We put forward a scheme to study the anisotropic magnetic couplings in Sr2IrO4 by mapping fully relativistic constrained noncollinear density functional theory including an on-site Hubbard U correction onto a general spin model Hamiltonian. This proc
edure 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 Sr2IrO4 arises from the interplay between structural distortions and the competition between isotropic exchange and DM interactions. A complete magnetic phase diagram with respect to the tetragonal distortion and the rotation of IrO6 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.
Magnetic anisotropy phenomena in bimetallic antiferromagnets Mn$_2$Au and MnIr are studied by first-principles density functional theory calculations. We find strong and lattice-parameter dependent magnetic anisotropies of the ground state energy, ch
emical potential, and density of states, and attribute these anisotropies to combined effects of large moment on the Mn 3$d$ shell and large spin-orbit coupling on the 5$d$ shell of the noble metal. Large magnitudes of the proposed effects can open a route towards spintronics in compensated antiferromagnets without involving ferromagnetic elements.
