@article{ijp2018643,
author={{Waddahou, A. and Chahid, M. and Maarouf, A. and Benzouine, F.},
title={Critical Behavior at Surfaces of Strong Coupling Paramagnetic Systems Exhibiting a Paramagnetic-Ferrimagnetic Transition},
journal={International Journal of Physics},
volume={6},
number={4},
pages={116--121},
year={2018},
url={http://pubs.sciepub.com/ijp/6/4/3},
issn={2333-4576},
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.},
doi={10.12691/ijp-6-4-3}
publisher={Science and Education Publishing}
}