Strain-tunable Berry curvature in quasi-two-dimensional chromium telluride

Abstract

Magnetic transition metal chalcogenides form an emerging platform for exploring spin-orbit driven Berry phase phenomena owing to the nontrivial interplay between topology and magnetism. Here we show that the anomalous Hall effect in pristine Cr₂Te₃ thin films manifests a unique temperature-dependent sign reversal at nonzero magnetization, resulting from the momentum-space Berry curvature as established by first-principles simulations. The sign change is strain tunable, enabled by the sharp and well-defined substrate/film interface in the quasi-two-dimensional Cr₂Te₃ epitaxial films, revealed by scanning transmission electron microscopy and depth-sensitive polarized neutron reflectometry. This Berry phase effect further introduces hump-shaped Hall peaks in pristine Cr₂Te₃ near the coercive field during the magnetization switching process, owing to the presence of strain-modulated magnetic layers/domains. The versatile interface tunability of Berry curvature in Cr₂Te₃ thin films offers new opportunities for topological electronics.

Fig. 1. Crystal structure of Cr₂Te₃ thin films.

a Atomistic structure of Cr₂Te₃ viewed along the crystallographic [210] direction. b Among the three Cr species, Cr1 (red) form sparse honeycombs that are stacked between those of Cr2/Cr3 (purple/blue) with sixfold in-plane symmetry (c). d Enhanced in-plane compressive strain at reduced thickness t, quantified by the relative change of the a lattice parameter via XRD for Cr₂Te₃ grown on Al₂O₃(0001) (solid) or SrTiO₃(111) (open). f Schematic of the film stacks, where the interfacial strain plays a pivotal role in inducing extraordinary magnetic and transport phenomena. Atomically resolved STM morphology of a 13 × 13 nm² surface after removing Se capping (e) and planar HAADF STEM image (g) of Cr₂Te₃ confirm the honeycomb-like Te lattice, where the HAADF intensity line scan reveals the Cr sites (h). i–m Cross-sectional images of Cr₂Te₃ films grown on SrTiO₃(111). The HAADF (i) and iDPC (j) imaging along the [210] zone axis of Cr₂Te₃ illustrates the dominating Te–Cr2/Cr3–Te layers. The enlarged view (dashed box region in i) of HAADF (k), DPC (l), and iDPC (m) images identify the random distribution of the interlayer Cr1 (circles), which deviates from the ideal Cr₂Te₃ structure with full occupancy. The color wheel in the DPC image indicates the projected electric field direction.

Fig. 2. Magnetic properties of Cr₂Te₃ thin films.

a Temperature dependence of the magnetization M of a typical 24 u.c. Cr₂Te₃ film under the zero-field-cool (ZFC) and field-cool (FC) conditions with an out-of-plane (OOP) external magnetic field μ₀H = 0.1 T. The Curie (T_C) and blocking (T_b) temperatures are labeled by the arrows. b Field dependence of M under OOP and in-plane (IP) configurations for t = 24 u.c. at selected temperatures (top three, black, green, and orange) and OOP M(H) for t = 6 and 3 u.c. at 2 K (bottom two, red and blue). For clarity, the curves are vertically shifted, and the IP data are magnified by a factor of 3. c Depth profiles of PNR nuclear (NSLD), magnetic (MSLD, at IP fields of 1, 0.8, and 0.05 T, respectively) and X-ray scattering length densities (SLD) of 24 u.c. Cr₂Te₃ on Al₂O₃(0001) with Te/AlO_x capping. The deduced spin configuration is schematically shown with red arrows overlaying with the MSLD profiles; the horizontal projection of the vectors corresponds to the IP M determined by PNR.

Fig. 3. The unconventional Hall effects in Cr₂Te₃ thin films.

a Magnetic field dependence of the Hall resistivity ρ_yx(H) at selected T for 6 u.c. Cr₂Te₃ on Al₂O₃(0001). b Hall traces Δρ_yx after removing the high-field ordinary Hall backgrounds. At T_S ~ 40 K, a sign change occurs in the anomalous Hall resistivity ρ_AHE, defined as the value of Δρ_yx when the system is fully magnetized under a positive H. Apart from the AHE hysteresis loop, additional hump-shaped features develop. c Temperature dependence of the anomalous Hall conductivity σ_AHE for t = 3–24 u.c. (symbols, where solid lines are guide for the eye and dashed lines are linear fit to low T data). d, e Thickness dependence of σ_AHE at 2 K (d), AHE sign reversal temperature T_S (e), and the T-intercept of the linear AHE component at low T.

Fig. 4. Berry curvature and anomalous Hall conductivity in Cr₂Te₃.

a, b Calculated Berry curvature Ω^z(k) (a) along the high symmetry k-paths in the Brillouin zone (right inset in a) and the corresponding electronic band structure (b). Left inset in a, nearly degenerate SOC anti-crossing bands contributing to the sharp peak in Ω^z(k) along A–L. c Anomalous Hall conductivity σ_AHE near the Fermi level ε_F, in equilibrium state (black), under compressive (blue) or tensile (red) strain conditions, respectively. The shades in c are guide for the eye showing the slight asymmetry of the energy dependence of σ_AHE above and below ε_F.

Fig. 5. Characteristics of hump-shaped Hall peaks in Cr₂Te₃.

a Simplified superposition of two AHE components with opposite sign and different coercive fields. b, c Minor loop scans of 6 u.c. Cr₂Te₃ film on Al₂O₃(0001) at T = 30 K, first fully magnetized at μ₀H = +3 T (complete loop shown in gray as guide for the eye) and then swept back and forth between +2 T and selected μ₀H_min. The experimental minor loops in b are qualitatively reproduced in c using simulations that underscore the significance of strain-driven multilayer/domain features and the sign reversal in ρ_AHE.