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arXiv:2203.02145 · Physical review. B./Physical review. B

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

Tatsuya Kaneko, Yuta Murakami, Shintaro Takayoshi, Andrew J. Millis

Published May 19, 2022• 1 citation
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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.

DOI
10.1103/physrevb.105.195126

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We investigate second-order magnetic responses of quantum magnets against ac magnetic fields. We focus on the case where the zzz component of the spin is conserved in the unperturbed Hamiltonian and the driving field is applied in the xyxyxy 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.
We consider s=1/2s=1/2s=1/2 spins in the presence of a constant magnetic field in the z direction and an ac magnetic field in the $x\ensuremath{-}z$ plane. A nonzero dc magnetization component in the y direction is a result of broken symmetries. A pairwise interaction between two spins is shown to resonantly increase the induced magnetization by one order of magnitude. We discuss the mechanism of this enhancement, which is due to additional avoided crossings in the level structure of the system.
We theoretically predict a nonequilibrium phase transition in quantum spin systems induced by a laser, which provides a purely quantum-mechanical way of coherently controlling magnetization. Namely, when a circularly polarized laser is applied to a spin system, the magnetic component of a laser is shown to induce a magnetization normal to the plane of polarization, leading to an ultrafast phase transition. We first demonstrate this phenomenon numerically for an S=1S=1S=1 antiferromagnetic Heisenberg spin chain, where a new state emerges with magnetization perpendicular to the polarization plane of the laser in place of the topologically ordered Haldane state. We then elucidate its physical mechanism by mapping the system to an effective static model. The theory also indicates that the phenomenon should occur in general quantum spin systems with a magnetic anisotropy. The required laser frequency is in the terahertz range, with the required intensity being within a prospective experimental feasibility.
The effect of the circularly polarized laser field on quantum spin systems in the steady-state regime, in which relaxation plays the central role, has been studied. The dynamical mean-field-like theory predicts several general results for the behavior of the time-average magnetization caused by the laser field. The induced magnetization oscillates with the frequency of the laser field (while Rabi-like oscillations, which modulate the latter in the dynamical regime, are damped by the relaxation in the steady-state regime). At high frequencies, that magnetization is determined by the value to which the relaxation process is directed. At low frequencies the slope of that magnetization as a function of the frequency is determined by the strength of the laser field. The anisotropy determines the resonance behavior of the time-averaged magnetization in both the ferromagnetic and antiferromagnetic cases with nonzero magnetic anisotropy. Nonlinear effects (in the magnitude of the laser field) have been considered. The effect of the laser field on quantum spin systems is maximal in resonance, where the time-averaged magnetization, caused by the laser field, is changed essentially. Out of resonance the changes in the magnetization are relatively small. The resonance effect is caused by the nonzero magnetic anisotropy. The resonance frequency is small (proportional to the anisotropy value) for spin systems with ferromagnetic interactions and enhanced by exchange interactions in the spin systems with antiferromagnetic couplings. We show that it is worthwhile to study the laser-field-induced magnetization of quantum spin systems caused by the high-frequency laser field in the steady-state regime in ``easy-axis'' antiferromagnetic spin systems (e.g., in Ising-like antiferromagnetic spin-chain materials). The effects of the Dzyaloshinskii-Moriya interaction and the spin-frustration couplings (in the case of the zigzag spin chain) have been analyzed.
The linear response of the quantum spin chain with the impurity to the bi-chromatic ac magnetic field has been calculated. The linearly polarized component of the ac field produces additional resonance absorption with respect to the one caused by the circularly polarized field. The strength of the absorption oscillates with the amplitude and the frequency of the linearly polarized magnetic field. Additional resonance absorption is weaker than the main absorption at the frequency of the circularly polarized field. The absorption due to the impurity can be seen in the absorptions at local levels and the delocalized states.
Identifying quantum spin liquids, magnon breakdown, or fractionalized excitations in quantum magnets is an ongoing challenge due to the ambiguity in interpreting excitation continua occurring in linear-response probes. Recently, it was proposed that techniques measuring higher-order response, such as two-dimensional coherent spectroscopy (2DCS), could resolve such ambiguities. Numerically simulating nonlinear response functions can, however, be computationally very demanding. We present an efficient Lanczos-based method to compute second-order susceptibilities χ 2 ( ω t , ω τ ) directly in the frequency domain. Applying this to extended Kitaev models describing α − RuCl 3 , we find qualitatively different nonlinear responses between intermediate magnetic field strengths and the high-field regime. To put these results into context, we derive the general 2DCS response of partially polarized magnets within the linear spin-wave approximation, establishing that χ 2 ( ω t , ω τ ) is restricted to a distinct universal form if the excitations are conventional magnons. Deviations from this form, as predicted in our Lanczos-based simulations for α − RuCl 3 , can hence serve in 2DCS experiments as direct criteria to determine whether an observed excitation continuum is of conventional two-magnon type or of different nature.
Circuits based on superconducting nanostructures are among the most promising platforms for quantum computing. Understanding how device geometry governs nonlinear electrodynamics is crucial for implementing superconducting quantum technologies. However, to date, research has largely been limited to superconducting nanostructures with collinearly aligned static and dynamic applied magnetic fields. Here, we analyze the dynamics of Meissner currents and Abrikosov vortices in a superconducting nanocube exposed to combined static and microwave magnetic fields, extending the analysis to a more general excitation geometry. We demonstrate that, in a noncollinear configuration, the magnetization component parallel to the static field develops a dominant second-harmonic response under the microwave driving. This effect is strongly enhanced when Meissner currents saturate at static fields just below the thresholds for successive vortex nucleation. By numerically solving the time-dependent Ginzburg-Landau equations, we show that the response originates from Meissner-current saturation combined with the nonlinear oscillations of normal-phase indentations, yielding an anisotropic second-harmonic signal that is directionally separated from, and not overshadowed by, the first-harmonic component of the dynamic magnetization. These findings are relevant for superconducting devices that require controllable high-frequency nonlinearity.