Hidden orders in spin-orbit entangled correlated insulators

Arun Paramekanti; Cesare Franchini; Dario Fiore Mosca; Leonid V. Pourovskii; Lorenzo Celiberti; Sergii Khmelevskyi

REVIEW 2 major objections 4 minor 297 references

Hidden orders in spin-orbit entangled correlated insulators

T0 review · 2 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Hidden multipolar orders become computable from first principles

desk verdict A genuinely useful review of multipolar hidden order theory, strong on synthesis and honest about open problems, but marred by a duplicated section and some rhetorical overreach on 'parameter-free' claims. read the letter →

arxiv 2509.01788 v1 pith:6G6LDLJR submitted 2025-09-01 cond-mat.str-el

Leonid V. Pourovskii , Dario Fiore Mosca , Lorenzo Celiberti , Sergii Khmelevskyi , Arun Paramekanti , Cesare Franchini This is my paper

classification cond-mat.str-el

keywords hiddenordermultipolarspin-orbitcouplingstronglycorrelatedinsulatorsdoubleperovskitesactinidedioxidesforcetheoreminHubbard-Iintersiteexchangeinteractions

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This Review argues that parameter-free ab initio methods—the force theorem in the Hubbard-I approximation, DFT+DMFT susceptibility approaches, and cluster exact diagonalization—have turned hidden multipolar orders in spin-orbit entangled insulators from a puzzle into a computable phenomenon. The central object is a low-energy many-body effective Hamiltonian built from local high-rank multipole moments of the spin-orbit entangled ground-state multiplet. Applied to 5d double perovskites and actinide dioxides, these methods reproduce observed phases, predict new ones, and show that high-rank exchange rather than dipole exchange often drives the order. The sympathetic reading is that material-specific multipolar order parameters can now be derived without adjustable parameters.

What carries the argument

The many-body effective Hamiltonian H = H_IEI + H_EM + H_EL + Σ H_1s, in which the intersite exchange term is a bilinear sum of multipolar operators O^Q_K(i) with coupling matrices V^{QQ'}_{KK'}(R_ij). The load-bearing identity is the multipole expansion of the ground-state multiplet density matrix, ρ = ⟨O^Q_K⟩ O^Q_K, which turns hidden order into defined rank-K order parameters. The FT-HI formula (Eq. 6) evaluates the exchange matrix elements from paramagnetic intersite propagators and derivatives of the Hubbard-I self-energy, making the whole construction parameter-free for Mott insulators.

What would settle it

For a material the method labels multipolar, such as Ba2MgReO6 or NpO2, compute the same multipolar intersite couplings with a charge-fluctuation-retaining method like full DFT+DMFT at the same U; if the leading couplings shift by more than the mean-field ordering energy (around a meV), the strong-coupling extraction is unreliable. Alternatively, find a predicted purely quadrupolar phase that shows a measurable local magnetic dipole at the ordering temperature.

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Extended reading notes

Core claim

The review's thesis is that the ordering degrees of freedom in hidden-order correlated insulators are local high-rank multipole moments of magnetic and charge density, and that intersite couplings among these moments can be computed from electronic structure without free parameters. The pipeline is: define the spin-orbit entangled ground-state multiplet, expand its density matrix in spherical tensor operators, extract intersite exchange from the paramagnetic DFT+Hubbard-I state via the force theorem or from cluster strong-coupling calculations, add Jahn-Teller electron-lattice terms, and solve the resulting many-body effective Hamiltonian by mean-field plus RPA. This reproduces the ferro-oct

Load-bearing premise

The correlated shell must have a fixed integer electron count because Coulomb repulsion suppresses charge fluctuations, and the low-energy physics must live in a well-separated ground-state multiplet with intersite couplings computed in the strong-coupling Hubbard-I limit; if that fails, the multipole expansion and the extracted exchange couplings break down.

Editorial extensions

If this is right

For a given double perovskite or actinide dioxide, the multipolar order——its rank, wavevector, and primary versus slave character——can be predicted before experiment; for example, A2WCl6 is predicted to host ferro-octupolar order.
Dipole-only theories miss the physics: even magnetic orders that look conventional, such as in PrO2 and NdN, carry large high-rank multipolar components and can be driven entirely by non-dipolar exchange.
Electron-lattice coupling must be included in the minimal model: quadrupolar orders are entangled with phonons through Jahn-Teller coupling, so structural and magnetic transitions can have the same origin.
The parameter-free pipeline is restricted to insulating phases where strong-coupling perturbation theory applies; metallic heavy-fermion multipolar systems remain beyond its reach.
Solving these Hamiltonians can generate measurable spectroscopic signatures, such as excitation gaps, neutron scattering intensities, and NMR lineshapes, which are the practical route to identifying hidden order in experiments.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the strong-coupling premise holds, a systematic strain scan of d2 double perovskites should switch between quadrupolar and octupolar ground states; the derived Hamiltonian could be solved under strain to map this phase boundary.
The multipolar defect centres described qualitatively—ions whose ground multiplets carry only quadrupolar and octupolar moments—could be developed as strain or electric-field-gradient sensors, since these moments couple to field gradients rather than magnetic fields.
A direct benchmark with full DFT+DMFT (retaining charge fluctuations) on one or two canonical materials would quantify the error of Hubbard-I-derived exchange couplings and mark where the parameter-free pipeline fails.
The surface and nanoscale regime is a natural test: if quadrupolar order is pinned at broken-symmetry surfaces, surface-sensitive probes should see local multipolar patterns distinct from the bulk phase.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

This is a review, not a new-results paper, and it should be judged on its synthesis. On that score it works: the review gives a genuinely useful map of the methods — force-theorem in Hubbard-I, DFT+U and DMFT, cluster strong-coupling approaches — and shows how each has been applied to specific d- and f-electron compounds. The comparison tables are practical, and the authors are honest about open problems, including the UO2 3q stabilization puzzle and the missing entropy in Ba2MgReO6. The heavy reliance on the authors' own FT-HI results is noticeable, but those results are checked against independent experiments (NpO2, PrO2, Ba2MgReO6), so the self-citation is not by itself a flaw.

The soft spots are real but manageable. The 'Approaches to electron-lattice interactions' section is repeated verbatim, an editorial slip that should be caught. The repeated claim that the methods are 'parameter-free' is not supported: U, JH, and Jahn-Teller couplings are inputs, sometimes fitted. More substantively, the entire strong-coupling framework rests on a well-defined integer occupancy and a well-separated ground-state multiplet, an assumption the review states but never quantifies for the 5d double perovskites that are the flagship examples, where U is only 2–4 eV and the bandwidth is not infinitesimal. The authors acknowledge the strong-coupling picture fails in metallic states, but they do not map where it starts to degrade. A short diagnostic — local occupancy variance or charge-multiplet weights — would strengthen the central claim considerably.

The reader's novelty score struck me as harsh. A review need not contain new equations to be valuable; its job is to consolidate, and this one does that well. The reader and stress-test are right about the load-bearing assumption, though I'd call it a limitation to be flagged, not a fatal flaw.

Who should read it: anyone entering the correlated-electron multipolar field, or a theorist wanting to compare available ab initio methods at a glance. It deserves serious peer review — with a request to fix the duplication and tone down the 'parameter-free' language. I'd accept after minor revisions.

Referee Report

2 major / 4 minor

Summary. This review surveys hidden multipolar order in spin-orbit entangled correlated insulators, with emphasis on ab initio and many-body methods for material-specific modeling. It introduces the ground-state multiplet formalism, multipole expansions, intersite exchange mechanisms, and electron-lattice (Jahn-Teller) couplings; then reviews DFT+U, DFT+DMFT, force-theorem in Hubbard-I, susceptibility-based, and cluster methods; and finally applies these to 5d double perovskites (d1, d2, d3), actinide dioxides, rare-earth mononitrides, heavy-fermion systems, and magnetoelectric materials. The central claim is that recent progress in modeling insulating multipolar phases stems from efficient ab initio methods enabling parameter-free, material-specific descriptions of hidden multipolar orders. The review is broad, generally balanced, and candid about open problems such as the UO2 3q stabilization and the missing entropy in Ba2MgReO6.

Significance. If the reviewed methods are reliable, this review documents a substantial advance in a difficult area: predicting multipolar order parameters and their microscopic mechanisms without resorting to purely model Hamiltonians. The paper is valuable as an up-to-date synthesis, with useful tables (Tables 1-2), figures, and explicit comparisons with experiments. It also honestly flags unsolved issues, which strengthens its credibility. However, the central 'parameter-free' claim is overstated: the methods use Hubbard U and Hund coupling as inputs, and electron-lattice methods require Jahn-Teller couplings and elastic constants. The strong-coupling integer-occupancy assumption underlying the force-theorem and cluster approaches is load-bearing but is not quantitatively assessed for the flagship 5d double perovskites. These issues affect the conclusions, but they are fixable within the scope of a review.

major comments (2)

[Conclusions and Future Perspectives] The statement that progress stems from 'parameter-free, material-specific descriptions' overstates the methods. The Hubbard U (and Hund coupling) for the correlated shell is an input; the text itself quotes U in the 2-4 eV range for double perovskites. Electron-lattice methods require Jahn-Teller couplings g_Gamma and elastic constants. The conclusion should be qualified as, e.g., 'few-parameter' or 'with interaction parameters determined from constrained DFT or empirical fits', and the abstract/introduction should be aligned accordingly.
[The ground-state multiplet and its moments / Force theorem in Hubbard-I] Equation (6) and the cluster perturbation expressions rely on the GSM assumption that charge fluctuations are suppressed and the correlated shell has integer occupancy. For 5d double perovskites, U/W is not very large (U ~ 2-4 eV and t2g bandwidth is comparable), yet no diagnostic such as the local occupancy variance or the weight of N +/- 1 charge multiplets is reported for the materials whose phase diagrams are claimed to be reproduced. The conclusions acknowledge that strong-coupling methods become generally invalid in the metallic state, but the review should also discuss where within the insulating regime the strong-coupling assumption may break down, especially for the d1 and d2 double perovskites used as flagship examples.

minor comments (4)

[Approaches to electron-lattice interactions] The section 'Approaches to electron-lattice interactions' is repeated verbatim twice, with identical equations numbered (8) and (9). The duplicate should be removed and equations renumbered; the later reference to 'equation (9)' in the MBEH-solving section should be updated.
[Figure 5] Figure 5 cross-references are inconsistent: NpO2 is cited in the text as Fig. 5c but the caption labels NpO2 as panel (b); PrO2 is cited as Fig. 5b but the caption labels PrO2 as panel (c); URu2Si2 is cited as Fig. 5e but the caption labels it as panel (d); NdN is cited as Fig. 5d but the caption labels it as panel (e).
[Figure 4] The text refers to 'Figure 4e' for the mean-field ordering energy of d2 double perovskites, but the caption places that panel at (g); the computed NMR spectra are at panel (e), not (g). Please correct these cross-references.
[General] There are several typos, e.g., 'quarupolar' (Box 1), 'quantum chemisty' (electron-lattice section), and 'mutipolar' (f-electron section). A careful proofreading pass is needed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the review's predictions are checked against independent experiments and the method chain is not functionally identical to its inputs.

