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Generalized incommensurability: Role of anomalously strong spin-orbit coupling for the spin ordering in the quasi-two-dimensional system FeSe

Piotr Chudzinski1,2, Abyay Ghosh2, and Myrta Grüning2,3

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Phys. Rev. B 112, 035419 – Published 18 July, 2025

DOI: https://doi.org/10.1103/s5cy-t1sf

Abstract

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.

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Phys. Rev. B 112, 035419– Published 18 July, 2025
  • Received 1 February 2025
  • Revised 31 May 2025
  • Accepted 1 July 2025
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