Cubic magnets with Dzyaloshinskii–Moriya interaction

Abstract Ground-state energy and spin-wave spectrum are studied theoretically using conventional exchange, Dzyaloshinskii–Moriya interaction, anisotropic exchange and cubic anisotropy. The spin-wave spectrum is strongly anisotropic: excitations with momentum q along and perpendicular to the helix wave vector k have linear and quadratic dispersion, respectively, if q ⪡ k . It is a result of the umklapp interaction connecting the spin-waves with q and q ± k . The classical ground-state energy depends on the magnetic field component along the vector k only. Transition to the ferromagnetic state holds at H > H c where g μ B H c = Ak 2 and A is the spin-wave stiffness at q ⪢ k . For low perpendicular field the helical order is stabilized by the spin-wave gap Δ . For g μ B H ⊥ Δ 2 there is Bose condensation of the spin-waves with momenta k and zero. The perpendicular susceptibility and the second harmonic of the spin rotation appear. For larger field the vector k establishes along the field and the condensation disappears. The theory is in agreement with the existing experimental data.