full rationale

This is a review article rather than a new derivation, and its central claim—that recently formulated ab initio methods enable material-specific descriptions of multipolar order—is supported by comparisons with external experiments (e.g., the two transitions in Ba2MgReO6, the hidden-order structure of NpO2 constrained by NMR and diffraction, and the non-collinear order of PrO2). The force-theorem Hubbard-I formula (Eq. 6) is quoted as derived in prior work and is used to compute intersite exchange matrices from DFT+HI electronic structure; these are then solved and compared to measured properties. I can find no place where a predicted quantity is identical, by construction, to a fitted parameter or to an input of the calculation. The strong-coupling integer-occupancy assumption is stated explicitly as a precondition and limitation of the methods, not as the predicted outcome; an assumption that restricts validity is not circular. Self-citations are frequent because the authors developed several of the reviewed methods, but the load-bearing validation is experimental and includes independent theoretical approaches; no specific reduction to a self-citation chain is exhibited. Any concern about the magnitude of charge fluctuations or the meaning of 'parameter-free' is a correctness or overclaim issue, not circularity.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

This review introduces no new free parameters or entities. However, its central thesis relies on strong-coupling assumptions (large U, GSM projection) and on fitted model parameters in the underlying ab initio methods, which are inputs from prior literature rather than outputs of this paper.

free parameters (2)

Hubbard U (and Hund coupling J_H) for correlated shell = material-dependent, typically 2-4 eV in double perovskites; from cRPA or fitted to spectra
The reviewed methods (DFT+U, DFT+DMFT, DFT+HI, FT-HI) require these as inputs; the review's claim of 'parameter-free' methods is weakened because U and J_H are not derived within the paper and vary by material.
Jahn-Teller coupling constants g_Gamma and elastic constants = numbers obtained by fitting DFT/quantum-chemistry potential-energy surfaces to the Jahn-Teller Hamiltonian
In the section 'Approaches to electron-lattice interactions', the couplings are extracted from fits of total energy vs distortion amplitude, i.e., fitted parameters.

assumptions (4)

domain assumption The correlated shell has a well-defined integer occupancy and a well-separated ground-state multiplet; charge fluctuations are suppressed by large U.
Section 'The ground-state multiplet and its moments', Eq. (1) and surrounding text; this is the basis for the multipole expansion and MBEH.
domain assumption The force theorem in the Hubbard-I approximation reproduces the lowest-order in hopping/U superexchange and is valid in Mott insulating phases.
Section 'Force theorem in Hubbard-I', text after Eq. (6): 'Its applicability is limited to Mott insulating phases, where the FT-HI formula ... reproduces the lowest-order in hopping/U contribution to superexchange.' This limits the scope to insulators.
domain assumption Mean-field decoupling of the MBEH is adequate to identify ordered phases; transition temperatures are overestimated by roughly factor two.
Section 'Solving the many-body effective Hamiltonian and calculating properties': 'the mean-field approximation leads to a systematic overestimation of transition temperatures... overestimation by about a factor of two was observed.' This is an accepted approximation with known error.
domain assumption The multipole expansion is complete within the GSM and coupling to states outside the GSM is perturbative.
Implicit in the projection onto the GSM throughout the methods section; states outside GSM are treated in second-order perturbation for kinetic exchange.

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Cite this review

Pith. "Pith review of Hidden orders in spin-orbit entangled correlated insulators." pith.science (2026). https://pith.science/paper/6G6LDLJR

@misc{pith2026250901788,
  author       = {Pith},
  title        = {Pith review of: Hidden orders in spin-orbit entangled correlated insulators},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6G6LDLJR}},
  note         = {Machine review of arXiv:2509.01788}
}

read the original abstract

In many materials, ordered phases and their order parameters are easily characterized by standard experimental methods. "Hidden order" refers to a phase transition in which an ordered state emerges without such an easily detectable order parameter, despite clear thermodynamic evidence of the transition. The underlying mechanisms for these unconventional states of matter stem from spin-orbit coupling, which intertwines inter-site exchange, classical electron-magnetic interactions, and electron-lattice effects. This physics is elusive to experimental probes and beyond traditional theories of insulating magnetism, requiring sophisticated methodologies for its exploration. In this Review, we survey exotic hidden-order phases in correlated insulators, particularly focusing on the latest progress in material-specific theories and numerical approaches. The relevant degrees of freedom in these phases are local high-rank multipole moments of magnetic and charge density that emerge from spin-orbit entangled correlated shells of heavy d and f electron ions and interact on the lattice via various mechanisms. We discuss approaches to modelling hidden orders in realistic systems via direct ab initio calculations or by constructing low-energy many-body effective Hamiltonian. We also describe how these new theoretical tools have helped to uncover driving mechanisms for recently discovered multipolar phases in double perovskites of heavy transition metals, and how they have proved instrumental in disentangling the role of various interactions in "traditional" f-electron multipolar materials like actinide dioxides. In both cases, material-specific theories have played a key role in interpreting and predicting experimental signatures of hidden orders.

Figures

Figures reproduced from arXiv: 2509.01788 by the authors.

**Figure 1.** Spin-orbit entangled phenomena. Interplay of spin-orbit coupling with band and correlation effects induces unusual interactions (left side), which, in turn, generate unconventional phenomena (right side), including hidden multipolar orders. Characteristic energy scales and key families of materials hosting hidden orders are listed for d- and f-electron systems. Representative multipolar order parameters are shown fo… view at source ↗

**Figure 2.** Levels structure, ground state multiplets and hopping paths in d 1 and d 2 spin-orbit double perovskites. (a) The conventional unit cell of A2BB′O6 cubic double perovskites. (b) The level splitting on the d 1 and d 2 shells of magnetic B ′ sites due to the octahedral crystal field and spin-orbit coupling. Electron density distribution for the ground-state multiplet orbitals is shown after Ref.190, the spin-up/spin-d… view at source ↗

**Figure 3.** Intersite exchange interaction (IEI) matrices for three Jeff=3/2 SO insulators calculated by the force theorem in Hubbard-I (FT-HI) method. Left. The d3 double perovskite (DP) Ba2YOsO6. In this case there is no spin-orbit entanglement within the Jeff=3/2 ground state (GS), and the dominating IEI are antiferroic dipole-dipole Heisenberg terms as expected for a pure spin-3/2 system. Perturbative admixture of excited m… view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Multipolar properties of d-electron systems computed with different methods a | Energy as a function of the canting angle for the 5d1 double perovskite (DP) Ba2NaOsO6 in the Jahn-Teller (JT) distorted phase with constrained DFT + U65 (left panel); graphical representat…

**Figure 5.** Figure 5: Multipolar orders of f-electron systems computed with different methods a | Total energy of UO2 vs magnetic canting angle along the 1k antiferromagnetic (AFM) ⟨001⟩ → 3k AFM → 1k AFM ⟨110⟩ transformation pathway calculated by constained DFT+U204. Inset shows 3k quadrup…

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Works this paper leans on

297 extracted references · 169 canonical work pages

[1]

Landau, L. D. & Lifshitz, E. M. Quantum Mechanics: Non-relativistic Theory (Pergamon Press, Oxford, 1965)

1965
[2]

Khomskii, D. I. Transition Metal Compounds (Cambridge University Press, Cambridge, 2014)

2014
[3]

Properties of semiconductors with an extremum loop

Rashba, E. Properties of semiconductors with an extremum loop. i. cyclotron and combinational resonance in a magnetic field perpendicular to the plane of the loop. Sov. Phys.-Solid State 2, 1109 (1960)

1960
[4]

V ., Chulkov, E

Bihlmayer, G., Noël, P., Vyalikh, D. V ., Chulkov, E. V . & Manchon, A. Rashba-like physics in condensed matter. Nat. Rev. Phys. 4, 642–659, DOI: 10.1038/s42254-022-00490-y (2022)

doi:10.1038/s42254-022-00490-y 2022
[5]

Hirsch, J. E. Spin hall effect. Phys. Rev. Lett. 83, 1834 (1999). 26/45

1999
[6]

Maciejko, J., Hughes, T. L. & Zhang, S.-C. The quantum spin hall effect. Annu. Rev. Condens. Matter Phys. 2, 31–53, DOI: https://doi.org/10.1146/annurev-conmatphys-062910-140538 (2011)

work page doi:10.1146/annurev-conmatphys-062910-140538 2011
[7]

& Cros, V

Fert, A., Reyren, N. & Cros, V . Magnetic skyrmions: Advances in physics and potential applications. Nat. Rev. Mater .2, 17031 (2017)

2017
[8]

Mott, N. F. & Peierls, R. Discussion of the paper by de boer and verwey. Proc. Phys. Soc. 49, 72, DOI: 10.1088/0959-5309/49/4S/308 (1937)

work page doi:10.1088/0959-5309/49/4s/308 1937

Show all 297 references

[9]

Mott, N. F. The basis of the electron theory of metals, with special reference to the transition metals. Proc. Phys. Soc. A 62, 416, DOI: 10.1088/0370-1298/62/7/303 (1949)

1949 doi
[10]

& Tokura, Y

Imada, M., Fujimori, A. & Tokura, Y . Metal-insulator transitions. Rev. Mod. Phys. 70, 1039–1263, DOI: 10.1103/RevModPhys.70.1039 (1998)

1998 doi
[11]

Morosan, E., Natelson, D., Nevidomskyy, A. H. & Si, Q. Strongly correlated materials. Adv. Mater. 24, 4896–4923, DOI: https://doi.org/10.1002/adma.201202018 (2012). https://onlinelibrary.wiley.com/doi/pdf/10. 1002/adma.201202018

2012 doi
[12]

Witczak-Krempa, W., Chen, G., Kim, Y . B. & Balents, L. Correlated quantum phenomena in the strong spin-orbit regime. Annu. Rev. Condens. Matter Phys. 5, 57–82, DOI: https://doi.org/10.1146/ annurev-conmatphys-020911-125138 (2014)

2014
[13]

Orbital Order and Fluctuations in Mott Insulators

Khaliullin, G. Orbital Order and Fluctuations in Mott Insulators. Prog. Theor. Phys. Suppl. 160, 155–202, DOI: 10.1143/PTPS.160.155 (2005). https://academic.oup.com/ptps/article-pdf/doi/10.1143/PTPS.160.155/ 5162453/160-155.pdf

2005 doi
[14]

G., Lee, E

Rau, J. G., Lee, E. K.-H. & Kee, H.-Y . Spin-orbit physics giving rise to novel phases in correlated systems: Iridates and related materials. Annu. Rev. Condens. Matter Phys. 7, 195–221, DOI: https://doi.org/10.1146/ annurev-conmatphys-031115-011319 (2016)

2016
[15]

K.-H., Yang, B.-J

Schaffer, R., Lee, E. K.-H., Yang, B.-J. & Kim, Y . B. Recent progress on correlated electron systems with strong spin–orbit coupling. Reports on Prog. Phys. 79, 094504, DOI: 10.1088/0034-4885/79/9/094504 (2016)

2016 doi
[16]

& Takagi, H

Takayama, T., Chaloupka, J., Smerald, A., Khaliullin, G. & Takagi, H. Spin–orbit-entangled electronic phases in 4d and 5d transition-metal compounds. J. Phys. Soc. Jpn. 90, 062001, DOI: 10.7566/JPSJ.90.062001 (2021). https://doi.org/10.7566/JPSJ.90.062001

2021 doi
[17]

