Concentration fluctuations in Fe$_{x}$Mn$_{1-x}$Si chiral ferromagnets in an external magnetic field

Magnetic $h$–$T$ diagrams of Fe$_{x}$Mn$_{1-x}$Si chiral helicoidal ferromagnets with the Dzyaloshinskii–Moriya interaction are studied within the theory of spin fluctuations. A specific analysis of the magnetic equations of state is based on a model of the electronic structure resulting from the LDA + U + SO DOS calculations in the virtual-crystal approximation. It is shown that, in the region of concentrations $x<$ 0.12, the Fermi level remains within the local minimum of the DOS. In this case, a helicoidal long-range order is realized, which undergoes a first-order transition induced by spin fluctuations and is accompanied by the formation of intermediate skyrmion phases induced by an external magnetic field. With an increase in x, the effects of concentration fluctuations, arising due to the chaotic distribution of the magnetic moments of manganese and iron over sites, suppress zero quantum spin fluctuations. In this case, the condition for the appearance of skyrmion phases is violated for $x>$ 0.12 and the region of the helicoidal ferromagnetic order is preserved up to concentrations $x_c$ = 0.20. In the interval 0.10 $<x<$ 0.20, the fluctuation-induced transition to the paramagnetic state is accompanied by the disappearance of local magnetization and the formation of a paramagnetic state with dynamic spin correlations.