  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.
