Emergent Anomalous Hall Effect from Surface States in the Altermagnet MnTe Thin Films

Abstract

Transport measurements on thin films of the prototypical altermagnet MnTe have reported conflicting phenomena of anomalous Hall effects (AHE), including opposite signs and thickness-independent resistivity. Here we resolve these discrepancies by separating bulk and surface contributions to the AHE for different crystal terminations. Using first-principles calculations and symmetry-based effective models, we show that although the bulk hosts a characteristic $g$-wave Fermi surface, surface states within the bulk gap acquire a ferromagnet-like spin polarization and dominate the AHE at experimentally relevant Fermi energies. While the surface magnetization follows the surface spin sublattice, the resulting AHE is uniquely determined by the bulk Néel order for a given termination. Both bulk and surface contributions are closely linked to a small but finite out-of-plane orbital magnetization. Incorporating realistic interfacial chemistry further reveals that a Te capping layer can reverse the surface AHE sign relative to that on an InP substrate. Our results establish a microscopic framework for interpreting and engineering AHE responses in altermagnetic thin films through interface design.

Figures (7)

• Figure 1: (a) Surface band structure with SOC. Red color represents the top surface projection (Te-termination) and gray color indicates the bulk bands in a slab model. (b) Schematics of the spin texture in bulk and surfaces. While bulk bands have a $g$-wave feature, top and bottom surface states are fully spin polarized along $+y$ and $-y$, respectively. The red and blue arrows depict the altermagnetic order. (c) Top and bottom surface states induce the same AHE due to the Berry curvature, though they exhibit opposite spin polarization ($\pm S_y$).
• Figure 2: Thickness and energy dependence of the intrinsic anomalous Hall conductance in MnTe slabs with different terminations. (a--c) $\sigma_{xy}^{2\mathrm{D}}(E)$ for slabs with (a) Te/Te, (b) Te/Mn, and (c) Mn/Mn terminations (top/bottom), for several thicknesses. The inset of (a) plots the surface band structure with projected Berry curvature $\Omega_{xy}$ near $\overline{\Gamma}$.
• Figure 3: (a) Layer-resolved AHC at $E_F$ in a Te--MnTe--Mn slab (Mn$_{19}$Te$_{19}$). Purple and khaki points represent Mn and Te atomic layers, respectively. (b,c) Corresponding slab structures, Néel-order configuration and corresponding Berry curvature represented by the self-rotating wavepackets. In the dashed boxes, the Mn atoms with the same spin direction share the same local environment. Hence, (b) and (c) share the same bulk Néel order. Because they are symmetric to each other by a $C_{2z}$ rotation, two slabs exhibit the same AHE ($\sigma_{xy}$).
• Figure 4: Illustration of the finite out-of-plane ($z$) spin moment and orbital moment in the bulk calculated by DFT. Both Mn sublattices are canting along the same $+z$ direction while all Te atoms exhibit net moments along $-z$. Dashed lines depict two cleaving planes to form Te-terminated surfaces with opposite surface spin sublattices.
• Figure 5: Comparison between band structures along $0.15\overline{\mathrm{M}}$--$\overline{\Gamma}$--0.15$\overline{\mathrm{K}}$ path for DFT calculated (solid) and effective model (dashed) bands, with the projection of (a) orbital hybridization $\langle p_x \rangle - \langle p_y \rangle$ without SOC, (b) orbital polarization $\langle L_z \rangle$, (c) spin polarization $\langle S_y\rangle$ and (d) twice $\langle S_z\rangle$. (b)-(d) are calculated with SOC. Grey background denotes bulk-like states.