General superexchange Hamiltonians for magnetic and orbital physics in eg and t2g systems

Material-specific super-exchange Hamiltonians are the key to studying spin and orbital physics in strongly correlated materials. Recently, via an irreducible-tensor operator representation, we derived the orbital superexchange Hamiltonian for t12g perovskites and successfully used it, in combination with many-body approaches, to explain orbital physics in these systems. Here, we generalize our method to eng and tn2g systems at arbitrary integer filling n, including both spin and orbital interactions. The approach is suitable for numerical implementations based on ab initio hopping parameters and realistic screened Coulomb interactions and allows for a systematic exploration of superexchange energy surfaces in a realistic context.