Magnetic phase diagram of the iron pnictides in the presence of spin-orbit coupling: Frustration between C 2 and C 4 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 C 2 (i.e., orthorhombic) symmetric stripe magnetic phase and two C 4 (i.e., tetragonal) symmetric magnetic phases. While the spin anisotropic interactions allow the magnetic moments to point in any direction in the C 2 phase, they restrict the possible moment orientations in the C 4 phases. As a result, an interesting scenario arises in which the spin anisotropic interactions favor a C 2 phase, but the other spin isotropic interactions favor a C 4 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 C 2 , C 4 , and mixed C 2 – C 4 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 C 2 and C 4 phases. Here, we argue that this frustration is the reason why most C 4 phases in the iron pnictides only appear inside the C 2 phase, and discuss additional manifestations of this frustration in the phase diagrams of these materials.