Geometric Photon-drag Effect in Unconventional Magnets

Abstract

The photon-drag effect is a nonlinear optical phenomenon in which the finite momentum carried by incident photons is transferred to charge carriers, thereby generating a dc photocurrent even in systems with inversion symmetry. Within the density-matrix formalism in the velocity gauge, and accounting for nonvertical optical transitions driven by finite photon momentum, we derive the nonlinear injection and shift conductivities that characterize the photon-drag photogalvanic response. We investigate these photon-drag responses in unconventional $p_x$-wave and $d_{x^2-y^2}$-wave magnets in the presence of Rashba spin-orbit coupling (RSOC), highlighting the distinct roles of symmetry and quantum geometry in shaping their nonlinear optical behavior. The key finding of our work is that, despite the broken inversion symmetry, the conventional photogalvanic response vanishes identically in the $q=0$ limit after Brillouin-zone integration in both unconventional magnetic phases, resulting in a nonlinear dc photocurrent entirely photon-drag driven. The two unconventional magnets exhibit qualitatively distinct responses governed by their symmetry properties: the $p$-wave magnet supports only linear injection and circular shift conductivities, whereas the $d$-wave altermagnet, which simultaneously breaks time-reversal and inversion symmetries, admits all linear and circular components. Our findings establish altermagnets as a promising platform for controlling symmetry-selective nonlinear photocurrents and may enable applications in polarization-sensitive photodetection, nonlinear optoelectronics, and quantum geometric photogalvanics.