Spin fluctuations and concentration magnetic transitions in chiral helical ferromagnets Fe$_{1-x}$Co$_{x}$Si

The fluctuation theory is applied to the study of concentration transformations in chiral helicoidal ferromagnetic quasi-binary unordered Fe$_{1-x}$Co$_{x}$Si alloys with Dzyaloshinsky–Moriya interaction. The ground state is described on the basis of the LDA + U + SO approximations used in ab initio calculations with additional allowance for concentration fluctuations associated with the difference in the potentials of the intra-atomic Hubbard interaction at the sites occupied by iron and cobalt. Solutions of the obtained equations of the magnetic state for the phases of the long-range and short-range orders with the right and left magnetic chirality are considered. The concentration dependences of the parameters of the intermode interaction are investigated, and the regions of the compositions in which magnetic phase transitions of the first kind induced by thermal fluctuations take place, accompanied by the appearance of fluctuations of the spin helix. It is shown that the transition with a change of the sign of magnetic chirality is accompanied by the appearance of a minimum in the concentration dependence of the mode-mode parameter and the appearance of quantum helicoidal ferromagnetism with a noticeable increase in zero spin fluctuations.