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physica status solidi (b)

Surface Magnetic Properties of a Transverse Ising Model with a Diluted Surface

Enaldo F. Sarmento, T. Kaneyoshi

Published Jul 1, 1990• 30 citations
Publisher

Abstract

Abstract Surface magnetic properties of semi‐infinite spin‐1/2 Ising ferromagnet with a diluted surface in an applied transverse field are investigated by the use of an effective‐field theory with correlations. A number of characteristic behaviors arise in the temperature and transverse field dependences of the surface magnetization. A similarity exists between the temperature plots and the transverse field plots for the surface magnetization, which proposes that the research of surface magnetization in an applied transverse field fixing temperature at a very low one may open a new method for clarifying a variety of problems in surface magnetism experimentally.

DOI
10.1002/pssb.2221600133

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Abstract Surface magnetic properties of semi‐infinite spin‐1/2 Ising ferromagnet with a diluted surface in an applied transverse field are investigated by the use of an effective‐field theory with correlations. A number of characteristic behaviors arise in the temperature and transverse field dependences of the surface magnetization. A similarity exists between the temperature plots and the transverse field plots for the surface magnetization, which proposes that the research of surface magnetization in an applied transverse field fixing temperature at a very low one may open a new method for clarifying a variety of problems in surface magnetism experimentally.
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.
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.
An effective-field theory that accounts for the self-spin correlation function is used to study the effect of surface dilution on the critical behavior of a ferromagnetic Ising film in transverse surface and bulk fields. Surface exchange enhancement (or reduction) is considered. It is shown that the surface and bulk fields affect the critical ratio of surface to bulk interactions, at which the surface orders before the bulk, in opposite ways. Although it is found that for the undiluted film this leads to a critical ratio that is practically insensitive to field for common bulk and surface field strengths, this feature is relaxed to a certain degree with surface dilution. The thickness dependence of the critical temperature, and phase diagrams in the fields, interaction strength ratio, and dilution parameter space, are presented.