Metallic Magnetism at Finite Temperatures

Abstract

With elevating temperature, various excited states of electrons appear. We present in Chap. 3 theories of the metallic ferromagnetism at finite temperatures. We start from the Stoner theory (i.e., the Hartree–Fock theory) and show that the theory without thermal spin fluctuations overestimates the Curie temperatures by a factor of ten in 3d transition metals. To describe the spin fluctuations, we introduce the functional integral method, and present the single-site spin fluctuation theory (SSF) obtained by a high-temperature approximation. We show how the local magnetic moments (LM) are developed in solids with increasing intra-atomic Coulomb interaction at finite temperatures. Next we present the dynamical CPA which completely describes both the dynamical charge and spin fluctuations within the single-site approximation. The dynamical CPA is the quantum version of the SSF and is equivalent to the dynamical mean-field theory. We prove the equivalence in Sect. 3.6. Finally we present the first-principles version of the dynamical CPA and discuss the quantitative aspects of the finite-temperature magnetism in 3d transition metals.