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Soviet Journal of Low Temperature Physics

Low-temperature properties of quasi-one-dimensional magnetic systems with an XY interaction

E. V. Ezerskaya

Published Sep 1, 1984• 0 citations
Publisher

Abstract

The effect of the interaction between XY chains on the spectrum of low-lying excitations of quasi-one-dimensional magnetic systems has been investigated. It has been shown that the energies of two-magnon bound states of a tube of three XY chains lie beyond the continuous spectrum for sufficiently high values of the total quasimomentum while the energies of the analogous states for a strip containing the same number of chains always belong to the continuous spectrum.

DOI
10.1063/10.0031179

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The effect of the interaction between XY chains on the spectrum of low-lying excitations of quasi-one-dimensional magnetic systems has been investigated. It has been shown that the energies of two-magnon bound states of a tube of three XY chains lie beyond the continuous spectrum for sufficiently high values of the total quasimomentum while the energies of the analogous states for a strip containing the same number of chains always belong to the continuous spectrum.
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Stationary states of a quasi-one-dimensional spin system with “comb” structure and with XY-exchange interaction along the chain and Ising interaction of “teeth” (J>0) are considered. The existence of bound states of an arbitrary number n of inverted spins in the “teeth” and a single state in the XY-chain is proved. For a positive constant of Ising exchange interaction, the energies of these states lie below the energies of the corresponding states in the continuous spectrum. For n⩾2, the energies of these states depend on the mutual arrangement of inverted spins in the “teeth.”
We study the energy spectrum of a dual spin chain with an XY interaction among nearest neighbors. This model is applicable in particular to the description of the magnetic properties of the compound Cu(NO3)2 · 2.5H2O. We obtain exact expressions for the energy and wave functions of the one- and two- magnon states. Analysis of the stationary states with a large number of excitations is carried out in terms of perturbation theory under the condition that the exchange interaction J1 between the members of a spin pair significantly exceeds the interaction between pairs, J2. For small ratios J2/J1 the curves of the thermodynamic functions obtained as functions of magnetic field indicate the presence of two critical fields at low temperatures (T≪J2), in agreement with the experimental data.
We studied the energy spectrum of a spin lattice formed by m XY spin-1/2 chains with Ising inter-chain coupling. For strong ferromagnetic coupling we found that the lowest-energy states for non-zero numbers of inverted spins on each XY chain have n-magnon bound character if n = ml − 1, where l = 2, 3,.... For a spin tube formed by three XY chains with strong ferromagnetic inter-chain coupling, the lowest-energy states are described by the XXZ spin-1/2 chain model with antiferromagnetic coupling.
The influence of a magnetic impurity on the elementary excitation spectrum of a two-dimensional Ising ferromagnet is investigated in a low transverse magnetic field. It is shown that in the case of a “ferromagnetic” impurity in a matrix of spin 1/2, from one to three local energy levels can be split off from the lower edge of the continuous spectrum of one-magnon states where the conditions for their existence impose quite strict constraints on the spin-Hamiltonian parameters. Three distinct spin configurations can be realized in the presence of an “antiferromagnetic” impurity in the crystal in the ground state. Single-magnon states of a ferromagnet are considered for those values of the spin-Hamiltonian parameters when two of them are realized. It is shown that from one to six local levels above or below the continuous spectrum band can appear, and their distance from the band edge can substantially exceed its width. Quasilocal energy levels originating within the continuous spectrum of the single-magnon states are also investigated.