Anisotropic Coulomb exchange as source of Kitaev and off-diagonal symmetric anisotropic couplings

Exchange underpins the magnetic properties of quantum matter. In its most basic form, it occurs through the interplay of Pauli's exclusion principle and Coulomb repulsion, being referred to as Coulomb exchange. Pauli's exclusion principle combined with inter-atomic electron hopping additionally leads to kinetic exchange and superexchange. Here we disentangle the different exchange channels in anisotropic Kitaev-Heisenberg context. By quantum chemical computations, we show that anisotropic Coulomb exchange, completely neglected so far in the field, may be as large as (or even larger than) other contributions -- kinetic exchange and superexchange. This opens new perspectives onto anisotropic exchange mechanisms and sets the proper conceptual framework for further research on tuning Kitaev-Heisenberg magnetism.