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  • Letter
  • Open Access

Second-order anomalous Hall effect controlled by electric fields in altermagnets

Arnob Mukherjee, Biplab Sanyal, Annica M. Black-Schaffer*, and Ankita Bhattacharya*,†

  • *These authors contributed equally to this work.
  • †Contact author: ankita.bhattacharya@physics.uu.se
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Phys. Rev. B 113, L220401 – Published 3 June, 2026

DOI: https://doi.org/10.1103/wb4y-tzln

Abstract

Altermagnets are a recently discovered class of compensated magnets with momentum-dependent spin splittings and unusual transport properties, even without a net magnetization. In the presence of combined fourfold rotation and time-reversal (C4T) symmetry, linear and also second order, driven by a Berry curvature dipole, anomalous Hall responses are forbidden in any pure d-wave altermagnet. Nevertheless, here we find that the nontrivial quantum metric of the occupied Bloch states allows for an electric field induced Berry curvature dipole, which generates a strong and tunable second-order Hall current, enabling it to be switched on or off by simply adjusting the relative orientation between the symmetry-reducing dc field and the ac probe field. Specifically, we investigate the electric field induced second-order anomalous Hall response in a two-dimensional Rashba-coupled altermagnet with varying dx2−y2 (B1g) and dxy (B2g) altermagnet symmetry to capture all possibilities. Crucially, the nonlinear signal is highly sensitive to the underlying symmetry of the altermagnetic order at specific doping levels, offering a purely electrical method to distinguish distinct altermagnetic orders. Our results position altermagnets as a promising platform for controllable nonlinear transport and spintronic applications.

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Phys. Rev. B 113, L220401– Published 3 June, 2026
  • Received 27 October 2025
  • Accepted 11 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.

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