Magnetic properties of ferromagnetic transition metals aboveTC: Qualitative aspects

Abstract

A theory is developed for the dynamic susceptibility ${\chi }_q\left(\omega \right)$ of itinerant ferromagnets above $T_C$. The underlying picture is the "fluctuating band theory" (advocated to apply to ferromagnetic transition metals) consistent with the existence of strong short-range magnetic order (SRMO) far above $T_C$. The dynamical properties derived here are expressed in terms of a static spin-density correlation function describing the static SRMO. The results obtained are the following: For wavelengths smaller than the range of the static SRMO we obtain a ${\chi }_q\left(\omega \right)$ representative of propagating spin waves above $T_C$ which are shifted from their low-temperature energies and have acquired a width due to the lack of long-range order. For wavelengths larger than the range of the static SRMO we obtain a magnetic response which has diffusive character. The crossover from propagating to diffusive behavior is also described by our theory. For ($q,\omega$) going to zero we obtain a Curie-Weiss law for the static susceptibility. The Curie-Weiss law is caused by SRMO changing slowly above $T_C$. We argue that SRMO above $T_C$ should change appreciably only on a temperature scale $T_S$ (the Stoner temperature), considerably larger than $T_C$. This is the reason for the slow change in SRMO at temperatures $T_C$ to $\sim 2T_C$ thereby inducing a Curie-Weiss law outside a small critical region around $T_C$.