Paramagnetic–ferrimagnetic transition in strong coupling paramagnetic systems: effect of cubic anisotropy interaction

Abstract The purpose of the present work is a quantitative investigation of the biquadratic exchange interaction effects on the paramagnetic–ferrimagnetic transition arising from two strongly coupled paramagnetic (1-spin) sublattices, of respective moments m and M . The free energy describing the physics of the system is of Landau type. In addition to the quadratic and quartic terms, in both m and M , this free energy involves two mixing interaction terms. The first is a lowest order coupling − CmM , where C wm 2 M 2 , where w >0 is the new coupling constant. These two interactions enter in competition, and then, they induce drastic changes of the magnetic behavior of the material. The main change is that, the presence of this high order coupling tends to destroy the ferrimagnetic order of the system. We first show that the introduction of this biquadratic interaction does not affect the values of critical exponents. Also, we find that the compensation temperature (when it exists) and the compensation magnetic field are shifted to their lowest values, in comparison with the w =0 case. The Arrott-phase-diagram shape is also investigated quantitatively. We show the existence of three regimes depending on the values of w . When the latter is small, we find that the region of competition between the coupling C and the applied magnetic field H becomes more narrow under the effect of w (by competition, we mean the passage from the antiparallel state to the parallel one). While for higher values of w , this competition disappears completely, and then, the system loses its ferrimagnetic character. Kinetics of the phase transition is also examined, when the temperature is lowered from an initial value T i to a final one T f very close to the critical temperature T c . As in the w =0 case, we find that kinetics is controlled by two kinds of relaxation times τ 1 and τ 2 . The former is the relevant time, and is associated to long-wavelength fluctuations driving the system to undergo a phase transition. The second is a short time, which controls local dynamics. Near T c , we show that, in particular, the longest relaxation time τ 1 becomes less important in comparison with that relative to the w =0 case. Finally, we note that the existence of two relaxation times is consistent with the predictions of a recent experiment, which was concerned with the 1/2-spin compounds Li x Ni 2− x O 2 , where the composition x is close to 1.