under an external field*

Many parallels have been drawn between the spin-orbit coupled Mott insulator Sr₂IrO₄ and the high-T_c superconducting cuprates. In the undoped compound, a one band J_eff=1/2 model has been shown to capture the observed magnetic order. In other regimes, the applicability of this model is less clear, and the correlated phases are less understood due to potentially complex multiorbital physics. We use a multiple order parameter, self-consistent mean-field approach to explore the relevance of multiorbital effects to possible exotic phases in Sr₂IrO₄ in an external magnetic field. We study the contributions from both spin and orbital degrees of freedom to the magnetic moment. We thus unravel what role spin orbit coupling plays for emerging orders. Implications for superconductivity and thermal Hall measurements are discussed.