Fluctuation-induced phase transitions and skyrmions in strongly correlated Fe$_{1-x}$Co$_{x}$Si with a disturbed crystal B20-type structure

The concentration and temperature transitions in strongly correlated Fe$_{1-x}$Co$_{x}$Si alloys with the Dzyaloshinski–Moriya (DM) interaction are considered in terms of the spin-fluctuation theory taking into account the results of LDA + U + SO calculations of the density of electronic states. It is shown that the concentration order–order transitions with change in the sign of the left spin chirality (at $x$ < 0.2) to the right that (at $x\le$ 0.2 $x$ < 0.65, and again to the left chirality at $x\ge$ 0.65 are related to the change in the sign of the parameter of the mode–mode interaction. It is also shown that, in the composition range of Fe$_{1-x}$Co$_{x}$Si with 0.2 $\le x<$ 0.65, the first-order transitions extended in temperature arise, accompanied by the appearance of an intermediate temperature range of the spin short-range order with a noncompensated local magnetization and the DM interaction. In an external magnetic field, in this temperature range at 0.2 $\le x$ < 0.65, skyrmion microstructures arise. At $x$ = 0.65, the mode–mode interaction parameter becomes be zero, the long-range order becomes ferromagnetic (since the experiment demonstrates the compensation of the DM interaction), and a temperature second-order transition appears instead of the extended first-order transition. The $(h–T)$ diagrams of magnetic states of Fe$_{1-x}$Co$_{x}$Si have been constructed; they agree with the experiment.