Exchange and exchange-relativistic effects in the excited states of 3$d$ ions in crystals

The use of the simplest Heisenberg or Dzyaloshinskii–Moriya-type spin Hamiltonians traditional for the ground orbital nondegenerate states does not allow the features of the exchange and exchange-relativistic couplings for the excited states of 3$d$ and 4$f$ ions in crystals to be correctly described. We have considered a generalized Hamiltonian of the exchange and superexchange couplings, which makes it possible to take into account the effects of orbital (quasi)degeneracy and the exchange mechanism of excitation transfer using a single approach. A new mechanism of the spin–other orbit exchange-relativistic couplings is discussed, in particular, the spin–orbital analog of the Dzyaloshinskii–Moriya interaction and its manifestation in the circular magnetooptics of weak ferromagnets.