Origin and consequence of an unpinned helical magnet: application to partial order in MnSi under pressure

We study a classical ferromagnetic Heisenberg model in the presence of Dzyaloshinskii-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 wavevector 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 wavevector magnitude. The surface formed by connecting these wavevectors 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 experimentalists choice of lattice Bragg peak through a geometric factor. A neutron scattering measurement near the Bragg point ($frac{2pi}{a}$,$frac{2pi}{a}$,0) naturally leads to a highest intensity along the (1,1,0) direction consistent with the observed anisotropy in MnSi [Pfleiderer {it{et al.}} Nature {bf{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.

Fate of partial order on the trillium and distorted windmill lattices

The classical Heisenberg model on the trillium and distorted windmill lattices exhibits a degenerate ground state within large-$N$ theory, where the degenerate wavevectors form a surface and line, in 3-dimensional space, respectively. We name such states partially ordered to represent the existence of long-range order along the direction normal to these degenerate manifolds. We investigate the effects of thermal fluctuations using Monte Carlo (MC) methods, and find a first order transition to a magnetically ordered state for both cases. We further show that the ordering on the distorted windmill lattice is due to order by disorder, while the ground state of the trillium lattice is unique. Despite these different routes to the realization of low temperature ordered phases, the static structure factors obtained by large-$N$ theory and MC simulations for each lattice show quantitative agreement in the cooperative paramagnetic regime at finite temperatures. This suggests that a remnant of the characteristic angle-dependent spin correlations of partial order remains above the transition temperatures for both lattices. The possible relevance of these results to $beta$-Mn, CeIrSi, and MnSi is discussed.