# High-harmonic generation in quantum spin systems

## TL;DR

This paper explores high-harmonic generation in one-dimensional quantum spin systems driven by magnetic fields, revealing how spin excitations influence the radiation spectrum and indicating potential for probing magnetic materials.

## Contribution

It introduces a theoretical framework for understanding HHG in spin chains and links spectral features to spin excitations and phase transitions.

## Key findings

- Plateau structures in HHG spectra explained by magnon processes.
- Magnetic field induces phase transition affecting HHG cutoff energies.
- High-harmonic signals can probe spin excitation spectra.

## Abstract

We theoretically study the high-harmonic generation (HHG) in one-dimensional spin systems. While in electronic systems the driving by AC electric fields produces radiation from the dynamics of excited charges, we consider here the situation where spin systems excited by a magnetic field pulse generate radiation via a time-dependent magnetization. Specifically, we study the magnetic dipole radiation in two types of ferromagnetic spin chain models, the Ising model with static longitudinal field and the XXZ model, and reveal the structure of the spin HHG and its relation to spin excitations. For weak laser amplitude, a peak structure appears which can be explained by time-dependent perturbation theory. With increasing amplitude, plateaus with well-defined cutoff energies emerge. In the Ising model with longitudinal field, the thresholds of the multiple plateaus in the radiation spectra can be explained by the annihilation of multiple magnons. In the XXZ model, which retains the $\mathbf{Z}_{2}$ symmetry, the laser magnetic field can induce a phase transition of the ground state when it exceeds a critical value, which results in a drastic change of the spin excitation character. As a consequence, the first cutoff energy in the HHG spectrum changes from a single-magnon to a two-magnon energy at this transition. Our results demonstrate the possibility of generating high-harmonic radiation from magnetically ordered materials and the usefulness of high-harmonic signals for extracting information on the spin excitation spectrum.