The eigenstates and eigenvalues for a triad consisting of three exchange-coupled Cr 3+ ions in ruby are derived from a phenomenological spin Hamiltonian. The terms included in the Hamiltonian are the isotropic, anisotropic and antisymmetric exchange interactions together with the single ion zero field term and dipole-dipole interaction term. The importance of each term is discussed in relation to various possible triads in ruby.
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Bates et al. (1971) studied this question.
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