Magnetovolume effects and thermal expansion in chiral helical ferromagnets Fe$_{1-x}$Co$_x$Si

Within the framework of the theory of band magnetism and the Heine model for the volume dependence of the electronic spectrum, an approach is being developed to study magneto-volume effects in chiral helical ferromagnets. Using Fe$_{1-x}$Co$_x$Si as an example, it was found that in the range of long-range order (at temperature $T < T_c$) the magnetovolume effect is determined by the amplitude of helicoidal spin spirals and leads to the experimentally observed negative volume thermal expansion coefficient. In the region of phase transitions of the first order (from $T_c$ to $T_s$) prolonged in temperature, a new mechanism of the magnetovolume effect is established due to the spatial fluctuations of spin spirals arising due to the difference in the Hubbard potentials of iron and cobalt. It is shown that the considered volume effects lead not only to the experimentally observed negative volume thermal expansion coefficient (VCTE) in the chiral spin short-range order phase, but also to a noticeable increase in the transition temperature to the paramagnetic state $(T > T_s)$.