Origin and consequences of unpinned helical order: Application to MnSi under pressure

Abstract

We study a classical ferromagnetic Heisenberg model in the presence of Dzyaloshinsky-Moriya interactions on the corner-shared triangle lattice formed by the Mn sites of MnSi. We show that a sizable spin helicity can be obtained only when the microscopic Moriya vectors lie parallel to the Mn-Mn bonds. Further, such vectors are shown to produce an unpinned helical order characterized by a particular ordering wave-vector magnitude but unpinned direction, dubbed partial order, at physically realizable temperatures. A consequence of such an unpinned helical ordering is that the neutron-scattering intensity is sharply peaked at this wave-vector magnitude. The surface formed by connecting these wave vectors is a sphere, around which the neutron-scattering weight is spread. We further show that the observed neutron-scattering intensity can be anisotropic along this surface and that this anisotropy is dependent on the experimentalist's choice of lattice Bragg peak through a geometric factor. A neutron-scattering measurement near the Bragg point $(\frac{2\ensuremath{\pi}}{a},\frac{2\ensuremath{\pi}}{a},0)$ naturally leads to a highest intensity along the (1,1,0) direction consistent with the observed anisotropy in MnSi [C. Pfleiderer et al., Nature (London) 427, 227 (2004)]. A possible mechanism for pinning the helical order and a way to distinguish an ordered and a partially ordered state in the context of neutron scattering are discussed.