Magneto-elastic interaction in cubic helimagnets with B20 structure

The magneto-elastic interaction in cubic helimagnets with B20 symmetry is considered. It is shown that this interaction is responsible for negative contribution to the square of the spin-wave gap $\mathrm{\Delta }$ which is alone has to disrupt assumed helical structure. It is suggested that competition between positive part of ${\mathrm{\Delta }}_I^2$ which stems from magnon-magnon interaction and its negative magneto-elastic part leads to the quantum phase transition observed at high pressure in $MnSi$ and $FeGe$. This transition has to occur when ${\mathrm{\Delta }}^2=0$. For $MnSi$ from rough estimations at ambient pressure both parts ${\mathrm{\Delta }}_I$ and $\mathrm{\mid }{\mathrm{\Delta }}_{ME}\mathrm{\mid }$ are comparable with the experimentally observed gap. The magneto-elastic interaction is responsible also for $2\text{m}k$ modulation of the lattice where $\text{m}k$ is the helix wave-vector and contribution to the magnetic anisotropy. Experimental observation by $x$-ray and neutron scattering the lattice modulation allows determine the strength of anisotropic part of the magneto-elastic interaction responsible for above phenomena and the lattice helicity.