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In a previous work a model was proposed for the phase transitions of crystalswith 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 modelassumes bilinear and biquadratic interactions between magnetic moments up tothe fifth neighbours, and for any given T the structure with the least freeenergy is obtained by a mean-field approximation (MFA). The interactionconstants are derived from ab initio energy calculations. In this work weimprove upon that model modifying the MFA in such a way that a continuous(instead of discontinuous) spectrum of excited states is available to thesystem. In the previous work, which dealt with LaMn_2Ge_2 and LaMn_2Si_2, wefound that transitions to different structures can be obtained for increasingT, in good qualitative agreement with experiment. The critical temperatures,however, were exaggerately high. With the new MFA we obtain essentially thesame behaviour concerning the phase transitions, and critical temperatures muchcloser to the experimental ones.

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