Theory of Magnetic Exchange Interactions:Exchange in Insulators and Semiconductors

Philip W.Anderson

Bell Telephone Laboratories, Incorporated, Murray Hill, New Jersey

Available online 30 May 2008.

This chapter discusses that the subject of exchange in magnetic materials is divided into two parts, referring to insulators and to metals. This distinction is useful from the magnetic point of view because in insulators the spins and magnetic moments whose alignments lead to magnetic effects are certainly localizable so that phenomenologically is described by a spin Hamiltonian that contains spin operators and exchange terms of Heisenberg type. It discusses that there is relationship among the mechanisms important in metals, such as conduction electron polarization, and those in insulators. The chapter provides historical discussion of the subjects of antiferromagnetism and of exchange in insulators. It focuses on the Heisenberg Hamiltonian, with a brief derivation and a discussion of some of the statistical theories of magnetism based upon it, primarily molecular field theory, which is by far the most generally useful in the experimental measurement of exchange. The chapter also describes older theories and presents ideas about super-exchange, and gives a discussion and a diagrammatic classification of all the possible higher-order processes.

I. Introduction ......................................................... 99
11. Historical Introduction. .............. ........... 101
111. Theories of Ferro-, Ferri-, and Antiferromagnetism. ...............
1. The Heisenberg Hamiltonian and Localizable Spins. ............
2. Statistical Theories of Magnetism.. . ............ 116
IV. Spin Waves .........................
VI. Theory of Superexchange.. ............................
V. Empirical Values of Exchange Constants in Insulators.. ...................
3. Formal Description of Magnetic Insulators: The Magnetic State.. ....... 142 146
4. Origin of Superexchange: Kinetic Exchange. ..
5. Potential Exchange and Other Exchange Effects.. ..................... 169
6. The Isolated Magnetic Ion: Ligand Fields lear Resonance .......................... ... 181
7. Semiempirical Approaches and Theoretical ................ 197
VII. Double Exchange.. .. ........................................ 209
Acknowledgments. ........................... 214 

https://sci-hub.tw/https://doi.org/10.1016/S0081-1947(08)60260-X