Electron correlations and many-body techniques in magnetism

Abstract

Recent progress in the theory of magnetism and electron correlations is reviewed to clarify the theories developed in the last decade and their mutual relations. A historical development of the theory of magnetism is outlined, and the dynamical coherent potential approximation (CPA) which completely takes account of the dynamical spin and charge fluctuations within the single-site approximation is introduced. Both the dynamical effects on various magnetic properties and the many-body band structure are shown to be explained on the same footing. It is shown that the dynamical CPA is equivalent to the other single-site theories of strongly correlated electrons: the many-body CPA, the dynamical mean-field theory (DMFT), and the projection operator method CPA (PM-CPA). These theories are elucidated with use of a common concept of effective medium or coherent potential. The effects of orbital degeneracy and the realistic calculation scheme are discussed with an emphasis on Hund’s rule coupling. Non-local theories of magnetism and electron correlations which go beyond the single-site approximation are presented. They include the molecular dynamics approach to the magnetic short range order, the dynamical cluster methods as a direct extension of the DMFT, and the self-consistent projection operator approach as an extension of the PM-CPA with use of the incremental cluster expansion. The current problems of their approaches and their future perspective are discussed.

Acknowledgements

The author would like to thank Professor P. Fulde for valuable discussions on the present subject and Professor M. C. Gutzwiller for critical reading of the manuscript and for encouragement of its publication.