LAUSR

We show how an accurate first-principles treatment of the canted-anti-ferromagnetic ground state of ${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$, a prototypical $5d$ correlated spin-orbit coupled material, can be obtained without invoking any free parameters, such as the Hubbard $U$ or tuning the spin-orbit coupling strength. Our theoretically predicted iridium magnetic moment of $0.250{\ensuremath{\mu}}_{B}$, canted by $12.{6}^{\ensuremath{\circ}}$ off the $a$ axis, is in accord with experimental results. By resolving the magnetic moments into their spin and orbital components, we show that our theoretically obtained variation of the magnetic scattering amplitude $\ensuremath{\langle}{M}_{m}\ensuremath{\rangle}$ as a function of the polarization angle is consistent with recent nonresonant magnetic x-ray scattering measurements. The computed value of the band gap (55 meV) is also in line with the corresponding experimental values. A comparison of the band structure to that of the cuprates suggests the presence of incommensurate charge-density wave phases in ${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$.