Strain-tunable anomalous Hall effect in hexagonal MnTe

TL;DR

The study shows that a small uniaxial strain detwins hexagonal MnTe into a single in-plane altermagnetic domain, enabling a direct link between in-plane moment orientation and the anomalous Hall effect. A strain-induced, spin-orbit–coupled distortion of the Berry curvature produces a linear-in-strain contribution to the AHE, allowing sign control near the altermagnetic transition temperature without shifting $T_{AM}$, and broadening the temperature window for AHE. The approach combines neutron scattering under strain, transport, elastocaloric measurements, and a phenomenological model to illuminate how Berry curvature and altermagnetic order interact under strain. These results point to strain-tunable, low-field magnetic sensors and spintronic devices based on altermagnets with minimal stray fields.

Abstract

The ability to control and manipulate time-reversal ($T$) symmetry-breaking phases with near-zero net magnetization is a sought-after goal in spintronic devices. The recently discovered hexagonal altermagnet manganese telluride ($α$-MnTe) is a prime example. It has a compensated altermagnetic ground state where the magnetic moments are aligned in each layer and stacked antiparallel along the $c$ axis, yet it exhibits a spontaneous anomalous Hall effect (AHE) that breaks the $T$-symmetry with a vanishingly small $c$-axis ferromagnetic (FM) moment. However, the presence of three 120$^\circ$ separated in-plane magnetic domains presents a challenge in understanding the origin of the AHE and the effective control of the altermagnetic state. Here we use neutron scattering to show that a compressive uniaxial strain along the next-nearest-neighbor Mn-Mn bond direction detwins $α$-MnTe into a single in-plane magnetic domain, aligning the in-plane moments along the same axis. Furthermore, we find that uniaxial strain (-0.2% to 0.1%) significantly sharpens the magnetic hysteresis loop and switches the sign of the AHE near room temperature. Remarkably, this is achieved without altering the altermagnetic phase-transition temperature or substantially changing the small $c$-axis FM moment. Combined with our phenomenological model, we argue that these effects result from the modification of the electronic Berry curvature by a combination of both spin-orbit coupling and strain. Our work not only unambiguously establishes the relationship between the in-plane moment direction and the AHE in $α$-MnTe but also paves the way for future applications in highly scalable, strain-tunable magnetic sensors and spintronic devices.

Figures (13)

