Superexchange Interaction in Magnetic Insulators with Spin Crossover

We present the derivation of a microscopic superexchange Hamiltonian for undoped magnetic insulators with an arbitrary spin. It is established that the sign of the (ferromagnetic or antiferromagnetic) superexchange between magnetic ions in the dⁿ configuration depends on the spin nature of virtual multielectron states d^{n± 1}, viz., low-spin or high-spin partners with S ± 1/2 relative to ground state of the dⁿ configuration with spin S. A macroscopic substantiation is given for the Goodenough–Kanamori rules and simple mean-field estimates connecting the magnetic ordering temperature with the exchange constant. The conventional Anderson superexchange for magnetic materials with spin S = 1/2 and the P/T magnetic phase diagram for ferroborate FeBO₃ with spin crossover S = (5/2 ↔ 1/2) at the Fe³⁺ ion under a high pressure are also reproduced as a test.