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Progress of Theoretical Physics Supplement

Specific Heat of a Quantum Spin Chain of an Easy-Plane Type under an In-Plane Magnetic Field

Toshio Tsuzuki

Published Jan 1, 1984• 3 citations
Publisher

Abstract

Quantum statistical mechanics is developed for an easy-plane ferromagnetic chain under an in-plane magnetic field. A pair product approximation is made for the density matrix. A transfer integral expression for the partition function is formulated by the use of the coherent state of spin. Specific heat is computed as a function of temperature and magnetic field for the case of strong single-ion anisotropy. From our qualitative study it is suggested that, beyond the sine-Gordon approximation, simultaneous consideration of the quantum effect and the instability against the off-plane fluctuation (the Kumar-Magyari-Thomas instability) is necessary to explain specific heat, in particular, and thermodynamic quantities, in general, of the present system.

DOI
10.1143/ptps.80.146

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Physical review. B, Condensed matter•Dec 1, 1995•25 citations
Quantum statistical mechanics is developed for an easy-plane ferromagnetic chain under an in-plane magnetic field. A pair product approximation is made for the density matrix. A transfer integral expression for the partition function is formulated by the use of the coherent state of spin. Specific heat is computed as a function of temperature and magnetic field for the case of strong single-ion anisotropy. From our qualitative study it is suggested that, beyond the sine-Gordon approximation, simultaneous consideration of the quantum effect and the instability against the off-plane fluctuation (the Kumar-Magyari-Thomas instability) is necessary to explain specific heat, in particular, and thermodynamic quantities, in general, of the present system.
A classical effective Hamiltonian for the quantum easy-plane ferromagnetic chain with an in-plane applied field is introduced by means of a path-integral variational method. It then becomes possible to include quantum effects of the out-of-plane fluctuations in an easily evaluable phase-space integral which approximates the quantum partition function. A comparison with experimental data for the excess specific heat of CsNiF3{\mathrm{CsNiF}}_{3}CsNiF3​ shows much improvement in the description of this system. In addition, new light is shed on the old problem of defining the classical counterpart of a spin Hamiltonian.
The thermodynamic properties of the quantum ferromagnetic chain with easy-plane single-ion anisotropy are evaluated over a wide temperature range. The basic theoretical method is a recently proposed one, called the pure-quantum self-consistent harmonic approximation (PQSCHA), which, starting from the original Hamiltonian operator scr\ifmmode \hat{H}\else \^{H}\fi{}, allows the definition of an effective classical Hamiltonian scrHeff{\mathit{scrH}}_{\mathrm{eff}}scrHeff​. We use the Villain transformation to canonical conjugate variables, in order to treat the quantum renormalizations within this framework. In the resulting effective Hamiltonian we restore classical spin variables, according to the classical counterpart of the Villain transformation. Provided that the quantum coupling parameter (which depends on the spin value and on the anisotropy constant) is not too large, this effective Hamiltonian is able to account for the quantum behavior, by means of classical-like calculations. We present a number of results for various quantum thermodynamic quantities, obtained numerically by the classical transfer-matrix method. Moreover, we also calculate static spin correlation functions. Finally, the case of the real ferromagnet CsNiF3{\mathrm{CsNiF}}_{3}CsNiF3​ is considered; even though the corresponding easy-plane anisotropy is rather weak, the experimental data for this system are shown to be well reproduced.
We calculate exactly the thermodynamics of ensembles of magnetic impurities with randomly distributed host-impurity couplings in the critical region of the uniaxial spin-1/2 quantum chain. We derive a finite set of integral equations describing the complete temperature and magnetic field dependence of the system. Exact numerical results for arbitrary values of temperature and external magnetic field are obtained. We show that for strong disorder the quenching of the impurity moments is absent. For weak disorder the screening persists, but with a critical non-Fermi-liquid behaviour of the magnetic susceptibility and specific heat. We point out that the `easy-plane' magnetic anisotropy does not qualitatively change the behaviour of the thermodynamic characteristics of the disordered impurities in the antiferromagnetic chain. On the other hand, anisotropy of ferromagnetic type can enhance the tendency to quenching of the impurities for strong disorder.
Earlier work on the T=0T=0T=0 dynamics of spin-1 chains with a strong easy-plane anisotropy is extended to include thermodynamics. Thus we carry out a systematic strong-coupling expansion to obtain analytical approximations for the spectrum of elementary excitations, the specific heat, and the magnetic susceptibility. Comparison with numerical data for the specific heat available in some important special cases indicates that our result is accurate for practically the entire temperature range. Similarly our calculation of the magnetic susceptibility reproduces to leading order a result obtained earlier through a molecular-field approximation and provides a definite improvement by including the two-loop correction. These theoretical predictions are directly relevant for a number of magnetic materials of current experimental interest.