Magnetic structure of MnSi under an applied field probed by polarized small-angle neutron scattering

Abstract

The magnetic structure of a single crystal MnSi under applied field has been studied by small angle diffraction with polarized neutrons below ${T}_{C}=28.7\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Experiments have shown that in zero field the magnetic structure of MnSi consists of four left-handed spiral domains oriented along four ⟨111⟩ axes. The magnetic field, applied along one of the ⟨111⟩ axes, produces a single domain helix oriented along the field at ${H}_{C1}\ensuremath{\approx}80\phantom{\rule{0.3em}{0ex}}\mathrm{mT}$ at low temperatures. The magnetic mosaic of the spin structure changes with the magnetic field and has a maximum at ${H}_{C1}$. The integral intensity of the Bragg reflection shows a sharp minimum at ${H}_{\mathit{in}}\ensuremath{\approx}160\phantom{\rule{0.3em}{0ex}}\mathrm{mT}$ attributed to an instability of the helix structure. When the field has a component perpendicular to the helix wave vector $\mathbf{k}$, it rotates toward the field direction in the field range $H<{H}_{\mathit{in}}$. Additionally, a second harmonic of the helix structure is induced by the perpendicular magnetic field for $H<{H}_{\mathit{in}}$. These three features are well explained accounting for the presence of a spin wave gap $\ensuremath{\Delta}\ensuremath{\sim}g{\ensuremath{\mu}}_{B}{H}_{\mathit{in}}∕\sqrt{2}\ensuremath{\simeq}12\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{eV}$, which provides the stability of the spin wave spectrum with respect to the perpendicular magnetic field. Further increase of the field leads to a magnetic phase transition from conical to a ferromagnetic state near ${H}_{C2}\ensuremath{\approx}600\phantom{\rule{0.3em}{0ex}}\mathrm{mT}$. The critical field ${H}_{C2}$ is related to the spin wave stiffness $A$ as $g{\ensuremath{\mu}}_{B}{H}_{C2}=A{k}^{2}$. Our findings are in agreement with the recently developed theory [Phys. Rev. B 73, 174402 (2006)] for cubic magnets with Dzyaloshinskii-Moriya interaction, which relates the major parameters of the spin wave spectrum (such as the spin wave stiffness and the gap) with the features of the spin structure of MnSi being observed under applied magnetic field.