Goodenough–Kanamori–Anderson Rules of Superexchange Applied to Ferrite Systems

This chapter contains discussions of superexchange (SE) fundamentals and the source of magnetic anisotropy in ferrite systems. It examines the behavior of spin collectives in response to RF electromagnetic stimulation. Goodenough's guidelines were complimented by a series of publications by Kanamori who refined his formalisms into a more rigorous mathematical context and together formed the empirical foundation of rules for understanding SE from the viewpoint of atomic bonding, electronic structure, and ligand field theory. These rules have been shown to validate the results of Anderson's rigorous mathematical SE theory and are now popularized by the names of its principles as the Goodenough–Kanamori–Anderson rules. The chapter considers fundamental origins of magnetic anisotropy in ferrites and posit ways to engineer this anisotropy from the spin Hamiltonian. It explores demonstrations by researchers who have established relationships between substitutional cations and ferrite magnetization, magnetic anisotropy field, and gyromagnetic behavior.