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Critical Behavior at Surfaces of Strong Coupling Paramagnetic Systems Exhibiting a Paramagnetic-Ferrimagnetic Transition

A. Waddahou1, M. Chahid1,, A. Maârouf1, F. Benzouine1

1Polymer Physics and Critical Phenomena Laboratory, Faculty of Sciences Ben M’sik, Hassan II University of Casablanca, P. O. Box 7955, Casablanca, Morocco

International Journal of Physics. 2018, 6(4), 116-121. DOI: 10.12691/ijp-6-4-3
Published online: July 27, 2018

Abstract

The purpose of this work is the investigation of the critical surface effects of two strongly coupled paramagnetic sublattices exhibiting a para-ferrimagnetic transition. The model is of Landau-Ginzburg type, whose bulk free energy is a functional of two kind of order parameters (local magnetizations) φ and This free energy involves, beside quadratic and quartic terms in both φ and , a lowest-order coupling, where Co<0 is the coupling constant measuring the interaction between the two sublattices. Two terms Hφ and are also introduced, to describe the interaction within an external magnetic field H. We introduce a surface free energy expanded in terms of the local order parameters. The magnetization at the surface are φs and We show, in particular, that the model can be reduced to an effective theory written in terms of the overall magnetization and the associated fraction of magnetization . This formulation leads us to define an effective extrapolation length λs. We then derive all the critical properties of the system close to the critical temperature Tc. In particular, we determine the critical behavior of the overall surface magnetization , in terms of b above and below Tc. The variations of s with the magnetic field H, and when a surface field Hs is applied actually at Tc, are derived. We determine, also, the associated susceptibilities at the surface χs and χs.s. The determination of the full profile of the magnetization close to the surface will be the subject of a future communication.

Keywords:

sublattices, coupling, paramagetism, ferrimagnetism, transition, critical surface effects
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