Fluctuations in itinerant-electron paramagnets

Abstract

We use a functional-integral approach to study spin fluctuations in strongly paramagnetic systems. Our basic approximation is to replace the exact free energy functional by a variationally chosen quadratic form in the fluctuating (paramagnon) fields. This leads to a susceptibility $\ensuremath{\chi}$ of the form $\overline{\ensuremath{\phi}}(1\ensuremath{-}U{\overline{\ensuremath{\phi}}}^{\ensuremath{-}1}$, where $\overline{\ensuremath{\phi}}$ is an averaged electron-hole bubble in the presence of a space- and time-varying random external potential. The random potential has Gaussian statistics, and its covariance matrix is determined self-consistently. In another language, $\overline{\ensuremath{\phi}}$ is a polarization bubble dressed with paramagnons in all orders of perturbation theory. When the fluctuations are small and effectively only one paramagnon dresses the bubble at a time, we recover the results of Murata and Doniach and of Moriya and Kawabata. For intermediate coupling and at temperatures well above the spin-fluctuation temperature, we find that $\overline{\ensuremath{\phi}}$ is given approximately by an average of the corresponding random-phase-approximation (RPA) bubble over a distribution of Fermi levels of width $\ensuremath{\approx}{(\mathrm{UkT})}^{\frac{1}{2}}$, producing approximate Curie-Weiss behavior in $\ensuremath{\chi}$. These conclusions are supported by calculations of $\ensuremath{\chi}$ for two model systems-one, for simplicity, with a Gaussian density of states, and the other with the density of states of paramagnetic Ni.