Khomskii, D. I. & Streltsov, S. V . Orbital effects in solids: Basics, recent progress, and opportunities.Chem. Rev. 121, 2992–3030, DOI: 10.1021/acs.chemrev.0c00579 (2021). PMID: 33314912, https://doi.org/10.1021/ acs.chemrev.0c00579

2021 doi
[18]

J., Krajewska, A

Browne, A. J., Krajewska, A. & Gibbs, A. S. Quantum materials with strong spin–orbit coupling: challenges and opportunities for materials chemists. J. Mater . Chem. C9, 11640–11654, DOI: 10.1039/D1TC02070F (2021)

2021 doi
[19]

& Khaliullin, G

Jackeli, G. & Khaliullin, G. Mott insulators in the strong spin-orbit coupling limit: From heisenberg to a quantum compass and kitaev models. Phys. Rev. Lett. 102, 017205, DOI: 10.1103/PhysRevLett.102.017205 (2009)

2009 doi
[20]

Calder, S. et al. Magnetically driven metal-insulator transition in naoso3. Phys. Rev. Lett. 108, 257209, DOI: 10.1103/PhysRevLett.108.257209 (2012)

2012 doi
[21]

Kim, B. et al. Lifshitz transition driven by spin fluctuations and spin-orbit renormalization in naoso3. Phys. Rev. B 94, 241113, DOI: 10.1103/PhysRevB.94.241113 (2016)

2016 doi
[22]

Spin liquids in frustrated magnets

Balents, L. Spin liquids in frustrated magnets. Nature 464, 199–208, DOI: 10.1038/nature08917 (2010)

2010 doi
[23]

A., Mclaughlin, A

de Vries, M. A., Mclaughlin, A. C. & Bos, J.-W. G. Valence bond glass on an fcc lattice in the double perovskite ba2ymoo6. Phys. Rev. Lett. 104, 177202, DOI: 10.1103/PhysRevLett.104.177202 (2010). 27/45

2010 doi
[24]

& Obata, Y

Sasaki, K. & Obata, Y . Studies of the dynamical jahn-teller effect on static magnetic susceptibility.J. Phys. Soc. Jpn. 28, 1157–1167, DOI: 10.1143/JPSJ.28.1157 (1970). https://doi.org/10.1143/JPSJ.28.1157

1970 doi
[25]

Heinze, S. et al. Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions. Nat. Phys. 7, 713–718, DOI: 10.1038/nphys2045 (2011)

2011 doi
[26]

Everschor-Sitte, K., Masell, J., Reeve, R. M. & Kläui, M. Perspective: Magnetic skyrmions—overview of recent progress in an active research field. J. Appl. Phys. 124, 240901, DOI: 10.1063/1.5048972 (2018). https://pubs.aip.org/aip/jap/article-pdf/doi/10.1063/1.5048972/19981128...

2018 doi
[27]

Dzialoshinskii, I. E. Sov. phys. jetp. Sov. Phys. JETP 5, 1259 (1957)

1957
[28]

New mechanism of anisotropic superexchange interaction

Moriya, T. New mechanism of anisotropic superexchange interaction. Phys. Rev. Lett. 4, 228–230, DOI: 10.1103/PhysRevLett.4.228 (1960)

1960 doi
[29]

Morrish, A. H. Canted Antiferromagnetism: Hematite (World Scientific, 1994)

1994
[30]

& Balents, L

Pesin, D. & Balents, L. Mott physics and band topology in materials with strong spin–orbit interaction. Nat. Phys. 6, 376–381, DOI: 10.1038/nphys1606 (2010)

2010 doi
[31]

Celiberti, L. et al. Spin-orbital jahn-teller bipolarons. Nat. Commun. 15, 2429, DOI: 10.1038/ s41467-024-46621-0 (2024)

2024
[32]

& Franchini, C

Fiore Mosca, D., Schnait, H., Celiberti, L., Aichhorn, M. & Franchini, C. The mott transition in the 5d1 compound ba2naoso6: A dft+dmft study with paw spinor projectors. Comput. Mater. Sci. 233, 112764, DOI: https://doi.org/10.1016/j.commatsci.2023.112764 (2024)

2023
[33]

& Paramekanti, A

Hart, K., Sutcliffe, R., Refael, G. & Paramekanti, A. Phonon-driven multipolar dynamics in spin-orbit coupled mott insulators (2024). 2404.17633

2024 arXiv
[34]

& Pourovskii, L

Khmelevskyi, S. & Pourovskii, L. V . Non-collinear magnetism driven by a hidden multipolar order in pro2. Commun. Phys. 7, 12, DOI: 10.1038/s42005-023-01503-7 (2024)

2024 doi
[35]

Soh, J.-R. et al. Spectroscopic signatures and origin of hidden order in Ba2MgReO6. Nat. Commun. 15, 10383, DOI: 10.1038/s41467-024-53893-z (2024)

2024 doi
[36]

Yahne, D. R. et al. Dipolar spin ice regime proximate to an all-in-all-out néel ground state in the dipolar- octupolar pyrochlore ce2sn2o7. Phys. Rev. X 14, 011005, DOI: 10.1103/PhysRevX.14.011005 (2024)

2024 doi
[37]

& Mydosh, J

Shah, N., Chandra, P., Coleman, P. & Mydosh, J. A. Hidden order in uru2si2. Phys. Rev. B 61, 564–569, DOI: 10.1103/PhysRevB.61.564 (2000)

2000 doi
[38]

Amitsuka, H. et al. Hidden order and weak antiferromagnetism in uru2si2. Phys. B: Condens. Matter 312-313, 390–396, DOI: https://doi.org/10.1016/S0921-4526(01)01343-6 (2002). The International Conference on Strongly Correlated Electron Systems

2002 doi
[39]

Chandra, P., lian, P., Mydosh, J. A. & Tripathi, V . Hidden orbital order in the heavy fermion metal uru2si2. Nature 417, 831–834, DOI: 10.1038/nature00795 (2002)

2002 doi
[40]

& Nordström, L

Cricchio, F., Bultmark, F., Grånäs, O. & Nordström, L. Itinerant magnetic multipole moments of rank five as the hidden order in uru2si2. Phys. Rev. Lett. 103, 107202, DOI: 10.1103/PhysRevLett.103.107202 (2009)

2009 doi
[41]

& Khaliullin, G

Jackeli, G. & Khaliullin, G. Magnetically hidden order of kramers doublets in d1 systems: sr2vo4. Phys. Rev. Lett. 103, 067205, DOI: 10.1103/PhysRevLett.103.067205 (2009)

2009 doi
[42]

& Balents, L

Chen, G., Pereira, R. & Balents, L. Exotic phases induced by strong spin-orbit coupling in ordered double perovskites. Phys. Rev. B 82, 174440, DOI: 10.1103/PhysRevB.82.174440 (2010)

2010 doi
[43]

S., Gingras, M

Gardner, J. S., Gingras, M. J. P. & Greedan, J. E. Magnetic pyrochlore oxides. Rev. Mod. Phys. 82, 53–107, DOI: 10.1103/RevModPhys.82.53 (2010)

2010 doi
[44]

Mydosh, J. A. & Oppeneer, P. M. Colloquium: Hidden order, superconductivity, and magnetism: The unsolved case of uru2si2. Rev. Mod. Phys. 83, 1301–1322, DOI: 10.1103/RevModPhys.83.1301 (2011). 28/45

2011 doi
[45]

Tsirlin, A. A. et al. Hidden magnetic order in cuncn. Phys. Rev. B 85, 224431, DOI: 10.1103/PhysRevB.85. 224431 (2012)

2012 doi
[47]

Sugiyama, J. et al. Hidden magnetic order in sr 2vo4 clarified with µ +sr. Phys. Rev. B 89, 020402, DOI: 10.1103/PhysRevB.89.020402 (2014)

2014 doi
[48]

& Hermele, M

Huang, Y .-P., Chen, G. & Hermele, M. Quantum spin ices and topological phases from dipolar-octupolar doublets on the pyrochlore lattice. Phys. Rev. Lett. 112, 167203, DOI: 10.1103/PhysRevLett.112.167203 (2014)

2014 doi
[49]

Zhao, L. et al. Evidence of an odd-parity hidden order in a spin–orbit coupled correlated iridate. Nat. Phys. 12, 32–36, DOI: 10.1038/nphys3517 (2016)

2016 doi
[50]

S., Friemel, G

Cameron, A. S., Friemel, G. & Inosov, D. S. Multipolar phases and magnetically hidden order: review of the heavy-fermion compound ce1−xlaxb6. Reports on Prog. Phys. 79, 066502, DOI: 10.1088/0034-4885/79/6/ 066502 (2016)

2016 doi
[51]

& Chen, G

Li, Y .-D., Wang, X. & Chen, G. Hidden multipolar orders of dipole-octupole doublets on a triangular lattice. Phys. Rev. B 94, 201114, DOI: 10.1103/PhysRevB.94.201114 (2016)

2016 doi
[52]

Lu, L. et al. Magnetism and local symmetry breaking in a mott insulator with strong spin orbit interactions. Nat. Commun. 8, 14407, DOI: 10.1038/ncomms14407 (2017)

2017 doi
[53]

& Chen, G

Li, Y .-D. & Chen, G. Symmetry enriched u(1) topological orders for dipole-octupole doublets on a pyrochlore lattice. Phys. Rev. B 95, 041106, DOI: 10.1103/PhysRevB.95.041106 (2017)

2017 doi
[54]

& Franchini, C

Kim, B., Khmelevskyi, S., Mohn, P. & Franchini, C. Competing magnetic interactions in a spin- 1 2 square lattice: Hidden order in sr2vo4. Phys. Rev. B 96, 180405, DOI: 10.1103/PhysRevB.96.180405 (2017)

2017 doi
[55]

& Chen, G

Liu, C., Li, Y .-D. & Chen, G. Selective measurements of intertwined multipolar orders: Non-kramers doublets on a triangular lattice. Phys. Rev. B 98, 045119, DOI: 10.1103/PhysRevB.98.045119 (2018)

2018 doi
[56]

Ishikawa, H. et al. Ordering of hidden multipoles in spin-orbit entangled 5d1 ta chlorides. Phys. Rev. B 100, 045142, DOI: 10.1103/PhysRevB.100.045142 (2019)

2019 doi
[57]

Gaudet, J. et al. Quantum spin ice dynamics in the dipole-octupole pyrochlore magnet ce2zr2o7. Phys. Rev. Lett. 122, 187201, DOI: 10.1103/PhysRevLett.122.187201 (2019)

2019 doi
[58]

Intertwined dipolar and multipolar order in the triangular-lattice magnet tmmggao4

Shen, Y .et al. Intertwined dipolar and multipolar order in the triangular-lattice magnet tmmggao4. Nat. Commun. 10, 4530, DOI: 10.1038/s41467-019-12410-3 (2019)

2019 doi
[59]

Rau, J. G. & Gingras, M. J. Frustrated quantum rare-earth pyrochlores. Annu. Rev. Condens. Matter Phys. 10, 357–386, DOI: https://doi.org/10.1146/annurev-conmatphys-022317-110520 (2019)

2019 doi
[60]

Hirai, D. et al. Detection of multipolar orders in the spin-orbit-coupled 5d mott insulator Ba2MgReo6. Phys. Rev. Res. 2, 022063, DOI: 10.1103/PhysRevResearch.2.022063 (2020)

2020 doi
[61]

