Temperature Dependence of Localized Moments in Metals

Abstract

Anderson's theory of localized magnetic states in metals is extended to finite temperatures assuming the metal-impurity states are populated in accordance with Fermi statistics. A procedure is given for determining the magnitude of the local moment at any temperature. If when unmagnetized at elevated temperatures the local state lies at the Fermi level, it will become magnetic at a critical temperature TC=k−1π−12Δ(1−πΔU−1)12, if kTC is small compared with 2Δ, the width of the state. Below TC the moment is then μ=2μBkU−1[3π(TC2−T2)]12. If the local state is unmagnetized at T = 0 and lies appreciably above or below the Fermi level, it may first become weakly magnetic before demagnetizing again at high temperatures. In general the temperature variation is greatest when Δ and U, the Coulomb repulsion between a pair of electrons localized in the state, or/and μ itself are small.