films opens the door to strain engineering of intermetallic alloys.
Due to the low sputtering yield of Mn, Mn3Pt thin films were sputtered from a Mn82Pt18 target onto (001)-oriented BaTiO3 (BTO) single-crystal substrates (5 × 5 × 0.5 mm3) in a radiofrequency sputtering system with a base pressure of 5 × 10−8 torr. The system was equipped with RHEED. The deposition was performed at 600 °C. The sputtering power and Ar gas pressure were 60 W and 5 mtorr, respectively. The deposition rate was 0.35 Å s−1, as determined by X-ray reflectivity measurements. After deposition, Mn3Pt films were heated to 730 °C in vacuum for annealing for 1 h. To avoid possible breaking of the BTO substrates during variations in temperature, the ramp rate was kept at 5 °C min−1 for both heating and cooling.
XRD measurements were performed in a four-circle PANalytical X-ray diffractometer with heating capability. A Cu-Ka1 X-ray was used in the diffractometer with a wavelength of 1.540598 Å. Electric fields were applied (using a Keithley 2400 source meter) to BTO substrates with silver paint coated on the back sides.
Cross-sectional wedged samples were prepared by mechanical thinning, precision polishing and ion milling. An electron-beam probe was utilized to scan thin films to achieve high resolution of local regions, and Z-contrast STEM images were taken by a high-angle annular dark-field detector on a Zeiss Libra 200 MC STEM system at 200 kV.
Electrical contacts onto the Mn3Pt films were made by Al wires via wire bonding. Electrical measurements were performed in a Quantum Design physical property measurement system combined with a Keithley 2400 source meter. The Van der Pauw geometry was used for Hall measurements. The electrical current used for both longitudinal and Hall resistance measurements was 100 µA.
Magnetic measurements were performed in a Quantum Design superconducting quantum interference device magnetometer with 10−11 A m2 sensitivity.
Calculations of the electronic structure of Mn3Pt were performed using Quantum ESPRESSO27 with fully relativistic ultrasoft pseudopotentials generated from PSLibrary 0.3.1, using the Perdew–Burke–Ernzerhof functional28. Lattice parameters are fixed to the experimentally determined values (a = 3.8659 Å, c = 3.8604 Å) for the 20 nm film at 360 K and within the 4 kV cm−1 electric field. The Berry curvature was calculated by first constructing an effective tight-binding Hamiltonian written in the maximally localized Wannier basis generated by Wannier90 as a post-processing step of the density functional theory calculation29, and then interpolating the Berry curvature to arbitrary k-points in the Brillouin zone. The intrinsic AHC was calculated by integrating the Berry curvature summed over filled bands on a 200 × 200 × 200 mesh of the Brillouin zone with adaptive refinement of 5 × 5 × 5 when the Berry curvature was larger than 100 Å2.
The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
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Z.Q.L. acknowledges financial support from the National Natural Science Foundation of China (NSFC grant no. 51771009) and a startup grant from Beihang University. H.C. and A.H.M. are supported by SHINES, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Basic Energy Sciences, under award #SC0012670, and Welch Foundation grant TBF1473. H.C. and A.H.M acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing high-performance computer resources for performing the electronic structure calculations. J.M.D.C. acknowledges support from Science Foundation Ireland contract no. 12/RC/2278. X.R.W. acknowledges supports from a Nanyang Assistant Professorship grant from Nanyang Technological University and Academic Research Fund Tier 1 (RG108/17S) from the Singapore Ministry of Education.
Supplementary Figure 1 and Supplementary Note 1