We study the canted magnetic state in ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ using fully relativistic density functional theory (DFT) including an on-site Hubbard $U$ correction. A complete magnetic phase diagram with respect to the tetragonal distortion and the rotation of ${\mathrm{IrO}}_6$ octahedra is constructed, revealing the presence of two types of canted to collinear magnetic transitions: a spin-flop transition with increasing tetragonal distortion and a complete quenching of the basal weak ferromagnetic moment below a critical octahedral rotation. Moreover, we put forward a scheme to study the anisotropic magnetic couplings by mapping magnetically constrained noncollinear DFT onto a general spin Hamiltonian. This procedure allows for the simultaneous account and direct control of the lattice, spin, and orbital interactions within a fully ab initio scheme. We compute the isotropic, single site anisotropy and Dzyaloshinskii-Moriya (DM) coupling parameters, and clarify that the origin of the canted magnetic state in ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ arises from the structural distortions and the competition between isotropic exchange and DM interactions.

• Received 20 March 2015
• Revised 1 June 2015

DOI:https://doi.org/10.1103/PhysRevB.92.054428