Half-Integer Quantization of In-Plane Anomalous Hall Effect Realized in a Magnetic Weyl Semimetal

Weyl semimetals host low-energy chiral quasiparticle excitations with linear non-degenerate band crossings (Weyl nodes) in the bulk. This nontrivial band topology is predicted to give rise to exotic transport behaviors, many of which remain unexplored. Here, we report the emergence of a half-integer quantized in-plane anomalous Hall effect (AHE) in the magnetic Weyl semimetal MnSb₂Te₄, where the in-plane Hall conductivity σ_yx(H || ab) takes discrete values of n*e²/2h, with integer n programmable via a post-growth hydrogen intake-and-release technique [1]. This quantized in-plane AHE, with both the applied field H and magnetization M in the ab-plane, is distinct from the Lorentz force driven Hall effect or a conventional planar Hall effect, suggesting a possible realization of a parity anomaly. We have previously shown that hydrogen incorporation modifies the Mn orbitals and tilts M toward the ab-plane, thereby transforming the Weyl phase [2] to reshape out-of-plane Berry curvature, and inducing a hysteretic σ_yx(H || ab) response. In this work, by decomposing the Hall response into planar and anomalous components, we demonstrate how half-quantum steps in σ_yx^AHE emerge and evolve with tunable M-tilt. By mapping its angular and field dependence across symmetry axes, and correlating transport signatures with band-structure evolution, we establish symmetry-controlled half-integer quantization as a robust, configurable phenomenon. Angle-dependent transport measurements reveal an unusual σ_yx(φ) ∝ cos(3φ) - sin(φ) dependence, consistent with mirror symmetry breaking while preserving the crystalline threefold rotational (C₃) symmetry, all leading to half-integer quantization and symmetry-engineered quantum states.

[1] H. Deng, L. Zhao, K. Park, J. Yan, K. Sobczak, A. Lakra, E. Buzi, L. Krusin-Elbaum, Nature Comms. 13, 2308 (2022).

[2] A. N. Tamanna, A. Lakra, X. Ding, E. Buzi, K. Park, K. Sobczak, H. Deng, G. Sharma, S. Tewari, L. Krusin-Elbaum, Nature Comms. 15, 9830 (2024).