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

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 and . 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 and , a lowest-order coupling, -Co where CoL, 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 s and s. As in a recent paper (whom the present work is an extension), we first reduce the model to an effective 4 -theory written in terms of the overall magnetization =+ and the associated fraction of magnetization a=/(+). For the ordinary transition where the extrapolation length is positive s>0, we determine the order parameter profile near surfaces. We show, in particular, that the magnetization behavior is governed, in addition of s and the bulk correlation length b-, 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 (ss=) and surface (at Tcs>Tc) transitions.