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Ferroelectrics

Incommensurate spin-peierls phases in the one-dimensional quantum isotropicXYmodel

Oleg Derzhko, Taras Krokhmalskii

Published Feb 1, 2001• 4 citations
Publisher

Abstract

Using the numerical approach for a study of the thermodynamic properties of the nonuniform one-dimensional spin-1/2 isotropic XY model in a transverse field we examine different lattice distortions to reveal which spin-Peierls phases are realized in the magnetic chain at zero temperature in the presence of external field.
DOI
10.1080/00150190108225110

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Using an extension of the Jordan - Wigner transformation (JWT) in two dimensions, the effects of weak interchain coupling on the spin - Peierls (SP) system is studied. The magnetic interaction is considered to be a quantum XY-interaction, and the spin - lattice distortion is treated quasiclassically. On the analogy of the stepped Peierls transition theory, we propose a stepped SP transition theory. We find that, when any finite transverse coupling is introduced between nearest chains, the usual SP transition will be modified, and the dimerization and the opening of the gap will no longer occur simultaneously. This leads to the appearance of a gapless SP phase over a certain temperature region.
We study spin-Peierls structural lattice instabilities for a spin-1/2 isotropic XYXYXY chain with three-site interactions of (XZX+YZY)(XZX+YZY)(XZX+YZY) type. Within the adopted adiabatic treatment we have to examine the ground-state energy or the Helmholtz free energy of the spin chain with exchange couplings varying coherently with a possible static lattice distortion pattern. Since the considered spin model can be converted into a system of noninteracting spinless fermions the required ground-state energy or the Helmholtz free energy can be calculated accurately without making any approximations. We examine rigorously several lattice distortion patterns focusing on dimerized and trimerized ones, which owe their presence to the spin-Peierls mechanism. We present phase diagrams illustrating the effect of the three-site interaction on the spin-Peierls lattice distortions. Finally we discuss some properties of the deformable spin chain in the ground state and at finite temperatures. In particular, we examine the transverse magnetization, the static transverse susceptibility and the specific heat illustrating the changes in these quantities due to lattice instabilities.
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.
In the present work we aim to characterize the lattice configurations and the magnetic behavior in the incommensurate phase of spin-Peierls systems. This phase emerges when the magnetic exchange interaction is coupled to the distortions of an underlying triangular lattice and has its experimental realization in the quasi-one-dimensional compound family TiOXXX (X=ClX=\text{Cl}X=Cl, Br). With a simple model of spin-1/21/21/2 chains inserted in a planar triangular geometry which couples them elastically, we are able to obtain the uniform-incommensurate and incommensurate-dimerized phase transitions seen in these compounds. Moreover, we follow the evolution of the wave vector of the distortions with temperature inside the incommensurate phase. Finally, we predict gapless spin excitations for the intermediate phase of TiOXXX compounds along with incommensurate spin-spin correlations, offering to experimentalists a candidate to observe an exotic Luttinger liquidlike behavior.