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

Low-energy paramagnetic excitations in the weak itinerant ferromagnet (WIF) MnSi have been studied by neutron scattering. The observed spectrum has a Lorentzian form ($\frac{\Gamma }{{\Gamma }^2}+{\omega }^2$) and is clearly separated from excitations in the Stoner continuum. The generalized susceptibility, $\chi \mathrm{}\left(q\right)\mathrm{}$, has been obtained by integrating the scattering intensity over energy. It is found that $\chi \mathrm{}\left(q\right)\mathrm{}$ depends upon the wave vector $q$ as $\chi {\mathrm{}\left(q\right)\mathrm{}}^{-1\mathrm{}}={\kappa }^2\mathrm{}\left(T\right)+q^2$ for $q\le 0.125\left(\frac{2\pi }{a}\right)$ with ${\kappa }^2\mathrm{}\left(T\right)={\kappa }_0^2(T-T_c)$. After extrapolating these results to $q=0\mathrm{}$, it is found that $\chi \mathrm{}(q=0\mathrm{})\mathrm{}$ 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 $\Gamma$ is found to be proportional to $\frac{q}{\chi \mathrm{}\left(q\right)\mathrm{}}$ as predicted by the MK theory, in contrast with the $\frac{q^2}{\chi \mathrm{}\left(q\right)\mathrm{}}$ 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 $T_c$.