@article{ijp2018652,
author={{Waddahou, A. and Chahid, M. and Maarouf, A.},
title={Order Parameter Profiles near Surfaces of Super-weak Ferrimagnetic Materials Exhibiting a Paramagnetic-Ferrimagnetic Transition},
journal={International Journal of Physics},
volume={6},
number={5},
pages={147--154},
year={2018},
url={http://pubs.sciepub.com/ijp/6/5/2},
issn={2333-4576},
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*_{o}φψ 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 φ^{4} -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.},
doi={10.12691/ijp-6-5-2}
publisher={Science and Education Publishing}
}