Optical nonlinear anomalous Hall effect reveals the hidden spin order in antiferromagnets

Abstract

Reading antiferromagnetic order remains a central obstacle for antiferromagnetic memory and logic because zero net magnetisation precludes conventional magnetic readout. Domain imaging typically relies on x-ray magnetic linear dichroism (XMLD) microscopy at synchrotron sources, but XMLD is even under time reversal and cannot distinguish 180{\deg}-reversed magnetic states. Here we report the first experimental observation of the optical nonlinear anomalous Hall effect, predicted for antiferromagnets with combined parity - time-reversal ($PT$) symmetry. The effect stems from light-induced interband electric-dipole transitions, where spin-orbit coupling induces an asymmetry between $\pm k$ states and generates a time-reversal-odd photocurrent whose sign flips upon 180{\deg} reversal of the N\'eel vector. In $PT$-symmetric CuMnAs, we use near-field excitation to map this photocurrent with sub-100-nm spatial resolution after current-induced spin-orbit-torque switching. The signal polarity follows local N\'eel vector reversal, enabling nanoscale imaging of antiferromagnetic texture and direct readout of 180{\deg}-reversed antiferromagnetic states that remain indistinguishable in XMLD and other time-reversal-even linear-dichroic probes. The optical nonlinear anomalous Hall effect thus reveals a new light-spin interaction and provides a scalable route to nanoscale readout of hidden spin order, with potential for ultrafast all-electrical and all-optical antiferromagnetic spintronic technologies.