• Figure 1: Neutron scattering experiments under uniaxial strain.a, Crystal structure of $\alpha$-MnTe. b, In-plane magnetic structure with the Mn$^{2+}$ moments along the next-nearest-neighbor (NNN) Mn--Mn bond direction, corresponding to $\left[1 \bar{1} 0 \right]$. c, Similar to b with the Mn$^{2+}$ moment along the nearest-neighbor (NN) Mn--Mn bond direction, corresponding to $\left[1 1 0 \right]$. d,e, Schematics of magnetic domain configurations with Mn moments aligned along the NNN Mn--Mn bond direction (as in b). (d) In the free-standing crystal, six symmetry-equivalent domains are uniformly populated, each color represents a pair of time-reversal-related domains $\rightleftarrows$ and $\leftrightarrows$ with the same in-plane moment direction, which in turn can be along one of three directions related by threefold rotation. (e) Under compressive uniaxial strain along the NNN Mn--Mn bond direction the sample is detwinned, leaving a single pair of domains with moments aligning along the uniaxial strain direction. f,g, Simulated pie-chart representations of magnetic Bragg-peak intensities. The colors represent fractional contribution from each magnetic domains populations corresponding to d and e. The circle area scales with the total intensity at each peak. h,i, Three-dimensional renderings of the simulated Bragg-peak intensities corresponding to f and g. j-o, Schematics and simulations analogous to d–i, but for Mn$^{2+}$ moments aligned along the NN Mn--Mn bond direction (as shown in c). Panels k, m, and n present symmetry-allowed domain configurations (under strain) that qualitatively reproduce the intensity patterns. Details of the domain selection inferred from the strained data are provided in Methods. p,q, Elastic neutron scattering intensity maps in the $HK$ plane at $L=1\, (r.l.u.)$ under compressive uniaxial strain along the NNN Mn--Mn bond direction at 240 K and 320 K. Dashed white circles mark the magnetic-only positions. The white arrow defines the azimuthal angle $\phi$ in the following panel. r, Azimuthal angular dependence of magnetic peak intensities of free-standing and strained samples and their differences. Color shading highlights that the two peaks perpendicular to the uniaxial stress direction are enhanced (red), whereas the other four are suppressed (blue). s-u, Three-dimensional visualization of the peaks intensity for the free-standing, strained, and difference data shown in r. The neutron scattering results under stress (t) are consistent with the single-domain simulation (i), confirming a fully-detwinned state with magnetic moments parallel to the uniaxial stress direction. All panels f-u are at $L=1\, (r.l.u.)$.
• Figure 1: Characterizations of single crystal hexagonal MnTe.a, Single crystal image. b, X-ray Laue diffraction pattern of a $\alpha$-MnTe single crystal. The crystallographic orientations along the $[1,1,0]$ and $[1,\bar{1},0]$ directions in real space are marked. Real-space axes ($\textbf{a}$, $\textbf{b}$) and corresponding reciprocal lattice vectors ($\textbf{a}^*$, $\textbf{b}^*$) are marked by blue and green arrows, respectively. c, Powder X-ray diffraction pattern at room temperature. Black circles represent experimental intensities and the red line shows the calculated intensities. The refinement yields $\chi^2 = 1.04$, confirming the pure $\alpha$-MnTe phase. d, Temperature dependence of magnetic susceptibility with magnetic fields applied along the in-plane and out-of-plane directions. e, Derivative of data in d, where the peak features mark the altermagnetic transition $T_{\mathrm{AM}}$. f, Energy-dispersive X-ray spectroscopy at room temperature. Tellurium and manganese peaks are marked by black and purple stars, respectively. The measured Mn:Te ratio is $1.026\pm0.014$.
• Figure 2: The AHE measurements in free-standing $\alpha$-MnTe.a, Schematic of the five-terminal Hall bar geometry used for electrical transport measurements. The current is applied along the NNN Mn--Mn bond direction and the magnetic field is along the $c$ axis. The colored hexagons represent the in-plane magnetic domain orientations. b, Illustration of uniformly distributed magnetic domains and domain boundaries. c,$\rho_{xy}^{\mathrm A}$ as function of temperature. Inset: Hall resistivity and magnetization hysteresis loops at 260 K after linear background subtraction. d, Temperature dependence of the normalized longitudinal resistivity $\rho_{xx}$ for samples grown by different methods. Samples #8 and #10, grown by flux method, exhibit AHE, whereas Samples #1 and #6, grown by chemical vapor transport and flux methods with different procedures, show no AHE. The vertical line marks the altermagnetic transition temperature ($T_{\mathrm{AM}}$). e, Arrhenius plot for extracting the thermal activation energy, with the same data in d. The dashed lines represent linear fits based on $\rho_{xx} \propto e^{\Delta/2k_{\mathrm B}T}$, where $k_{\mathrm B}$ is the Boltzmann constant and $\Delta$ is the activation energy gap, i.e. the charge gap. f, Summary of the charge gap for various samples. All samples exhibiting AHE (yellow stars) lie within a narrow range of 15--18 meV.
• Figure 2: Neutron scattering analysis of strain effects in $\alpha$-MnTe.a, Mechanical uniaxial stress device for neutron scattering experiments. A square plate-shaped sample with mass of $\sim$90 mg was mounted in the device as indicated by the red arrow. Compressive stress $\sigma^-$ was applied by tightening the screw on the right along the NNN Mn--Mn bond direction in real space. b, Schematic of the $(H, -0.5H)\times(0,K)$ reciprocal space plane at $L=1\, (r.l.u.)$ in the altermagnetically ordered phase. Blue markers indicate the magnetic-only Bragg reflections used in our analysis, where nuclear contributions are absent, while gray markers denote Bragg positions with nuclear intensity. c, Azimuthal angular dependence of magnetic peak intensities of free-standing and strained samples with background subtracted from the measurements at $320$ K ($>T_{\mathrm{AM}}$) . d-f, Neutron diffraction patterns of the free-standing sample. The intensities were integrated within the annular region enclosed by the two dashed circles, restricted to the areas of the six magnetic Bragg peaks. The integration region is enlarged for clarity in b. g-i, Similar plots to d-f for the same sample under compressive strain. The white arrows represent the uniaxial compressive strain direction.
• Figure 3: Sign reversal of the AHE in $\alpha$-MnTe driven by uniaxial strain and temperature.a, Schematic showing the orientation of uniaxial stress applied along the crystal NNN Mn--Mn bond direction in strained transport measurements. Blue arrows represent compressive stress $\sigma^{-}$, while red arrows indicate tensile stress $\sigma^{+}$. The electrical current is along the same direction. Magnetic field is applied out-of-plane. b, Comparison of Hall resistivity $\Delta\rho_{xy}$ (linear background subtracted) as a function of magnetic field between a sample in the free-standing state and strained state at 290 K. Arrows denote the magnetic-field sweep directions. $H_c^{+}$ and $H_c^{-}$ represent the coercive fields. c-e,$\Delta\rho_{xy}$ (linear background subtracted) under different strain levels at 240, 233, and 230 K, respectively. Thin (thick) black arrows denote magnetic-field sweeps down (up). The curves are vertically offset for clarity. f-h, Corresponding longitudinal resistivity $\rho_{xx}$ measured under the same strain and temperature conditions as in b-d. The data have been shifted vertically by subtracting constant offsets. i, The extracted anomalous Hall resistivity $\rho_{xy}^{\mathrm A}$ as a function of strain at different temperatures. The red shading denotes positive $\rho_{xy}^{\mathrm A}$, corresponding to a clockwise hysteresis loop (top-right inset), while the light blue shading indicates negative $\rho_{xy}^{\mathrm A}$, corresponding to a counterclockwise hysteresis loop (bottom-left inset).