Para-ferrimagnetic transition in strong coupling paramagnetic systems: Landau theory approach

Abstract

We consider here the continuous Landau model describing the para-ferrimagnetic transition, in two strongly coupled Pauli-paramagnetic sublattices, with respective magnetic moments m and M. The free energy of the system contains, in addition to quadratic and quartic terms in both moments m and M, a coupling term — CmM, where C < 0 is the coupling constant between the two sublattices. Two terms — Hm and — HM are also introduced, to describe the interaction with an external magnetic field H. We first show the existence of a certain C-dependent transition temperature T c, which marks the passage from a paramagnetic phase ( m = M = 0) to a ferrimagnetic one, where the moments are oriented antiparallel and M tot = m + M ≠ 0. To each value of C corresponds a transition temperature T c, for which we give the explicit dependence on C. The set of all points ( T c, − C) constitutes a continuous line, in the ( T c, − C)-plane, along which the system undergoes a para-ferrimagnetic transition. Second, we determine, around T c and for fixed C, the variation of M tot( T) with T at H = 0, M tot( H) at T = T c with (small) H, and of the total magnetic susceptibility at H = 0 on T. These latter behaviors are found to be similar to those of the usual para-ferromagnetic transition. We completely determine the shape of Arrott diagram plots, in the ( H/ M tot, M tot 2)-plane. In particular, we demonstrate the existence of a region of strong competition between the coupling C and the field H. This occurs below a certain C-depending temperature T 1, at which the competition region becomes very narrow, and the system abruptly loses its ferrimagnetic order. From the analytical form of the Arrott diagram, we extract the variation of M tot with H, for fixed T < T c and C. Our results are in good agreement with those of a recent numerical analysis. Finally, we calculate the four partial pair-correlation functions of the magnetic species ( m) and ( M), from which we deduce the four partial and total magnetic susceptibilities.