  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.
