The magnetic structure of MnSi under an applied field

Below TC = 29 K the weak itinerant ferromagnet MnSi becomes ordered in a left-handed spin helical structure as a result of the Dzyaloshinskii-Moriya (DM) interaction. We give a recipe for calculating the orientation of the helix under an applied field. The recipe is derived on a basis of a theory recently developed for cubic magnets with DM interaction. The theory evaluates the ground state energy and the spin wave spectrum. It is shown that in zero field the orientation of the helix depends solely on the anisotropic exchange interaction and cubic anisotropy. Under an applied field the helix possesses two types of magnetic susceptibility: one parallel and another perpendicular to the applied magnetic field. The perpendicular susceptibility is related to the fact that the helical structure itself is unstable with respect to the small magnetic field H applied perpendicularly to the wavevector k. The spin wave gap Δ provides the stability of the spin wave spectrum of the helix structure and its presence may be revealed in the magnetic field behaviour. Our calculations show the essence of the field-induced transformations of the magnetic structure related to the spin wave gap. The experimental data provide the evidence for its existence. On the basis of our findings we discuss a possible scenario for the quantum phase transition in MnSi