Stabilizing the spin vortex crystal phase in two-dimensional iron-based superconductors

We present an investigation of the magnetic structure for iron-based superconductors (FeSCs) when inversion symmetry is broken, such as in substrate-supported monolayers or in the presence of a $c$-axis electric field. We perform group-, mean-field-, and density-functional-theoretic analyses on a model system of monolayer iron selenide (FeSe) on a strontium titanate $[{\mathrm{SrTiO}}_{3}$(001)] substrate. Our group- and mean-field-theoretic calculations are more generally applicable to thin films of the rest of the 11 (e.g., FeSe) family of iron-based superconductors, as well as to thin films of the 111 (e.g., LiFeAs) and 1111 (e.g., LaOFeAs) families, as these all belong to the same space group. We find that in systems with a collinear antiferromagnetic phase in bulk, when inversion symmetry is broken, the transition is instead into a ``spin vortex crystal'' phase and that a further phase transition can occur at a lower temperature in some circumstances. The spin vortex crystal is a ${C}_{4}$-symmetric magnetic phase which is related to this parent ${C}_{2}$-symmetric collinear antiferromagnetic (stripe) phase which is ubiquitous among the iron-based superconductors.