Second-order magnetic responses in quantum magnets: Magnetization under ac magnetic fields

TL;DR

This paper explores second-order magnetic responses in quantum magnets under ac magnetic fields, revealing how different polarizations induce distinct nonlinear effects and linking magnetization to linear response properties.

Contribution

It demonstrates the nonlinear magnetic effects induced by circularly polarized fields in quantum magnets and connects these effects to the linear response via the dynamical spin structure factor.

Findings

Linearly polarized fields induce second-harmonic responses.

Circularly polarized fields generate zero-frequency magnetization.

Magnetization magnitude correlates with the linear response dynamical spin structure factor.

Abstract

We investigate second-order magnetic responses of quantum magnets against ac magnetic fields. We focus on the case where the $z$ component of the spin is conserved in the unperturbed Hamiltonian and the driving field is applied in the $xy$ plane. We find that linearly polarized driving fields induce a second-harmonic response, while circularly polarized fields generate only a zero-frequency response, leading to a magnetization with a direction determined by the helicity. Employing an unbiased numerical method, we demonstrate the nonlinear magnetic effect driven by the circularly polarized field in the XXZ model and show that the magnitude of the magnetization can be predicted by the dynamical spin structure factor in the linear response regime.