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 $t_{2g}^1$ perovskites and successfully used it, in combination with many-body approaches, to explain orbital physics in these systems. Here, we generalize our method to $e_g^n$ and $t_{2g}^n$ 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.

• Received 6 December 2021
• Accepted 16 February 2022

DOI:https://doi.org/10.1103/PhysRevB.105.115104