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  • Open Access

Theory of clusterization in orbitally degenerate transition-metal compounds driven by lattice instabilities

Soshun Ozaki1,2,3,*, Kota Mitsumoto1, and Chisa Hotta1,†

  • *Contact author: soshunozaki@gmail.com
  • †Contact author: chisa@phys.c.u-tokyo.ac.jp
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Phys. Rev. B 114, 245127 – Published 20 October, 2026

DOI: https://doi.org/10.1103/jq18-lrtj

Abstract

We derive an effective orbital-lattice model with quantum S=1 degrees of freedom for transition-metal compounds, providing a microscopic understanding of cluster formation driven by the cooperative interplay of spin, orbital, and lattice degrees of freedom. Motivated by the trimerized phases observed in LiVS2 and LiVO2, we consider a triangular-lattice three-orbital system with two electrons per site occupying the threefold-degenerate t2g manifold. Starting from a multiorbital Kanamori-Hubbard Hamiltonian, we project the low-energy sector onto the local S=1 triplet manifold, in which two electrons occupy different orbitals according to Hund's coupling. The resulting effective model exhibits exchange networks whose geometry is determined by the orbital configuration. However, the orbital-driven exchange interactions alone do not stabilize the experimentally observed trimer phase. We find that by incorporating ionic lattice displacements that modulate transfer integrals and induce bond-dependent exchange couplings on shortened and elongated bonds, the phase competition is qualitatively altered, leading to the robust stabilization of a trimerized ground state within a fully quantum-mechanical framework. We further show that a simplified orbital-lattice model, in which the spin-exchange energy is replaced by effective bond energies, faithfully reproduces the essential ground-state properties of the microscopic model. This reduced description enables large-scale finite-temperature simulations and reveals a rich sequence of thermal phase transitions, including first-order, second-order, and Kosterlitz-Thouless transitions into distinct spin-, orbital-, and lattice-ordered phases.

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Phys. Rev. B 114, 245127– Published 20 October, 2026
  • Received 16 June 2026
  • Accepted 30 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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