V ., Rønnow, H

Aeppli, G., Balatsky, A. V ., Rønnow, H. M. & Spaldin, N. A. Hidden, entangled and resonating order.Nat. Rev. Mater. 5, 477–479, DOI: 10.1038/s41578-020-0207-z (2020)

2020 doi
[62]

Zvereva, E. A. et al. Hidden magnetic order in the triangular-lattice magnet li2mnteo6. Phys. Rev. B 102, 094433, DOI: 10.1103/PhysRevB.102.094433 (2020)

2020 doi
[63]

Maharaj, D. D. et al. Octupolar versus néel order in cubic5d2 double perovskites. Phys. Rev. Lett. 124, 087206, DOI: 10.1103/PhysRevLett.124.087206 (2020)

2020 doi
[64]

Sibille, R. et al. A quantum liquid of magnetic octupoles on the pyrochlore lattice. Nat. Phys. 16, 546–552, DOI: 10.1038/s41567-020-0827-7 (2020). 29/45

2020 doi
[65]

Fiore Mosca, D. et al. Interplay between multipolar spin interactions, jahn-teller effect, and electronic correlation in a Jeff = 3 2 insulator. Phys. Rev. B 103, 104401, DOI: 10.1103/PhysRevB.103.104401 (2021)

2021 doi
[66]

V ., Mosca, D

Pourovskii, L. V ., Mosca, D. F. & Franchini, C. Ferro-octupolar order and low-energy excitations ind2 double perovskites of osmium. Phys. Rev. Lett. 127, 237201, DOI: 10.1103/PhysRevLett.127.237201 (2021)

2021 doi
[67]

Pourovskii, L. V . & Khmelevskyi, S. Hidden order and multipolar exchange striction in a correlated f- electron system. Proc. Natl. Acad. Sci. 118, e2025317118, DOI: 10.1073/pnas.2025317118 (2021). https: //www.pnas.org/doi/pdf/10.1073/pnas.2025317118

2021 doi
[68]

Smith, E. M. et al. Case for a u(1)π quantum spin liquid ground state in the dipole-octupole pyrochlore ce2zr2o7. Phys. Rev. X 12, 021015, DOI: 10.1103/PhysRevX.12.021015 (2022)

2022 doi
[69]

Distinguishing thermodynamics and spectroscopy for octupolar u(1) spin liquid of ce pyrochlores

Chen, G. Distinguishing thermodynamics and spectroscopy for octupolar u(1) spin liquid of ce pyrochlores. Phys. Rev. Res. 5, 033169, DOI: 10.1103/PhysRevResearch.5.033169 (2023)

2023 doi
[70]

& Paramekanti, A

V oleti, S., Pradhan, K., Bhattacharjee, S., Saha-Dasgupta, T. & Paramekanti, A. Probing octupolar hidden order via janus impurities. npj Quantum Mater. 8, 42, DOI: 10.1038/s41535-023-00575-6 (2023)

2023 doi
[71]

H., Urru, A

Verbeek, X. H., Urru, A. & Spaldin, N. A. Hidden orders and (anti-)magnetoelectric effects in cr2o3 and α−fe2o3. Phys. Rev. Res. 5, L042018, DOI: 10.1103/PhysRevResearch.5.L042018 (2023)

2023 doi
[72]

Szilva, A. et al. Quantitative theory of magnetic interactions in solids. Rev. Mod. Phys. 95, 035004, DOI: 10.1103/RevModPhys.95.035004 (2023)

2023 doi
[73]

Santini, P. et al. Multipolar interactions in f -electron systems: The paradigm of actinide dioxides. Rev. Mod. Phys. 81, 807–863, DOI: 10.1103/RevModPhys.81.807 (2009)

2009 doi
[74]

& Nordström, L

Bultmark, F., Cricchio, F., Grånäs, O. & Nordström, L. Multipole decomposition of LDA+ u energy and its application to actinide compounds. Phys. Rev. B 80, 035121, DOI: 10.1103/PhysRevB.80.035121 (2009)

2009 doi
[75]

Pourovskii, L. V . Two-site fluctuations and multipolar intersite exchange interactions in strongly correlated systems. Phys. Rev. B 94, 115117, DOI: 10.1103/PhysRevB.94.115117 (2016)

2016 doi
[76]

& Savrasov, S

Pi, S.-T., Nanguneri, R. & Savrasov, S. Calculation of multipolar exchange interactions in spin-orbital coupled systems. Phys. Rev. Lett. 112, 077203, DOI: 10.1103/PhysRevLett.112.077203 (2014)

2014 doi
[77]

& Savrasov, S

Pi, S.-T., Nanguneri, R. & Savrasov, S. Anisotropic multipolar exchange interactions in systems with strong spin-orbit coupling. Phys. Rev. B 90, 045148, DOI: 10.1103/PhysRevB.90.045148 (2014)

2014 doi
[78]

Fiore Mosca, D., Pourovskii, L. V . & Franchini, C. Modeling magnetic multipolar phases in density functional theory. Phys. Rev. B 106, 035127, DOI: 10.1103/PhysRevB.106.035127 (2022)

2022 doi
[79]

E., Tehrani, A

Schaufelberger, L., Merkel, M. E., Tehrani, A. M., Spaldin, N. A. & Ederer, C. Exploring energy landscapes of charge multipoles using constrained density functional theory. Phys. Rev. Res. 5, 033172, DOI: 10.1103/ PhysRevResearch.5.033172 (2023)

2023
[80]

Kimata, M. et al. X-ray study of ferroic octupole order producing anomalous hall effect. Nat. Commun. 12, 5582, DOI: 10.1038/s41467-021-25834-7 (2021)

2021 doi
[81]

F., McEwen, K

McMorrow, D. F., McEwen, K. A., Steigenberger, U., Rønnow, H. M. & Yakhou, F. X-ray resonant scattering study of the quadrupolar order in upd3. Phys. Rev. Lett. 87, 057201, DOI: 10.1103/PhysRevLett.87.057201 (2001)

2001 doi
[82]

& Caciuffo, R

Santini, P., Carretta, S., Magnani, N., Amoretti, G. & Caciuffo, R. Hidden order and low-energy excitations in npo2. Phys. Rev. Lett. 97, 207203, DOI: 10.1103/PhysRevLett.97.207203 (2006)

2006 doi
[83]

Magnani, N. et al. Inelastic neutron scattering study of the multipolar order parameter in npo2. Phys. Rev. B 78, 104425, DOI: 10.1103/PhysRevB.78.104425 (2008)

2008 doi
[84]

& Karppinen, M

Vasala, S. & Karppinen, M. A2bbo6 perovskites: A review. Prog. Solid State Chem. 43, 1–36, DOI: https://doi.org/10.1016/j.progsolidstchem.2014.08.001 (2015). 30/45

2014 doi
[85]

Chen, J., Feng, H. L. & Yamaura, K. Review of progress in the materials development of re, os, and ir-based double perovskite oxides. Mater. Today Phys. 40, 101302, DOI: https://doi.org/10.1016/j.mtphys.2023.101302 (2024)

2023
[86]

& Chibotaru, L

Iwahara, N., Huang, Z., Neefjes, I. & Chibotaru, L. F. Multipolar exchange interaction and complex order in insulating lanthanides. Phys. Rev. B 105, 144401, DOI: 10.1103/PhysRevB.105.144401 (2022)

2022 doi
[87]

Ning, H. et al. A coherent phonon-induced hidden quadrupolar ordered state in ca2ruo4. Nat. Commun. 14, 8258, DOI: 10.1038/s41467-023-44021-4 (2023)

2023 doi
[88]

The Jahn-Teller Effect (Cambridge University Press, Cambridge, 2006)

Bersuker, I. The Jahn-Teller Effect (Cambridge University Press, Cambridge, 2006)

2006
[89]

& Chibotaru, L

Iwahara, N. & Chibotaru, L. F. Vibronic order and emergent magnetism in cubic d1 double perovskites. Phys. Rev. B 107, L220404, DOI: 10.1103/PhysRevB.107.L220404 (2023)

2023 doi
[90]

& Pourovskii, L

Fiore Mosca, D., Franchini, C. & Pourovskii, L. V . Interplay of superexchange and vibronic effects in the hidden order of ba2mgreo6 from first principles. Phys. Rev. B 110, L201101, DOI: 10.1103/PhysRevB.110.L201101 (2024)

2024 doi
[91]

A., Fiebig, M

Spaldin, N. A., Fiebig, M. & Mostovoy, M. The toroidal moment in condensed-matter physics and its relation to the magnetoelectric effect. J. Physics: Condens. Matter 20, 434203, DOI: 10.1088/0953-8984/20/43/434203 (2008)

2008 doi
[92]

& Jungwirth, T

Šmejkal, L., Sinova, J. & Jungwirth, T. Emerging research landscape of altermagnetism. Phys. Rev. X 12, 040501, DOI: 10.1103/PhysRevX.12.040501 (2022)

2022 doi
[93]

M., Sinova, J

Jungwirth, T., Fernandes, R. M., Sinova, J. & Smejkal, L. Altermagnets and beyond: Nodal magnetically- ordered phases (2024). 2409.10034

2024 arXiv
[94]

& Spaldin, N

Ederer, C. & Spaldin, N. A. Towards a microscopic theory of toroidal moments in bulk periodic crystals. Phys. Rev. B 76, 214404, DOI: 10.1103/PhysRevB.76.214404 (2007)

2007 doi
[95]

& Motome, Y

Hayami, S., Yanagi, Y ., Kusunose, H. & Motome, Y . Electric toroidal quadrupoles in the spin-orbit-coupled metal cd2re2o7. Phys. Rev. Lett. 122, 147602, DOI: 10.1103/PhysRevLett.122.147602 (2019)

2019 doi
[96]

& Hayami, S

Yatsushiro, M., Kusunose, H. & Hayami, S. Multipole classification in 122 magnetic point groups for unified understanding of multiferroic responses and transport phenomena. Phys. Rev. B 104, 054412, DOI: 10.1103/PhysRevB.104.054412 (2021)

2021 doi
[97]

& Spaldin, N

Bhowal, S. & Spaldin, N. A. Ferroically ordered magnetic octupoles in d-wave altermagnets. Phys. Rev. X 14, 011019, DOI: 10.1103/PhysRevX.14.011019 (2024)

2024 doi
[98]

A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics

Dzyaloshinsky, I. A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids 4, 241–255, DOI: https://doi.org/10.1016/0022-3697(58)90076-3 (1958)

1958 doi
[99]

Anisotropic superexchange interaction and weak ferromagnetism

Moriya, T. Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120, 91–98, DOI: 10.1103/PhysRev.120.91 (1960)

1960 doi
[100]

& Watanabe, H

Takeda, T., Yamaguchi, Y . & Watanabe, H. Magnetic structure of srfeo3.J. Phys. Soc. Jpn. 33, 967–969, DOI: 10.1143/JPSJ.33.967 (1972). https://doi.org/10.1143/JPSJ.33.967

1972 doi
[101]

Liu, P. et al. Anisotropic magnetic couplings and structure-driven canted to collinear transitions in sr2iro4 by magnetically constrained noncollinear dft. Phys. Rev. B 92, 054428, DOI: 10.1103/PhysRevB.92.054428 (2015)

2015 doi
[102]

