Cubic magnets with Dzyaloshinskii-Moriya interaction at low temperature

Magnetic properties of noncentrosymmetric cubic helimagnets (MnSi, etc.) at low T are studied theoretically using conventional exchange, Dzyaloshinskii-Moriya interaction, anisotropic exchange and magnetic dipolar interaction. Structure in magnetic field and spin-wave spectrum are considered. In low field g mu H-B(1)=root Delta 2, where Delta is the spin-wave gap, the helix axis k turns along the field. A transition to ferromagnetic state occurs at g mu H-B(c)=Ak(2), where A is the spin-wave stiffness at momenta q > k. It is observed that the spin-wave spectrum is strongly anisotropic: excitations with q parallel to k and q perpendicular to k have linear and quadratic dispersion at q < k respectively if one neglects the gap Delta. This is a result of umklapp interaction connecting the spin-waves with momenta q and q +/- k. This interaction leads to infinite set of equations for the Green functions. The simplest n=1 approximation is applicable at q=0 and q > k. Further n=2 approximation gives correct result at q < k. Results of both approximations are qualitative at q similar to k. The weak field (H < H-1) perpendicular to k deforms the helix and the second harmonics of the spin rotation appears. The spin-wave gap is a result of the spin-wave interaction considered in the Hartree-Fock approximation and cubic anisotropy. Properties of the ESR and neutron scattering are considered. The theoretical results are in agreement with existing experimental data.