Multipolar magnetism in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>d</mml:mi></mml:math>-orbital systems: Crystal field levels, octupolar order, and orbital loop currents
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Bibliographic record
Abstract
Quantum magnets with spin $J=2$, which arise in spin-orbit coupled Mott insulators, can potentially display multipolar orders. Motivated by gaining a better microscopic understanding of the local physics of such $d$-orbital quantum magnets, we carry out an exact diagonalization study of a simple octahedral crystal field Hamiltonian for two electrons, incorporating spin-orbit coupling (SOC) and interactions. While the rotationally invariant Kanamori interaction in the ${t}_{2g}$ sector leads to a fivefold degenerate $J=2$ manifold, we find that either explicitly including the ${e}_{g}$ orbitals, or going beyond the rotationally invariant Coulomb interaction within the ${t}_{2g}$ sector, causes a degeneracy breaking of the $J=2$ levels. This can lead to a low-lying non-Kramers doublet carrying quadrupolar and octupolar moments and an excited triplet which supports magnetic dipole moments, bolstering our previous phenomenological proposal for the stabilization of ferro-octupolar order in heavy transition metal oxides. We show that the spontaneous time-reversal symmetry breaking due to ferro-octupolar ordering within the non-Kramers doublet leads to electronic orbital loop currents. The resulting internal magnetic fields can potentially explain the small fields inferred from muon-spin relaxation ($\ensuremath{\mu}\mathrm{SR}$) experiments on cubic $5{d}^{2}$ osmate double perovskites ${\mathrm{Ba}}_{2}{\mathrm{ZnOsO}}_{6}$, ${\mathrm{Ba}}_{2}{\mathrm{CaOsO}}_{6}$, and ${\mathrm{Ba}}_{2}{\mathrm{MgOsO}}_{6}$, which were previously attributed to weak dipolar magnetism. We make further predictions for oxygen NMR experiments on these materials. We also study the reversed level scheme, where the $J=2$ multiplet splits into a low-lying magnetic triplet and excited non-Kramers doublet, presenting single-ion results for the magnetic susceptibility in this case, and pointing out its possible relevance for the rhenate ${\mathrm{Ba}}_{2}{\mathrm{YReO}}_{6}$. Our work highlights the intimate connection between the physics of heavy transition metal oxides and that of $f$-electron based heavy fermion compounds.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it