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Ab initio determination of excitation energies and magnetic couplings in correlated, quasi two-dimensional iridates

To determine the strength of essential electronic and magnetic interactions in the iridates Sr$_2$IrO$_4$ and Ba$_2$IrO$_4$ - potential platforms for high-temperature superconductivity - we use many-body techniques from wavefunction-based electronic-structure theory. Multiplet physics, spin-orbit interactions, and Ir-O hybridization are all treated on equal footing, fully {\it ab initio}. Our calculations put the lowest d-d excitations of Sr$_2$IrO$_4$/Ba$_2$IrO$_4$ at 0.69/0.64 eV, substantially lower than in isostructural cuprates. Charge-transfer excitations start at 3.0/1.9 eV and the magnetic nearest-neighbor exchange coupling is 51/58 meV. Available experimental results are fully consistent with these values, which strongly constrains the parametrization of effective iridate Hamiltonians.