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Low Temperature Physics

Stationary states of a quasi-one-dimensional magnetic system with “comb” structure

E. V. Ezerskaya

Published Sep 1, 1995• 0 citations
Publisher

Abstract

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.”

DOI
10.1063/10.0033881

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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.
The effect of impurities on the spectrum of one-magnon excitations of two quasi-one-dimensional spin systems—a double XY chain with an impurity atom and an analogous chain with an impurity link, in which two identical impurity atoms occupy neighboring nodes on different XY chains—is studied. The conditions for the existence of impurity levels and their number are determined for the system with one impurity, and for the system with an impurity link the explicit expressions for the energy and wave functions of localized states are also determined.
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.
We studied the energy spectrum of two coupled XY spin-1/2 chains with different exchange integrals and inter-chain interaction of Ising type. The thorough analytical treatment of two-magnon states was given for finite and infinite lattice strips. To study the case of macroscopic number of inverted spins we used the corresponding density matrix renormalization group (DMRG) simulation. We also derived the self-consistent Bardeen-Cooper-Schrieffer (BCS) estimates for the lowest energies of the system. The comparison of the BCS and the DMRG estimates has shown incorrect behaviour of the BCS approximation for energy as a function of the intra-chain exchange integrals. To use the analytical results for two-magnon bound states we proposed a simple approximate formula for the lowest n -magnon energies of an infinite ladder with a more correct dependence on model parameters.
A quasi-one-dimensional system with strong attraction between electrons on the same site is analyzed in terms of an equivalent weakly interacting array of Heisenberg-Ising spin chains. The single-chain ground-state properties and elementary excitation spectrum are discussed. It is shown that for certain ranges of the coupling constants, gapless excitations rather widely believed to be present do not in fact exist. Some inadequacies in a recent derivation of a mean-field ordering temperature for interacting spin chains are pointed out, and a new derivation is given. The application of this technique to the quasi-one-dimensional electron system is discussed.