Proliferation of Competing Magnetic Orders in Iron Pnictides from the Interplay of Quantum Fluctuations and Spin-Orbit Coupling

The magnetic phase diagram of the iron pnictides has been the subject of extensive studies in recent years. Experiments on a number of different compounds have revealed the emergence of several distinct magnetic orders as the putative quantum critical point is approached. Here we demonstrate that such a proliferation of magnetic orders can be naturally explained as a consequence of the interplay between strong quantum fluctuations and spin-orbit coupling (SOC), observed to be sizable in the pnictides. A finite SOC results in spin anisotropy which, at the mean-field level, leads to the appearance of new phases by allowing admixtures of single- and double-Q phases. Beyond mean-field we employ a renormalization group (RG) approach for the quantum phase transition and show that the RG flow of the spin-anisotropic system is fundamentally different than the isotropic one. While the isotropic system only displays fixed trajectories resulting in first-order transitions, the anisotropic case features an additional stable Gaussian fixed point. This indicates an enhanced magnetic degeneracy near the quantum phase transition. Such a scenario can naturally account for the fact that several types of magnetic order appear in close proximity near optimal doping in the experimental phase diagram.