Magnetic phase diagram of the iron pnictides in the presence of spin-orbit coupling: Frustration between C2 and C4 magnetic phases

We investigate the impact of spin anisotropic interactions, promoted by spin-orbit coupling, on the magnetic phase diagram of the iron-based superconductors. Three distinct magnetic phases with Bragg peaks at (π,0) and (0, π) are possible in these systems: one C₂ (i.e., orthorhombic) symmetric stripe magnetic phase and two C₄ (i.e., tetragonal) symmetric magnetic phases. While the spin anisotropic interactions allow the magnetic moments to point in any direction in the C₂ phase, they restrict the possible moment orientations in the C₄ phases. As a result, an interesting scenario arises in which the spin anisotropic interactions favor a C₂ phase, but the other spin isotropic interactions favor a C₄ phase. We study this frustration via both mean-field and renormalization-group approaches. We find that, to lift this frustration, a rich magnetic landscape emerges well below the magnetic transition temperature, with interesting C₂, C₄, and mixed C₂ – C₄ phases. Near the putative magnetic quantum critical point, spin anisotropies promote a stable Gaussian fixed point in the renormalization-group flow, which is absent in the spin isotropic case, and is associated with a near-degeneracy between C₂ and C₄ phases. Here, we argue that this frustration is the reason why most C₄ phases in the iron pnictides only appear inside the C₂ phase, and discuss additional manifestations of this frustration in the phase diagrams of these materials.