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

A. Waddahou¹, M. Chahid^1, , A. Maârouf¹ and 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

Cite this paper:
A. Waddahou, M. Chahid, A. Maârouf and F. Benzouine. Critical Behavior at Surfaces of Strong Coupling Paramagnetic Systems Exhibiting a Paramagnetic-Ferrimagnetic Transition. International Journal of Physics. 2018; 6(4):116-121. doi: 10.12691/ijp-6-4-3

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 C_o<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 φ_s 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 λ_s. We then derive all the critical properties of the system close to the critical temperature T_c. In particular, we determine the critical behavior of the overall surface magnetization , in terms of _b above and below T_c. The variations of _s with the magnetic field H, and when a surface field H_s is applied actually at T_c, are derived. We determine, also, the associated susceptibilities at the surface χ_s and χ_s.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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