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Soviet Journal of Low Temperature Physics

High-frequency properties of a one-dimensional spin system with anisotropic interaction

Vladimir Kleiner, O. N. Mikhailov, V. M. Tsukernik

Published Jun 1, 1977• 0 citations
Publisher

Abstract

The nonlinear response of an xy spin chain with anisotropic interaction to an alternating magnetic field polarized along a chosen axis (longitudinal pumping) is considered. The high-frequency magnetization of the system is determined in two limiting cases, namely, a small amplitude of the high-frequency field and a small exchange anisotropy.

DOI
10.1063/10.0029511

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The nonlinear response of an xy spin chain with anisotropic interaction to an alternating magnetic field polarized along a chosen axis (longitudinal pumping) is considered. The high-frequency magnetization of the system is determined in two limiting cases, namely, a small amplitude of the high-frequency field and a small exchange anisotropy.
The spin–Peierls phase transition in a quasi-one-dimensional XY chain of S=1/2 of spins interacting through an anisotropic exchange interaction is studied as a function of the degree of anisotropy γ. The spin–Peierls state is described using a mean field theory. As γ increases (small value of the anisotropy), the transition temperature Tc decreases. For intermediate values of the anisotropy parameter γ, a tricritical point separating the regions of first and second order phase transitions is obtained. For larger values of γ, a total suppression of the spin–Peierls state is predicted. Finally, a very unusual temperature dependent gap of the elementary spin excitations is predicted for the anisotropic XY system.
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In the recent literature, there have been discussions of nonlinear spin excitations in one-dimensional, anisotropic Heisenberg spin chains. These have the character of localized excitations, which emerge from the time-dependent classical equations of motion. We show that for a given frequency, in a finite spin chain one has a hierarchy of nonlinear excitations, whose envelopes have the appearance of a one soliton, two soliton,..., states. Also, we consider the nature of these nonlinear excitations in an applied magnetic field of frequency \ensuremath{\omega}, and explore aspects of the transient behavior of the system in response to a time varying external field. \textcopyright{} 1996 The American Physical Society.
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.
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The anisotropic XY-model in a transverse field (s=1/2) on the one-dimensional alternating superlattice (closed chain) is considered. The solution of the model is obtained by introducing a generalized Jordan-Wigner transformation which maps the system onto a non-interacting fermion gas. The exact excitation spectrum is determined by reducing the problem to a diagonalization of a block matrix, and it is shown that it is numerically identical to the one obtained by using the approximate transfer matrix method . The induced magnetization and the susceptibility χzzχ^{zz}χzz are determined as a function of the transverse field, and it is shown that, at T=0, the susceptibility presents multiple singularities. It is also shown, as expected, that this critical behaviour driven by transverse field belongs to the same universality class of the model on the alternating chain.