Impact of spin-orbit coupling on the magnetic phase diagram of the iron pnictides*

Experimental research over the past few years has shown the presence of sizeable spin-orbit coupling (SOC) in the iron pnictides [1]. Here, we focus on the impact of SOC on the magnetic phase diagram of the iron pnictides and in particular the implications for competing magnetic states and quantum criticality. Magnetism in the pnictides occurs in three distinct types. The prevalent magnetic phase is the C₂ symmetric stripe magnetism, with moments parallel to the ordering vector. Additionally, there are two tetragonal, or C₄, magnetic phases, one with out-of-plane moments observed close to optimal doping in several compounds [2], and another with in-plane moments forming a spin-vortex structure [3]. The intimate relation between the ordering vectors and the moment direction is a direct consequence of SOC. Interestingly, a proliferation of different magnetic phases in close proximity in the phase diagram is observed in different pnictide materials as the putative magnetic quantum critical point is approached, e.g. by changing doping or pressure. We demonstrate, using a renormalization group approach, that such a behavior is a natural consequence of the interplay between magnetic quantum fluctuations and SOC. Formally, this is due to the emergence of a Gaussian fixed point leading to an enhanced magnetic degeneracy. This leads to an increase in the phase space of fluctuations which can enhance the transition temperature of superconductivity. Furthermore, we show how a rich landscape of magnetic phases emerges as a result of frustration between spin-anisotropic and spin-isotropic interactions. These novel phases consist of admixtures of the known C₂ and C₄ orders, and provide possible candidates for experimental observations [4].

[1] Borisenko et al, Nat. Phys. 12, 311 (2016).
[2] Allred et al, Nat. Phys. 12, 493 (2016).
[3] Meier et al, npj Quant. Mat. 3, 5 (2018).
[4] Wang et al, PRB 93, 014514 (2016).