Institute of Fundamental Technological Research

We study 2D spin and orbital systems, in a classical limit, in a regime where their coupling is so strong that orbital fluctuations are able to change the sign of spin exchange. Our aim is to understand how different phases in the orbital sector determine the ordering in the spin sector. The existence of intermediate vortex crystal (VC) phases, beside the canonical Kosterlitz and Thouless (KT) phases is now a well-established fact. Recently, we found [Phys. Rev. Res. 6, 043154 (2024)] that such a phase can explain the phase diagram of FeSe, specific parameters used here come from that ab initio work. Motivated by this, here we develop a renormalization group (RG) method which can capture the formation of the VC phase. We achieve it by incorporating orbital vortex-vortex interactions through space-dependent incommensurability. Simultaneously, we incorporate the coupling with the spin sector for both short- and long-range interactions. We then derive a phase diagram including the effects of long-range interactions and spin-orbit coupling. The presence of the intermediate VC phase in the orbital sector changes the scaling of long-range spin-spin interactions, making them relevant under specific conditions. We thus find a way to bypass the Mermin-Wagner theorem: the regular arrangement of orbital vortices can induce a long-range order in the 2D spin system.

renormalization group, iron-based superconductors

We calculated the structural, electronic, and magnetic properties of FeSe within density-functional theory at
the generalized gradient approximation level. First, we studied how the bandwidth of the d-bands at the Fermi
energy is renormalized by adding simple corrections: Hubbard U , Hund’s J, and by introducing long-range
magnetic orders. We found that introducing either a striped or a staggered dimer antiferromagnetic order brings
the bandwidths—which are starkly overestimated at the generalized gradient approximation level—closer to
those experimentally observed. Second, for the ferromagnetic, the striped, checkerboard, and staggered dimer
antiferromagnetic order, we investigate the change in magnetic formation energy with local magnetic moment
of Fe at a pressure up to 6 GPa. The bilinear and biquadratic exchange energies are derived from the Heisenberg
model and noncollinear first-principles calculations, respectively. We found a nontrivial behavior of the spin-
exchange parameters on the magnetization, and we put forward a field-theory model that rationalizes these results
in terms of two-dimensional spin and orbital fluctuations. The character of these fluctuations can be either that
of a standard density wave or a topological vortex. Topological vortices can result in mesoscopic magnetization
structures.