MIT OpenCourseWare http ocw mit edu 8 512 Theory of Solids II Spring 2009 For information about citing these materials or our Terms of Use visit http ocw mit edu terms 1 Lecture 14 Local Moment Magnetism Lecture 15 Exchange Interactions We begin with a discussion of the magnetism due to spins and Hund s rule in isolated ions Reading Aschcroft and Mermin Chapter 31 Then the e ect of the solid state is discussed by introducing the concept of crystal eld splitting For transition metals the crystal eld e ect is stronger than the spin orbit e ect and we work in the orbital angular momentum basis On the other hand for rare earths the reverse is true and one works in the basis of J We discuss the transition metal case in some detail covering the Jahn Teller theorem and the splitting of the d band into T2g and Eg orbitals in a cubic crystal eld Then the spin orbit e ect is introduced perturba tively leading to the e ective g tensor and anisotropy in the magnetic Hamiltonian The exchange interactions between two magnetic ions is discussed as the Heisenberg exchange via the Hubbard model Some examples of ferromagnetic and antiferromagnetic exchange are discussed The concept of double exchange is illustrated by considering doping of LaMnO3 by Sr substitution
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