& Kanazawa, N

Tokura, Y . & Kanazawa, N. Magnetic skyrmion materials.Chem. Rev. 121, 2857–2897, DOI: 10.1021/acs. chemrev.0c00297 (2021). PMID: 33164494, https://doi.org/10.1021/acs.chemrev.0c00297

2021 doi
[103]

& Bellaiche, L

Xu, C., Xu, B., Dupé, B. & Bellaiche, L. Magnetic interactions in bifeo3: A first-principles study. Phys. Rev. B 99, 104420, DOI: 10.1103/PhysRevB.99.104420 (2019). 31/45

2019 doi
[104]

& Cui, Q

Yang, H., Liang, J. & Cui, Q. First-principles calculations for dzyaloshinskii–moriya interaction. Nat. Rev. Phys. 5, 43–61, DOI: 10.1038/s42254-022-00529-0 (2023)

2023 doi
[105]

& Yang, H

Fert, A., Chshiev, M., Thiaville, A. & Yang, H. From early theories of dzyaloshinskii–moriya interactions in metallic systems to today’s novel roads. J. Phys. Soc. Jpn. 92, 081001, DOI: 10.7566/JPSJ.92.081001 (2023). https://doi.org/10.7566/JPSJ.92.081001

2023 doi
[106]

& Das Sarma, S

Pan, H., Wu, F. & Das Sarma, S. Band topology, hubbard model, heisenberg model, and dzyaloshinskii-moriya interaction in twisted bilayer wse2. Phys. Rev. Res. 2, 033087, DOI: 10.1103/PhysRevResearch.2.033087 (2020)

2020 doi
[107]

& Blügel, S

Heide, M., Bihlmayer, G. & Blügel, S. Describing dzyaloshinskii–moriya spirals from first principles. Phys. B: Condens. Matter 404, 2678–2683, DOI: https://doi.org/10.1016/j.physb.2009.06.070 (2009)

2009 doi
[108]

Dzyaloshinskii–moriya coupling in 3d insulators

Moskvin, A. Dzyaloshinskii–moriya coupling in 3d insulators. Condens. Matter 4, DOI: 10.3390/ condmat4040084 (2019)

2019
[109]

Kuepferling, M. et al. Measuring interfacial dzyaloshinskii-moriya interaction in ultrathin magnetic films. Rev. Mod. Phys. 95, 015003, DOI: 10.1103/RevModPhys.95.015003 (2023)

2023 doi
[110]

Camley, R. E. & Livesey, K. L. Consequences of the dzyaloshinskii-moriya interaction. Surf. Sci. Reports 78, 100605, DOI: https://doi.org/10.1016/j.surfrep.2023.100605 (2023)

2023
[111]

Low moments in heavy-fermion systems

Buyers, W. Low moments in heavy-fermion systems. Phys. B: Condens. Matter 223-224, 9–14, DOI: https://doi.org/10.1016/0921-4526(96)00027-0 (1996). Proceedings of the International Conference on Strongly Correlated Electron Systems

1996 doi
[112]

Erkelens, W. et al. Neutron scattering study of the antiferroquadrupolar ordering in ceb6 and ce0.75la0.25b6. J. Magn. Magn. Mater. 63-64, 61–63, DOI: https://doi.org/10.1016/0304-8853(87)90522-1 (1987)

1987 doi
[113]

& Thalmeier, P

Shiina, R., Shiba, H. & Thalmeier, P. Magnetic-field effects on quadrupolar ordering in aγ 8-quartet system ceb
[114]

J. Phys. Soc. Jpn. 66, 1741–1755, DOI: 10.1143/JPSJ.66.1741 (1997). https://doi.org/10.1143/JPSJ.66.1741

1997 doi
[115]

& Ishikawa, M

Kitagawa, J., Takeda, N. & Ishikawa, M. Possible quadrupolar ordering in a kondo-lattice compound ce3pd20ge6. Phys. Rev. B 53, 5101–5103, DOI: 10.1103/PhysRevB.53.5101 (1996)

1996 doi
[116]

Antiferro-quadrupolar ordering and multipole interactions in prpb 3

Tayama, T.et al. Antiferro-quadrupolar ordering and multipole interactions in prpb 3. J. Phys. Soc. Jpn. 70, 248–258, DOI: 10.1143/JPSJ.70.248 (2001). https://doi.org/10.1143/JPSJ.70.248

2001 doi
[117]

Suzuki, H., Takagi, S., Onodera, H

Tanida, H., S. Suzuki, H., Takagi, S., Onodera, H. & Tanigaki, K. Possible low-temperature strongly correlated electron behavior from multipole fluctuations in prmg3 with cubic non-kramers γ3 doublet ground state. J. Phys. Soc. Jpn. 75, 073705, DOI: 10.1143/JPSJ.75.073705 (200...

2006 doi
[118]

& Khaliullin, G

Liu, H. & Khaliullin, G. Pseudo-jahn-teller effect and magnetoelastic coupling in spin-orbit mott insulators. Phys. Rev. Lett. 122, 057203, DOI: 10.1103/PhysRevLett.122.057203 (2019)

2019 doi
[119]

& Oppeneer, P

Suzuki, M.-T., Ikeda, H. & Oppeneer, P. M. First-principles theory of magnetic multipoles in condensed matter systems. J. Phys. Soc. Jpn. 87, 041008, DOI: 10.7566/JPSJ.87.041008 (2018). https://doi.org/10.7566/JPSJ. 87.041008

2018 doi
[120]

& Spaldin, N

Thöle, F. & Spaldin, N. A. Magnetoelectric multipoles in metals. Philos. Transactions Royal Soc. A: Math. Phys. Eng. Sci. 376, 20170450, DOI: 10.1098/rsta.2017.0450 (2018). https://royalsocietypublishing.org/doi/ pdf/10.1098/rsta.2017.0450

2017
[121]

Electronic Higher Multipoles in Solids.Prog

Kuramoto, Y . Electronic Higher Multipoles in Solids.Prog. Theor. Phys. Suppl. 176, 77–96, DOI: 10.1143/ PTPS.176.77 (2008). https://academic.oup.com/ptps/article-pdf/doi/10.1143/PTPS.176.77/5324654/176-77. pdf

2008 doi
[122]

& Kiss, A

Kuramoto, Y ., Kusunose, H. & Kiss, A. Multipole orders and fluctuations in strongly correlated electron systems. J. Phys. Soc. Jpn. 78, 072001, DOI: 10.1143/JPSJ.78.072001 (2009). https://doi.org/10.1143/JPSJ. 78.072001. 32/45

2009 doi
[123]

Resonating valence bonds: A new kind of insulator? Mater

Anderson, P. Resonating valence bonds: A new kind of insulator? Mater. Res. Bull. 8, 153–160, DOI: https://doi.org/10.1016/0025-5408(73)90167-0 (1973)

1973 doi
[124]

& Balents, L

Savary, L. & Balents, L. Quantum spin liquids: a review. Reports on Prog. Phys. 80, 016502, DOI: 10.1088/0034-4885/80/1/016502 (2016)

2016 doi
[125]

& Saito, G

Shimizu, Y ., Miyagawa, K., Kanoda, K., Maesato, M. & Saito, G. Spin liquid state in an organic mott insulator with a triangular lattice. Phys. Rev. Lett. 91, 107001, DOI: 10.1103/PhysRevLett.91.107001 (2003)

2003 doi
[126]

Powell, B. J. & McKenzie, R. H. Quantum frustration in organic mott insulators: from spin liquids to unconventional superconductors. Reports on Prog. Phys. 74, 056501, DOI: 10.1088/0034-4885/74/5/056501 (2011)

2011 doi
[127]

Plumb, K. W. et al. α − rucl3: A spin-orbit assisted mott insulator on a honeycomb lattice. Phys. Rev. B 90, 041112, DOI: 10.1103/PhysRevB.90.041112 (2014)

2014 doi
[128]

& Bert, F

Mendels, P. & Bert, F. Quantum kagome antiferromagnet zncu3(oh)6cl2. J. Phys. Soc. Jpn. 79, 011001, DOI: 10.1143/JPSJ.79.011001 (2010). https://doi.org/10.1143/JPSJ.79.011001

2010 doi
[129]

Winter, S. M. et al. Models and materials for generalized kitaev magnetism. J. Physics: Condens. Matter 29, 493002, DOI: 10.1088/1361-648X/aa8cf5 (2017)

2017 doi
[130]

& Nagler, S

Takagi, H., Takayama, T., Jackeli, G., Khaliullin, G. & Nagler, S. E. Concept and realization of kitaev quantum spin liquids. Nat. Rev. Phys. 1, 264–280, DOI: 10.1038/s42254-019-0038-2 (2019)

2019 doi
[131]

Kim, B. J. et al. Novel Jeff = 1/2 mott state induced by relativistic spin-orbit coupling in sr2iro4. Phys. Rev. Lett. 101, 076402, DOI: 10.1103/PhysRevLett.101.076402 (2008)

2008 doi
[132]

Comin, R. et al. na2iro3 as a novel relativistic mott insulator with a 340-mev gap. Phys. Rev. Lett. 109, 266406, DOI: 10.1103/PhysRevLett.109.266406 (2012)

2012 doi
[133]

& Yang, Z

Ju, W., Liu, G.-Q. & Yang, Z. Exotic spin-orbital mott insulating states in bairo3. Phys. Rev. B 87, 075112, DOI: 10.1103/PhysRevB.87.075112 (2013)

2013 doi
[134]

Hybrid functionals applied to perovskites

Franchini, C. Hybrid functionals applied to perovskites. J. Physics: Condens. Matter 26, 253202, DOI: 10.1088/0953-8984/26/25/253202 (2014)

2014 doi
[135]

& Biermann, S

Martins, C., Aichhorn, M. & Biermann, S. Coulomb correlations in 4d and 5d oxides from first principles—or how spin–orbit materials choose their effective orbital degeneracies. J. Physics: Condens. Matter 29, 263001, DOI: 10.1088/1361-648X/aa648f (2017)

2017 doi
[136]

& Coleman, P

Dzero, M., Sun, K., Galitski, V . & Coleman, P. Topological kondo insulators.Phys. Rev. Lett. 104, 106408, DOI: 10.1103/PhysRevLett.104.106408 (2010)

2010 doi
[137]

& Okamoto, S

Xiao, D., Zhu, W., Ran, Y ., Nagaosa, N. & Okamoto, S. Interface engineering of quantum hall effects in digital transition metal oxide heterostructures. Nat. Commun. 2, 596, DOI: 10.1038/ncomms1602 (2011)

2011 doi
[138]

Dzsaber, S. et al. Kondo insulator to semimetal transformation tuned by spin-orbit coupling. Phys. Rev. Lett. 118, 246601, DOI: 10.1103/PhysRevLett.118.246601 (2017)

2017 doi
[139]

Chen, L. et al. Topological semimetal driven by strong correlations and crystalline symmetry. Nat. Phys. 18, 1341–1346, DOI: 10.1038/s41567-022-01743-4 (2022)

2022 doi
[140]

Caviglia, A. D. et al. Tunable rashba spin-orbit interaction at oxide interfaces. Phys. Rev. Lett. 104, 126803, DOI: 10.1103/PhysRevLett.104.126803 (2010)

2010 doi
[141]

Wadehra, N. et al. Planar hall effect and anisotropic magnetoresistance in polar-polar interface of lavo3-ktao3 with strong spin-orbit coupling. Nat. Commun. 11, 874, DOI: 10.1038/s41467-020-14689-z (2020)

