Order Parameter Profiles near Surfaces of Super-weak Ferrimagnetic Materials Exhibiting a Paramagnetic-Ferrimagnetic Transition

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

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

Cite this paper:
A. Waddahou, M. Chahid and A. Maârouf. Order Parameter Profiles near Surfaces of Super-weak Ferrimagnetic Materials Exhibiting a Paramagnetic-Ferrimagnetic Transition. International Journal of Physics. 2018; 6(5):147-154. doi: 10.12691/ijp-6-5-2

Abstract

The aim of this paper is to determine the full order parameter profiles close to the surface for a system made of two strongly coupled paramagnetic sublattices of respective moments φ and ψ. The material exhibits a para-ferrimagnetic transition at some critical temperature T_c greater than the room temperature. The free energy describing the physics of the system is of Landau type, and involves, beside quadratic and quartic terms in both φ and ψ, a lowest-order coupling, -C_oφψ where C_o<0 is the coupling constant measuring the interaction between the two sublattices. We consider here below a film of thickness L, and the free energy is then a sum of bulk and surface contributions expanded in terms of the local order parameters. The magnetization at the surface are φ_s and ψ_s. As in a recent paper (whom the present work is an extension), we first reduce the model to an effective φ⁴ -theory written in terms of the overall magnetization =φ+ψ and the associated fraction of magnetization η_a=φ/(φ+ψ). For the ordinary transition where the extrapolation length is positive λ_s>0, we determine the order parameter profile near surfaces. We show, in particular, that the magnetization behavior is governed, in addition of λ_s and the bulk correlation length ξ_b^-, by a new length L_a. We have interpreted this latter as the width of the ordered ferrimagnetic layer close to the surface. Finally, we examine the extraordinary (λ_s<0), special (λ_s=∞) and surface (at T_cs>T_c) transitions.

Keywords:
sublattices coupling paramagnetism ferrimagnetism transition order parameter profiles

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