Spin Hamiltonian of hyper-kagome Na4Ir3O8

We derive the spin Hamiltonian for the quantum spin liquid Na4Ir3O8, and then estimate the direct and superexchange contributions between near neighbor iridium ions using a tight-binding parametrization of the electronic structure. We find a magnitude of the exchange interaction comparable to experiment for a reasonable value of the on-site Coulomb repulsion. For one of the two tight-binding parametrizations we have studied, the direct exchange term, which is isotropic, dominates the total exchange. This provides support for those theories proposed to describe this quantum spin liquid that assume an isotropic Heisenberg model.