Within the limits of the Hubbard model supplemented with allowance for relativistic antisymmetric Dzyaloshinskii–Moriya interaction, the spin fluctuation theory of helical band ferromagnetism is developed. The magnetic state equation is derived for the nonuniform order parameter together with expressions for the Neel temperature and the wave vector of a spin structure. The effect of pressure on the helical ferromagnetism is analyzed based on the LDA + U + SO calculations of the MnSi electronic structure at different pressures. It is shown that with increasing pressure, the effect of zero-spin fluctuations that reduce the Neel temperature is amplified, and at a pressure of 15.2 kb a quantum transition takes place accompanied by vanishing of the longrange magnetic order.
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