Geometrically frustrated magnets, exemplified by Heisenberg antiferromagnets on triangular and kagome lattices, exhibit macroscopically degenerate ground states due to competing nearest-neighbor exchange interactions. In real materials, however, small perturbations such as further-neighbor exchange, quantum fluctuations, and spin–lattice coupling (SLC) play a crucial role in lifting this degeneracy, consistent with the third law of thermodynamics, which requires the entropy to vanish at absolute zero temperature. Here, SLC refers to the coupling between spin degrees of freedom and local lattice distortions. The importance of the spin–Jahn–Teller effect as a degeneracy-lifting mechanism became widely recognized following the theoretical work of Penc et al. [Phys. Rev. Lett. 93, 197203 (2004)], which microscopically incorporated SLC to reproduce the low-temperature structural transition and the 1/2 magnetization plateau observed in pyrochlore systems. Building on this, Bergman et al. proposed a complementary microscopic framework, the site-phonon model, that incorporates effective second- and third-neighbor interactions arising from SLC and thereby enables a descriptio of magnetic long-range order [Phys. Rev. B 74, 134409 (2006)]. We have applied the site-phonon model to various crystal lattices and, using classical Monte Carlo simulations, investigated how SLC influences the ground state.

　For the kagome lattice, we find that SLC does not induce long-range order at zero field and low temperatures. In an applied magnetic field, a finite SLC stabilizes a 2-up-1-down state with a √3×√3 superstructure; upon increasing the coupling strength further, a 5-up-4-down state with a 3×3 superstructure emerges [A]. These magnetic structures are accompanied by 1/3 and 1/9 magnetization plateaus, respectively. Such plateaus have recently been reported experimentally and appear to be well explained by our theory.

　We also investigated the role of SLC in the breathing pyrochlore lattice. The regular pyrochlore lattice only exhibits magnetic structures based on 2-up-2-down or 3-up-1-down configurations. By introducing breathing anisotropy (i.e., reducing J'/J from unity), we find that tetrahedron-based superstructures composed of mixed 2-up-2-down and 3-up-1-down motifs emerge [B]. Consistent with this picture, in the model compound LiGaCr₄O₈ the magnetization process exhibits two successive metamagnetic transitions just below the 1/2-magnetization plateau, indicative of the formation of a magnetic superstructure [C].

References

[A] M. Gen and H. Suwa, Phys. Rev. B 105, 174424 (2022). (Original paper [13])
[B] K. Aoyama, M. Gen et al., Phys. Rev. B 104, 184411 (2021). (Original paper [8])
[C] M. Gen et al., Proc. Natl. Acad. Sci. U.S.A. 120, e2302756120 (2023). (Original paper [22])