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Communications in Theoretical Physics

Spin Waves in a Surface-Diluted Quantum Spin system

Song-Tao Dai, Zhen‐Ya Li, Chuan‐Zhang Yang

Published Dec 1, 1993• 0 citations
Publisher

Abstract

A theoretical investigation of the effects of surface dilution on spin waves in a semi-infinite transverse Ising model (TIM) is presented. Within the framework of the double-time Green's function theory, the local density of spin-wave states is obtained by the application of the cluster-Bethe-lattice (CBL) method. Numerical calculations of paramagnetic phases reveal that surface dilution will lead to appearance of the localized spin-wave states whose frequencies are bulk independent while the corresponding density of states is a function of the exchange interactions. Increase of the bulk exchange interactions between the surface and the bulk spins tends to diminish the localized spin-wave states. Dependence of the local density of states on the concentration p of the magnetic atoms is similar with that in a three-dimensional infinite TIM which has been discussed in our previous paper.

DOI
10.1088/0253-6102/20/4/393

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A theoretical investigation of the effects of surface dilution on spin waves in a semi-infinite transverse Ising model (TIM) is presented. Within the framework of the double-time Green's function theory, the local density of spin-wave states is obtained by the application of the cluster-Bethe-lattice (CBL) method. Numerical calculations of paramagnetic phases reveal that surface dilution will lead to appearance of the localized spin-wave states whose frequencies are bulk independent while the corresponding density of states is a function of the exchange interactions. Increase of the bulk exchange interactions between the surface and the bulk spins tends to diminish the localized spin-wave states. Dependence of the local density of states on the concentration p of the magnetic atoms is similar with that in a three-dimensional infinite TIM which has been discussed in our previous paper.
The transverse Ising system with a diluted surface and a modified surface-bulk interaction J(subscript ┴) is studied by the use of an effective field method within the framework of a single-site cluster theory. The surface antiferromagnetic exchange interaction JS is distributed randomly and has a concentration p. The new parameter p strongly affects the phase diagram obtained in the pure case (p=1). Indeed, some qualitatively interesting features have been found, both in the absence and in the presence of the surface transverse field. In particular, we defined a critical value p(superscript *) of p, separating two qualitatively different behaviors of the system.
The effect of surface and bulk transverse fields on the phase transitions of a semi-infinite spin-1 ferromagnetic Ising model is investigated within a finite cluster approximation with an expansion technique for cluster identities of spin-1 localized spin systems. The phase diagrams are determined as a function of the ratio of bulk and surface transverse fields, the temperature and the transverse field of the surface. They show that the systems exhibit a variety of phase transitions. A dead layer is also obtained in a special region of space parameters.
Abstract The phase diagram of the three‐dimensional transverse Ising system with competing surface and bulk exchange interactions is studied by the use of an effective‐field method within the framework of a single‐site cluster theory. In addition to this pure case, which shows qualitatively interesting features, we investigated the effects of the bond dilution on the obtained phase diagram. In particular, we studied the influence of the surface dilution parameter on the surface transitions. We find a number of characteristic behaviours of the surface both in the absence and in the presence of the surface transverse field. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Within the framework of an effective-field theory with correlation evaluated for the Ising model with transverse field, the authors discuss the following cases: a diluted ferromagnetic square lattice with a transverse field; the magnetic behaviour of a transverse Ising model with diluted surface in a simple cubic lattice; and the surface magnetism of random transverse field at the surface. The surface magnetism is examined as a function of Delta =(J s /J)-1, the concentrations p and q of magnetic atoms at the surface, and Omega s and Omega b , the surface and bulk transverse field respectively. The phase diagrams for surface ordering are obtained and some characteristic behaviours of magnetism at the diluted surface are presented. The present framework is quite superior to the standard MFA, and whenever comparison is possible a satisfactory qualitative (and to a certain extent quantitative) agreement with results available in the literature is found.
Within the framework of the effective field theory, with a probability distribution technique that accounts for the single-site spin correlations, we examine the critical behavior of a diluted spin-1/2 Ising film. The critical temperature of the system is studied as a function of the thickness of the film, the concentration of magnetic atoms, the strength of the transverse field and the couplings. It is shown that for the ratio of the surface couplings to the bulk ones R = Js/J less than a critical value R,, the critical temperature of the film Tc/J is smaller than the bulk critical temperature Tc^B/J and for R ≥ Rc, Tc/J is larger than the bulk critical temperature Tc^B/J and Tc^S/J of the corresponding semi-infinite system. As the film thickness L is increased further Tc/J increases for R ≤ Rc (decreases for R 2 R,) and approaches asymptotically for large values of L the bulk critical temperature Tc^B/J (the surface critical temperature Tc^S/J) of the corresponding semi-infinite system.
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