From the Hubbard model to classical spin-fluctuation theory.

Abstract

In this paper we develop a microscopic foundation for the Murata-Doniach model of spin fluctuations which has been widely used in connection with band-structure calculations. The main result of the paper is the formulation of the partition function of an itinerant system as a functional integral over magnetization modes, and an explicit formula for the energy functional appearing in the exponent of the Boltzmann factor. Such a derivation is made since former theoretical investigations focus on the interaction part of the parition function Z/${\mathit{Z}}_{0}$, whereas the Murata-Doniach model is formulated in terms of a functional integral for the complete partition function Z. We start with an approximate description of magnetic excitations of noninteracting fermions with collective modes, and derive a bosonlike partition function for these magnetization modes. This is combined with the well-known result for the interaction part of the partition function in the Hubbard model obtained by functional-integral theory. The leading term of the energy functional appearing in the exponent of the parition function agrees with that of the Ginzburg-Landau expansion for the energy of a classical magnetization field. In the course of the transformation to a bosonlike system we predict that the cutoff wave vector ${\mathit{q}}_{\mathit{c}}$ which must be introduced in the classical model is temperature dependent with ${\mathit{q}}_{\mathit{c}}$\ensuremath{\sim}${\mathit{T}}^{1/3}$. It is shown that the frequencies of the collective modes are reduced by the Stoner enhancement factor compared with the one-particle excitation energies of Stoner theory.