Low-energy paramagnetic spin fluctuations in the weak itinerant ferromagnet MnSi

Abstract

Low-energy paramagnetic excitations in the weak itinerant ferromagnet (WIF) MnSi have been studied by neutron scattering. The observed spectrum has a Lorentzian form ($\frac{\ensuremath{\Gamma}}{{\ensuremath{\Gamma}}^{2}}+{\ensuremath{\omega}}^{2}$) and is clearly separated from excitations in the Stoner continuum. The generalized susceptibility, $\ensuremath{\chi}(q)$, has been obtained by integrating the scattering intensity over energy. It is found that $\ensuremath{\chi}(q)$ depends upon the wave vector $q$ as $\ensuremath{\chi}{(q)}^{\ensuremath{-}1}={\ensuremath{\kappa}}^{2}(T)+{q}^{2}$ for $q\ensuremath{\le}0.125(\frac{2\ensuremath{\pi}}{a})$ with ${\ensuremath{\kappa}}^{2}(T)={\ensuremath{\kappa}}_{0}^{2}(T\ensuremath{-}{T}_{c})$. After extrapolating these results to $q=0$, it is found that $\ensuremath{\chi}(q=0)$ follows the Curie-Weiss law, suggesting that the observed spin fluctuations correspond to the Moriya-Kawabata (MK) spin fluctuations responsible for the Curie-Weiss dependence of the static susceptibility of a WIF. The linewidth $\ensuremath{\Gamma}$ is found to be proportional to $\frac{q}{\ensuremath{\chi}(q)}$ as predicted by the MK theory, in contrast with the $\frac{{q}^{2}}{\ensuremath{\chi}(q)}$ relation expected in a Heisenberg system. These results provide the first direct experimental evidence for the existence of MK spin fluctuations in a WIF above ${T}_{c}$.