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

A. Waddahou1, M. Chahid1,, A. Maârouf1

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

International Journal of Physics. 2018, 6(5), 147-154. DOI: 10.12691/ijp-6-5-2
Received August 11, 2018; Revised September 21, 2018; Accepted October 07, 2018

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 Tc 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, -Coφψ where Co<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 φs and ψs. 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 ηa=φ/(φ+ψ). For the ordinary transition where the extrapolation length is positive λs>0, we determine the order parameter profile near surfaces. We show, in particular, that the magnetization behavior is governed, in addition of λs and the bulk correlation length ξb-, by a new length La. We have interpreted this latter as the width of the ordered ferrimagnetic layer close to the surface. Finally, we examine the extraordinary (λs<0), special (λs=∞) and surface (at Tcs>Tc) transitions.

Keywords:

sublattices, coupling, paramagnetism, ferrimagnetism, transition, order parameter profiles
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