  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.