2020 doi
[142]

& Ueno, K

Okuma, H., Katayama, Y . & Ueno, K. Large rashba parameter for 4d strongly correlated perovskite oxide SrNbo3 ultrathin films. Phys. Rev. Mater .8, 015001, DOI: 10.1103/PhysRevMaterials.8.015001 (2024). 33/45

2024 doi
[143]

Spin orientation of two-dimensional electrons driven by temperature-tunable competition of spin–orbit and exchange–magnetic interactions

Generalov, A.et al. Spin orientation of two-dimensional electrons driven by temperature-tunable competition of spin–orbit and exchange–magnetic interactions. Nano Lett. 17, 811–820, DOI: 10.1021/acs.nanolett.6b04036 (2017). PMID: 28032768, https://doi.org/10.1021/acs.nanolett.6b04036

2017 doi
[144]

Generalov, A. et al. Strong spin-orbit coupling in the noncentrosymmetric kondo lattice. Phys. Rev. B 98, 115157, DOI: 10.1103/PhysRevB.98.115157 (2018)

2018 doi
[145]

& Lucignano, P

Bercioux, D. & Lucignano, P. Quantum transport in rashba spin–orbit materials: a review. Reports on Prog. Phys. 78, 106001, DOI: 10.1088/0034-4885/78/10/106001 (2015)

2015 doi
[146]

C., Nitta, J., Frolov, S

Manchon, A., Koo, H. C., Nitta, J., Frolov, S. M. & Duine, R. A. New perspectives for rashba spin–orbit coupling. Nat. Mater. 14, 871–882, DOI: 10.1038/nmat4360 (2015)

2015 doi
[147]

Density Functional Theory for Magnetism and Magnetic Anisotropy , 1–23 (Springer Interna- tional Publishing, Cham, 2018)

Bihlmayer, G. Density Functional Theory for Magnetism and Magnetic Anisotropy , 1–23 (Springer Interna- tional Publishing, Cham, 2018)

2018
[148]

T., Goodman, G

Carnall, W. T., Goodman, G. L., Rajnak, K. & Rana, R. S. A systematic analysis of the spectra of the lanthanides doped into single crystal LaF3. The J. Chem. Phys. 90, 3443–3457, DOI: 10.1063/1.455853 (1989)

1989 doi
[149]

Moore, K. T. & van der Laan, G. Nature of the 5 f states in actinide metals. Rev. Mod. Phys. 81, 235–298, DOI: 10.1103/RevModPhys.81.235 (2009)

2009 doi
[150]

Taylor, A. E. et al. Spin-orbit coupling controlled j = 3/2 electronic ground state in 5d3 oxides. Phys. Rev. Lett. 118, 207202, DOI: 10.1103/PhysRevLett.118.207202 (2017)

2017 doi
[151]

Paramekanti, A. et al. Spin-orbit coupled systems in the atomic limit: rhenates, osmates, iridates. Phys. Rev. B 97, 235119, DOI: 10.1103/PhysRevB.97.235119 (2018)

2018 doi
[152]

& Bleaney, B

Abragam, A. & Bleaney, B. Electron Paramagnetic Resonance of Transition Ions. Oxford Classic Texts in the Physical Sciences (OUP Oxford, 2012)

2012
[153]

Density matrix theory and applications (Plenum Press, New York, 1996)

Blum, K. Density matrix theory and applications (Plenum Press, New York, 1996)

1996
[154]

Sakurai, J. J. Modern Quantum Mechanics (Revised Edition) (Addison Wesley, 1993)

1993
[155]

& Tugushev, V

Dubovik, V . & Tugushev, V . Toroid moments in electrodynamics and solid-state physics.Phys. Reports 187, 145–202, DOI: https://doi.org/10.1016/0370-1573(90)90042-Z (1990)

1990 doi
[156]

A., Fechner, M., Bousquet, E., Balatsky, A

Spaldin, N. A., Fechner, M., Bousquet, E., Balatsky, A. & Nordström, L. Monopole-based formalism for the diagonal magnetoelectric response. Phys. Rev. B 88, 094429, DOI: 10.1103/PhysRevB.88.094429 (2013)

2013 doi
[157]

& Kusunose, H

Hayami, S. & Kusunose, H. Microscopic description of electric and magnetic toroidal multipoles in hybrid orbitals. J. Phys. Soc. Jpn. 87, 033709, DOI: 10.7566/JPSJ.87.033709 (2018)

2018 doi
[158]

& Yanase, Y

Watanabe, H. & Yanase, Y . Group-theoretical classification of multipole order: Emergent responses and candidate materials. Phys. Rev. B 98, 245129, DOI: 10.1103/PhysRevB.98.245129 (2018)

2018 doi
[159]

& Kusunose, H

Hayami, S., Yatsushiro, M., Yanagi, Y . & Kusunose, H. Classification of atomic-scale multipoles under crystallographic point groups and application to linear response tensors. Phys. Rev. B 98, 165110, DOI: 10.1103/PhysRevB.98.165110 (2018)

2018 doi
[161]

& Arita, R

Huebsch, M.-T., Nomoto, T., Suzuki, M.-T. & Arita, R. Benchmark for ab initio prediction of magnetic structures based on cluster-multipole theory. Phys. Rev. X 11, 011031, DOI: 10.1103/PhysRevX.11.011031 (2021)

2021 doi
[162]

hidden order

Kung, H.-H. et al. Chirality density wave of the "hidden order" phase in URu2Si2. Science 347, 1339–1342, DOI: 10.1126/science.1259729 (2015). https://www.science.org/doi/pdf/10.1126/science.1259729. 34/45

2015 doi
[163]

W., Fisher, I

Ye, M., Rosenberg, E. W., Fisher, I. R. & Blumberg, G. Lattice dynamics, crystal-field excitations, and quadrupolar fluctuations of ybru2ge2. Phys. Rev. B 99, 235104, DOI: 10.1103/PhysRevB.99.235104 (2019)

2019 doi
[164]

Ye, M. et al. Raman spectroscopy of f -electron metals: An example of ceb6. Phys. Rev. Mater .3, 065003, DOI: 10.1103/PhysRevMaterials.3.065003 (2019)

2019 doi
[165]

V olkov, P. A.et al. Critical charge fluctuations and emergent coherence in a strongly correlated excitonic insulator. npj Quantum Mater. 6, 52, DOI: 10.1038/s41535-021-00351-4 (2021)

2021 doi
[166]

Patri, A. S. et al. Unveiling hidden multipolar orders with magnetostriction. Nat. Commun. 10, 4092, DOI: 10.1038/s41467-019-11913-3 (2019)

2019 doi
[167]

E., Bachmann, M

Ye, L., Sorensen, M. E., Bachmann, M. D. & Fisher, I. R. Measurement of the magnetic octupole susceptibility of prv2al20 (2023). 2309.04633

2023 arXiv
[168]

Lovesey, S. W. & Khalyavin, D. D. Lone octupole and bulk magnetism in osmate 5d2 double perovskites. Phys. Rev. B 102, 064407, DOI: 10.1103/PhysRevB.102.064407 (2020)

2020 doi
[169]

Urru, A. et al. Neutron scattering from local magnetoelectric multipoles: A combined theoretical, computa- tional, and experimental perspective. Phys. Rev. Res. 5, 033147, DOI: 10.1103/PhysRevResearch.5.033147 (2023)

2023 doi
[170]

& Spaldin, N

Urru, A. & Spaldin, N. A. Magnetic octupole tensor decomposition and second-order magnetoelectric effect. Annals Phys. 447, 168964, DOI: https://doi.org/10.1016/j.aop.2022.168964 (2022)

2022
[171]

W., Zhao, Z

Harter, J. W., Zhao, Z. Y ., Yan, J.-Q., Mandrus, D. G. & Hsieh, D. A parity-breaking electronic nematic phase transition in the spin-orbit coupled metal cd2re2o7. Science 356, 295–299, DOI: 10.1126/science.aad1188 (2017). https://www.science.o...

2017 doi
[172]

& Lovesey, S

van der Laan, G. & Lovesey, S. W. Electronic multipoles in second harmonic generation and neutron scattering. Phys. Rev. B 103, 125124, DOI: 10.1103/PhysRevB.103.125124 (2021)

2021 doi
[173]

Taniguchi, T. et al. Nmr observation of ferro-quadrupole order in prti2al20. J. Phys. Soc. Jpn. 85, 113703, DOI: 10.7566/JPSJ.85.113703 (2016). https://doi.org/10.7566/JPSJ.85.113703

2016 doi
[174]

Field-induced switching of ferro-quadrupole order parameter in prti2al20

Taniguchi, T.et al. Field-induced switching of ferro-quadrupole order parameter in prti2al20. J. Phys. Soc. Jpn. 88, 084707, DOI: 10.7566/JPSJ.88.084707 (2019). https://doi.org/10.7566/JPSJ.88.084707

2019 doi
[175]

Anderson, P. W. Antiferromagnetism. theory of superexchange interaction. Phys. Rev. 79, 350–356, DOI: 10.1103/PhysRev.79.350 (1950)

1950 doi
[176]

Goodenough, J. B. Theory of the role of covalence in the perovskite-type manganites [La, m(II)]Mno3. Phys. Rev. 100, 564–573, DOI: 10.1103/PhysRev.100.564 (1955)

1955 doi
[177]

Superexchange interaction and symmetry properties of electron orbitals

Kanamori, J. Superexchange interaction and symmetry properties of electron orbitals. J. Phys. Chem. Solids 10, 87–98, DOI: https://doi.org/10.1016/0022-3697(59)90061-7 (1959)

1959 doi
[178]

Gehring, G. A. & Gehring, K. A. Co-operative jahn-teller effects. Reports on Prog. Phys. 38, 1, DOI: 10.1088/0034-4885/38/1/001 (1975)

1975 doi
[179]

K I Kugel’, K. I. & Khomskii, D. I. The jahn-teller effect and magnetism: transition metal compounds. Sov. Phys. Uspekhi 25, 231–256 (1982)

1982
[180]

Khomskii, D. I. Transition Metal Compounds (Cambridge University Press, 2014)

2014
[181]

Theory of the coupling between conduction electrons and moments of 3d and 4f ions in metals

Hirst, L. Theory of the coupling between conduction electrons and moments of 3d and 4f ions in metals. Adv. Phys. 27, 231–285, DOI: 10.1080/00018737800101374 (1978)

1978 doi
[182]

& Loewenhaupt, M

Fulde, P. & Loewenhaupt, M. Magnetic excitations in crystal-field split 4f systems. Adv. Phys. 34, 589–661, DOI: 10.1080/00018738500101821 (1985)

1985 doi
[183]

& Mackintosh, A

Jensen, J. & Mackintosh, A. R. Rare Earth Magnetism: Structures and Excitations (Clarendon Press, Oxford, 1991). 35/45

1991
[184]

& Balents, L

Chen, G. & Balents, L. Spin-orbit coupling in d2 ordered double perovskites. Phys. Rev. B 84, 094420, DOI: 10.1103/PhysRevB.84.094420 (2011)

2011 doi
[185]

& Trivedi, N

Svoboda, C., Zhang, W., Randeria, M. & Trivedi, N. Orbital order drives magnetic order in and double perovskite mott insulators. Phys. Rev. B 104, DOI: 10.1103/PhysRevB.104.024437 (2021)

