Transitions involving conical magnetic phases in a model with bilinear and biquadratic interactions

In a previous work a model was proposed for the phase transitions of crystals with localized magnetic moments which at low temperature have a "conical" arrangement that at higher T transforms into a more symmetrical structure (depending on the compound) before becoming totally disordered. The model assumes bilinear and biquadratic interactions between magnetic moments up to the fifth neighbours, and for any given T the structure with the least free energy is obtained by a mean-field approximation (MFA). The interaction constants are derived from ab initio energy calculations. In this work we improve upon that model modifying the MFA in such a way that a continuous (instead of discontinuous) spectrum of excited states is available to the system. In the previous work, which dealt with LaMn_2Ge_2 and LaMn_2Si_2, we found that transitions to different structures can be obtained for increasing T, in good qualitative agreement with experiment. The critical temperatures, however, were exaggerately high. With the new MFA we obtain essentially the same behaviour concerning the phase transitions, and critical temperatures much closer to the experimental ones.