Cubic magnets with Dzyaloshinskii-Moriya interaction

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 mu(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 Delta. For g mu(B) H-perpendicular to < Delta root 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. (c) 2006 Elsevier B.V. All rights reserved.