2021 doi
[186]

A., Teller, E

Jahn, H. A., Teller, E. & Donnan, F. G. Stability of polyatomic molecules in degenerate electronic states - i—orbital degeneracy. Proc. Royal Soc. London. Ser. A - Math. Phys. Sci. 161, 220–235, DOI: 10.1098/rspa. 1937.0142 (1937)

1937
[187]

Bersuker, I. B. & Polinger, V . Z.Vibronic Interactions in Molecules and Crystals (Springer Berlin Heidelberg, 1989)

1989
[188]

Streltsov, S. V . & Khomskii, D. I. Jahn-teller effect and spin-orbit coupling: Friends or foes? Phys. Rev. X 10, 031043, DOI: 10.1103/PhysRevX.10.031043 (2020)

2020 doi
[189]

V ., Temnikov, F

Streltsov, S. V ., Temnikov, F. V ., Kugel, K. I. & Khomskii, D. I. Interplay of the jahn-teller effect and spin-orbit coupling: The case of trigonal vibrations. Phys. Rev. B 105, 205142, DOI: 10.1103/PhysRevB.105.205142 (2022)

2022 doi
[190]

Bersuker, I. B. Pseudo-jahn–teller effect—a two-state paradigm in formation, deformation, and transformation of molecular systems and solids. Chem. Rev. 113, 1351–1390, DOI: 10.1021/cr300279n (2013)

2013 doi
[191]

Dynamic jahn–teller phenomena in heavy transition metal compounds

Iwahara, N. Dynamic jahn–teller phenomena in heavy transition metal compounds. J. Phys. Soc. Jpn. 93, 121003, DOI: 10.7566/JPSJ.93.121003 (2024). https://doi.org/10.7566/JPSJ.93.121003

2024 doi
[192]

Lejaeghere, K. et al. Reproducibility in density functional theory calculations of solids. Science 351, aad3000, DOI: 10.1126/science.aad3000 (2016)

2016 doi
[193]

& Kresse, G

Franchini, C., Bayer, V ., Podloucky, R., Paier, J. & Kresse, G. Density functional theory study of mno by a hybrid functional approach. Phys. Rev. B 72, 045132, DOI: 10.1103/PhysRevB.72.045132 (2005)

2005 doi
[194]

Franchini, C. et al. Exceptionally strong magnetism in the 4d perovskites rtco3 (r = Ca, sr, ba). Phys. Rev. B 83, 220402, DOI: 10.1103/PhysRevB.83.220402 (2011)

2011 doi
[195]

Archer, T. et al. Exchange interactions and magnetic phases of transition metal oxides: Benchmarking advanced ab initio methods. Phys. Rev. B 84, 115114, DOI: 10.1103/PhysRevB.84.115114 (2011)

2011 doi
[196]

I., Zaanen, J

Anisimov, V . I., Zaanen, J. & Andersen, O. K. Band theory and mott insulators: Hubbard u instead of stoner i. Phys. Rev. B 44, 943–954, DOI: 10.1103/PhysRevB.44.943 (1991)

1991 doi
[197]

Description of multipole in f-electron systems

Kusunose, H. Description of multipole in f-electron systems. J. Phys. Soc. Jpn. 77, 064710, DOI: 10.1143/ JPSJ.77.064710 (2008). https://doi.org/10.1143/JPSJ.77.064710

2008 doi
[198]

Lovesey, S. W. Theory of neutron scattering by electrons in magnetic materials. Phys. Scripta 90, 108011, DOI: 10.1088/0031-8949/90/10/108011 (2015)

2015 doi
[199]

& Liechtenstein, A

Shick, A., Pickett, W. & Liechtenstein, A. Ground and metastable states in γ-ce from correlated band theory. J. Electron Spectrosc. Relat. Phenom. 114-116, 753–758, DOI: https://doi.org/10.1016/S0368-2048(00)00394-7 (2001). Proceeding of the Eight International Conference on E...

doi
[200]

Larson, P., Lambrecht, W. R. L., Chantis, A. & van Schilfgaarde, M. Electronic structure of rare-earth nitrides using the LSDA+ u approach: Importance of allowing 4 f orbitals to break the cubic crystal symmetry. Phys. Rev. B 75, 045114, DOI: 10.1103/PhysRevB.75.045114 (2007)

2007 doi
[201]

Jomard, G., Amadon, B., Bottin, F. m. c. & Torrent, M. Structural, thermodynamic, and electronic properties of plutonium oxides from first principles. Phys. Rev. B 78, 075125, DOI: 10.1103/PhysRevB.78.075125 (2008)

2008 doi
[202]

& Bertolus, M

Dorado, B., Amadon, B., Freyss, M. & Bertolus, M. DFT + U calculations of the ground state and metastable states of uranium dioxide. Phys. Rev. B 79, 235125, DOI: 10.1103/PhysRevB.79.235125 (2009). 36/45

2009 doi
[203]

Allen, J. P. & Watson, G. W. Occupation matrix control of d- and f-electron localisations using dft + u. Phys. Chem. Chem. Phys. 16, 21016–21031, DOI: 10.1039/C4CP01083C (2014)

2014 doi
[204]

& Dudarev, S

Ma, P.-W. & Dudarev, S. L. Constrained density functional for noncollinear magnetism. Phys. Rev. B 91, 054420, DOI: 10.1103/PhysRevB.91.054420 (2015)

2015 doi
[205]

Dudarev, S. L. et al. Parametrization of LSDA + u for noncollinear magnetic configurations: Multipolar magnetism in uo2. Phys. Rev. Mater .3, 083802, DOI: 10.1103/PhysRevMaterials.3.083802 (2019)

2019 doi
[206]

H., Blügel, S., Zeller, R

Dederichs, P. H., Blügel, S., Zeller, R. & Akai, H. Ground states of constrained systems: Application to cerium impurities. Phys. Rev. Lett. 53, 2512–2515, DOI: 10.1103/PhysRevLett.53.2512 (1984)

1984 doi
[207]

Tehrani, A. M. & Spaldin, N. A. Untangling the structural, magnetic dipole, and charge multipolar orders in Ba2MgReO6. Phys. Rev. Mater. 5, DOI: 10.1103/PhysRevMaterials.5.104410 (2021)

2021 doi
[208]

non-dynamical

Yoon, S. et al. A “non-dynamical” way of describing room-temperature paramagnetic manganese oxide. Phys. Chem. Chem. Phys. 21, 15932–15939, DOI: 10.1039/C9CP00280D (2019)

2019 doi
[209]

& Zunger, A

Varignon, J., Bibes, M. & Zunger, A. Mott gapping in3d abo3 perovskites without mott-hubbard interelectronic repulsion energy u. Phys. Rev. B 100, 035119, DOI: 10.1103/PhysRevB.100.035119 (2019)

2019 doi
[210]

& Rozenberg, M

Georges, A., Kotliar, G., Krauth, W. & Rozenberg, M. J. Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions. Rev. Mod. Phys. 68, 13–125 (1996)

1996
[211]

I., Poteryaev, A

Anisimov, V . I., Poteryaev, A. I., Korotin, M. A., Anokhin, A. O. & Kotliar, G. First-principles calculations of the electronic structure and spectra of strongly correlated systems: dynamical mean-field theory. J. Physics: Condens. Matter 9, 7359 (1997)

1997
[212]

Lichtenstein, A. I. & Katsnelson, M. I. Ab initio calculations of quasiparticle band structure in correlated systems: Lda++ approach. Phys. Rev. B 57, 6884–6895 (1998)

1998
[213]

Kotliar, G. et al. Electronic structure calculations with dynamical mean-field theory. Rev. Mod. Phys. 78, 865–951, DOI: 10.1103/RevModPhys.78.865 (2006)

2006 doi
[214]

& with Predictive Power for Strongly Correlated Materials, D

Pavarini, E., Koch, E., V ollhardt, D., Lichtenstein, A. & with Predictive Power for Strongly Correlated Materials, D. F. F. . D. M.-F. A. The LDA+DMFT Approach to Strongly Correlated Materials: Lecture Notes of the Autumn School 2011 Hands-on LDA+DMFT at F orschungszentrum Jü...

2011
[215]

& Kotliar, G

Haule, K. & Kotliar, G. Arrested kondo effect and hidden order in uru2si2. Nat. Phys. 5, 796–799, DOI: 10.1038/nphys1392 (2009)

2009 doi
[216]

E., Tehrani, A

Merkel, M. E., Tehrani, A. M. & Ederer, C. Probing the mott insulating behavior of ba2mgreo6 with DFT + DMFT. Phys. Rev. Res. 6, 023233, DOI: 10.1103/PhysRevResearch.6.023233 (2024)

2024 doi
[217]

Mackintosh, A. R. & Andersen, O. Electrons at the fermi surface. chap. The electronic structure of transition metals (Cambridge University Press, 1980)

1980
[218]

I., Katsnelson, M

Liechtenstein, A. I., Katsnelson, M. I. & Gubanov, V . A. Exchange interactions and spin-wave stiffness in ferromagnetic metals. J. Phys. F: Met. Phys. 14, L125, DOI: 10.1088/0305-4608/14/7/007 (1984)

1984 doi
[219]

& Gubanov, V

Liechtenstein, A., Katsnelson, M., Antropov, V . & Gubanov, V . Local spin density functional approach to the theory of exchange interactions in ferromagnetic metals and alloys. J. Magn. Magn. Mater. 67, 65–74, DOI: https://doi.org/10.1016/0304-8853(87)90721-9 (1987)

1987 doi
[220]

Katsnelson, M. I. & Lichtenstein, A. I. First-principles calculations of magnetic interactions in correlated systems. Phys. Rev. B 61, 8906–8912, DOI: 10.1103/PhysRevB.61.8906 (2000)

2000 doi
[221]

renormalized magnetic force theorem

Bruno, P. Exchange interaction parameters and adiabatic spin-wave spectra of ferromagnets: A “renormalized magnetic force theorem”. Phys. Rev. Lett. 90, 087205, DOI: 10.1103/PhysRevLett.90.087205 (2003). 37/45

2003 doi
[223]

& Terakura, K

Solovyev, I., Hamada, N. & Terakura, K. Crucial role of the lattice distortion in the magnetism of lamno3. Phys. Rev. Lett. 76, 4825–4828, DOI: 10.1103/PhysRevLett.76.4825 (1996)

1996 doi
[224]

Electron correlations in narrow energy bands

Hubbard, J. Electron correlations in narrow energy bands. Proc. Roy. Soc. (London) A 276 , 238, DOI: 10.1098/rspa.1963.0204 (1963)

1963
[225]

Lebègue, S. et al. Electronic structure and spectroscopic properties of thulium monochalcogenides. Phys. Rev. B 72, 245102, DOI: 10.1103/PhysRevB.72.245102 (2005)

2005 doi
[226]

V ., Delaney, K

Pourovskii, L. V ., Delaney, K. T., Van de Walle, C. G., Spaldin, N. A. & Georges, A. Role of atomic multiplets in the electronic structure of rare-earth semiconductors and semimetals. Phys. Rev. Lett. 102, 096401, DOI: 10.1103/PhysRevLett.102.096401 (2009)

2009 doi
[227]

