Converge the orbitally ordered branch beyond the accessible c-axis range

Construct and converge dynamical mean-field theory solutions for the orbitally ordered $d_{xz}/d_{yz}$ state at larger $c$-axis lattice parameters, thereby determining the opposite side of the orbital hysteresis loop in expanded SrVO3.

Background

In the expanded structure, the crystal-field splitting creates an effectively quarter-filled, locally degenerate dxz/dyzd_{xz}/d_{yz} doublet that is predicted to undergo commensurate orbital ordering at wave vector (π,π,π)(\pi,\pi,\pi). However, unconstrained DMFT iterations become unstable at sufficiently large elongation because the occupations and self-energies attempt to break the local orbital symmetry and alternate between iterations. The authors therefore cannot continue the cc-axis scan or directly obtain the orbitally ordered branch without enforcing orbital symmetry or using a supercell.

References

Strictly speaking, for this reason we were not able to continue the $c$-axis scan of Fig.~\ref{fig:srvo3_dmft_occ} to larger values and probe the other side of the indicated hysteresis. There, an explicit symmetry enforcement of the $d_{xz}$/$d_{yz}$ orbitals or a supercell setup would be necessary to converge the DMFT calculation into its orbitally degenerate or orbitally ordered state, respectively.

— Tuning crystal-fields by He-irradiation and orbital Widom line in SrVO$_3$ films  (2608.14362 - Pickem et al., 14 Aug 2026) in Section 4, subsection “Ordering instabilities,” footnote following the discussion of orbital order