B., Kolorenˇc, J., Lichtenstein, A

Shick, A. B., Kolorenˇc, J., Lichtenstein, A. I. & Havela, L. Electronic structure and spectral properties of am, cm, and bk: Charge-density self-consistent LDA + HIA calculations in the fp-lapw basis. Phys. Rev. B 80, 085106, DOI: 10.1103/PhysRevB.80.085106 (2009)

2009 doi
[228]

Locht, I. L. M. et al. Standard model of the rare earths analyzed from the hubbard i approximation. Phys. Rev. B 94, 085137, DOI: 10.1103/PhysRevB.94.085137 (2016)

2016 doi
[229]

Strongly Correlated Electron Materials: Dynamical Mean-Field Theory and Electronic Structure

Georges, A. Strongly Correlated Electron Materials: Dynamical Mean-Field Theory and Electronic Structure. AIP Conf. Proc. 715, 3–74, DOI: 10.1063/1.1800733 (2004)

2004 doi
[230]

& Chibotaru, L

Iwahara, N., Ungur, L. & Chibotaru, L. F. ˜ J-pseudospin states and the crystal field of cubic systems. Phys. Rev. B 98, 054436, DOI: 10.1103/PhysRevB.98.054436 (2018)

2018 doi
[231]

Orbital Ordering V ersus the Traditional Approach in the Cooperative Jahn–Teller Effect: A Comparative Study, 685–725 (Springer Berlin Heidelberg, Berlin, Heidelberg, 2009)

Polinger, V . Orbital Ordering V ersus the Traditional Approach in the Cooperative Jahn–Teller Effect: A Comparative Study, 685–725 (Springer Berlin Heidelberg, Berlin, Heidelberg, 2009)

2009
[232]

Pourovskii, L. V . Multipolar interactions and magnetic excitation gap ind3 spin-orbit mott insulators. Phys. Rev. B 108, 054436, DOI: 10.1103/PhysRevB.108.054436 (2023)

2023 doi
[233]

Hubbard model in infinite dimensions: A quantum monte carlo study

Jarrell, M. Hubbard model in infinite dimensions: A quantum monte carlo study. Phys. Rev. Lett. 69, 168–171, DOI: 10.1103/PhysRevLett.69.168 (1992)

1992 doi
[234]

Gull, E. et al. Continuous-time monte carlo methods for quantum impurity models. Rev. Mod. Phys. 83, 349–404, DOI: 10.1103/RevModPhys.83.349 (2011)

2011 doi
[235]

& Nomura, Y

Otsuki, J., Yoshimi, K., Shinaoka, H. & Nomura, Y . Strong-coupling formula for momentum-dependent susceptibilities in dynamical mean-field theory. Phys. Rev. B 99, 165134, DOI: 10.1103/PhysRevB.99.165134 (2019)

2019 doi
[236]

& Jeschke, H

Otsuki, J., Yoshimi, K., Shinaoka, H. & Jeschke, H. O. Multipolar ordering from dynamical mean field theory with application to ceb6. Phys. Rev. B 110, 035104, DOI: 10.1103/PhysRevB.110.035104 (2024)

2024 doi
[237]

Anderson, P. W. New approach to the theory of superexchange interactions. Phys. Rev. 115, 2–13, DOI: 10.1103/PhysRev.115.2 (1959)

1959 doi
[238]

Anderson, P. W. Theory of magnetic exchange interactions:exchange in insulators and semiconductors. vol. 14 of Solid State Physics , 99–214, DOI: https://doi.org/10.1016/S0081-1947(08)60260-X (Academic Press, 1963)

1947 doi
[239]

& Ceulemans, A

Mironov, V ., Chibotaru, L. & Ceulemans, A. First-order phase transition in uo2: The interplay of the 5f2–5f2 superexchange interaction and jahn–teller effect. In Advances in Quantum Chemistry , vol. 44 of Advances in Quantum Chemistry, 599–616, DOI: https://doi.org/10.1016/S0...

2003 doi
[240]

& Chibotaru, L

Iwahara, N. & Chibotaru, L. F. Exchange interaction between j multiplets. Phys. Rev. B 91, 174438, DOI: 10.1103/PhysRevB.91.174438 (2015)

2015 doi
[241]

& Paramekanti, A

V oleti, S., Haldar, A. & Paramekanti, A. Octupolar order and ising quantum criticality tuned by strain and dimensionality: Application to d-orbital mott insulators. Phys. Rev. B 104, 174431, DOI: 10.1103/PhysRevB. 104.174431 (2021)

2021 doi
[242]

Schrieffer, J. R. & Wolff, P. A. Relation between the anderson and kondo hamiltonians. Phys. Rev. 149, 491–492, DOI: 10.1103/PhysRev.149.491 (1966)

1966 doi
[243]

H., Khaliullin, G

Kim, B. H., Khaliullin, G. & Min, B. I. Magnetic couplings, optical spectra, and spin-orbit exciton in 5d electron mott insulator sr2iro4. Phys. Rev. Lett. 109, 167205, DOI: 10.1103/PhysRevLett.109.167205 (2012)

2012 doi
[244]

M., Li, Y ., Jeschke, H

Winter, S. M., Li, Y ., Jeschke, H. O. & Valentí, R. Challenges in design of kitaev materials: Magnetic interactions from competing energy scales. Phys. Rev. B 93, 214431, DOI: 10.1103/PhysRevB.93.214431 (2016)

2016 doi
[245]

H., Efremov, D

Kim, B. H., Efremov, D. V . & van den Brink, J. Spin-orbital excitons and their potential condensation in pentavalent iridates. Phys. Rev. Mater .3, 014414, DOI: 10.1103/PhysRevMaterials.3.014414 (2019)

2019 doi
[246]

& Chibotaru, L

Iwahara, N., Vieru, V . & Chibotaru, L. F. Spin-orbital-lattice entangled states in cubicd1 double perovskites. Phys. Rev. B 98, 075138, DOI: 10.1103/PhysRevB.98.075138 (2018)

2018 doi
[247]

E., Hampel, A., Ederer, C

Peil, O. E., Hampel, A., Ederer, C. & Georges, A. Mechanism and control parameters of the coupled structural and metal-insulator transition in nickelates. Phys. Rev. B 99, 245127, DOI: 10.1103/PhysRevB.99.245127 (2019)

2019 doi
[248]

B., Peil, O

Georgescu, A. B., Peil, O. E., Disa, A. S., Georges, A. & Millis, A. J. Disentangling lattice and electronic contributions to the metal–insulator transition from bulk vs. layer confined rnio 3. Proc. Natl. Acad. Sci. 116, 14434–14439, DOI: 10.1073/pnas.1818728116 (2019)

2019 doi
[249]

& Pourovskii, L

Delange, P., Biermann, S., Miyake, T. & Pourovskii, L. Crystal-field splittings in rare-earth-based hard magnets: An ab initio approach. Phys. Rev. B 96, 155132, DOI: 10.1103/PhysRevB.96.155132 (2017)

2017 doi
[250]

& Giannozzi, P

Baroni, S., de Gironcoli, S., Dal Corso, A. & Giannozzi, P. Phonons and related crystal properties from density-functional perturbation theory. Rev. Mod. Phys. 73, 515–562, DOI: 10.1103/RevModPhys.73.515 (2001)

2001 doi
[251]

Pourovskii, L. V . & Khmelevskyi, S. Quadrupolar superexchange interactions, multipolar order, and magnetic phase transition in uo2. Phys. Rev. B 99, 094439, DOI: 10.1103/PhysRevB.99.094439 (2019)

2019 doi
[252]

& Zunger, A

Trimarchi, G., Wang, Z. & Zunger, A. Polymorphous band structure model of gapping in the antiferromagnetic and paramagnetic phases of the mott insulators mno, feo, coo, and nio. Phys. Rev. B 97, 035107, DOI: 10.1103/PhysRevB.97.035107 (2018)

2018 doi
[253]

D., Boothroyd, A

Rotter, M., Le, M. D., Boothroyd, A. T. & Blanco, J. A. Dynamical matrix diagonalization for the calculation of dispersive excitations. J. Physics: Condens. Matter 24, 213201, DOI: 10.1088/0953-8984/24/21/213201 (2012)

2012 doi
[254]

& Shiba, H

Shiina, R., Sakai, O. & Shiba, H. Magnetic form factor of elastic neutron scattering expected for octupolar phases in Ce1−xLaxB6 and NpO2. J. Phys. Soc. Jpn. 76, 094702, DOI: 10.1143/JPSJ.76.094702 (2007)

2007 doi
[255]

Schollwöck, U., Richter, J., Farnell, D. J. J. & Bishop, R. F. (eds.) Quantum Magnetism (Springer Berlin Heidelberg, 2004)

2004
[256]

Sandvik, A. W. Computational Studies of Quantum Spin Systems. AIP Conf. Proc. 1297, 135–338, DOI: 10.1063/1.3518900 (2010)

2010 doi
[257]

The density-matrix renormalization group in the age of matrix product states

Schollwöck, U. The density-matrix renormalization group in the age of matrix product states. Annals Phys. 326, 96–192, DOI: https://doi.org/10.1016/j.aop.2010.09.012 (2011). January 2011 Special Issue. 39/45

2010 doi
[258]

& Sakai, O

Thalmeier, P., Shiina, R., Shiba, H. & Sakai, O. Theory of multipolar excitations in ceb 6. J. Phys. Soc. Jpn. 67, 2363–2371, DOI: 10.1143/JPSJ.67.2363 (1998). https://doi.org/10.1143/JPSJ.67.2363

1998 doi
[259]

& Halperin, B

Englman, R. & Halperin, B. Cooperative dynamic jahn-teller effect. i. molecular field treatment of spinels. Phys. Rev. B 2, 75–94, DOI: 10.1103/PhysRevB.2.75 (1970)

1970 doi
[260]

Khaliullin, G., Churchill, D., Stavropoulos, P. P. & Kee, H.-Y . Exchange interactions, jahn-teller coupling, and multipole orders in pseudospin one-half 5d2 mott insulators. Phys. Rev. Res. 3, 033163, DOI: 10.1103/ PhysRevResearch.3.033163 (2021)

2021
[261]

Devereaux, T. P. & Hackl, R. Inelastic light scattering from correlated electrons. Rev. Mod. Phys. 79, 175–233, DOI: 10.1103/RevModPhys.79.175 (2007)

2007 doi
[262]

Kim, B. J. & Khaliullin, G. Resonant inelastic x-ray scattering operators for t2g orbital systems. Phys. Rev. B 96, 085108, DOI: 10.1103/PhysRevB.96.085108 (2017)

2017 doi
[263]

Lovesey, S. W. Theory of Neutron Scattering from Condensed Matter (Clarendon Press, Oxford, 1984)

1984
[264]

Paramekanti, A., Maharaj, D. D. & Gaulin, B. D. Octupolar order in d-orbital mott insulators. Phys. Rev. B 101, 054439, DOI: 10.1103/PhysRevB.101.054439 (2020)

2020 doi
[265]

Yuan, B. et al. Determination of hund’s coupling in 5d oxides using resonant inelastic x-ray scattering. Phys. Rev. B 95, 235114, DOI: 10.1103/PhysRevB.95.235114 (2017)

2017 doi
[266]

Nag, A. et al. Origin of magnetic moments and presence of spin-orbit singlets in ba2yiro6. Phys. Rev. B 98, 014431, DOI: 10.1103/PhysRevB.98.014431 (2018)

2018 doi
[267]

Cong, R. et al. Effects of charge doping on mott insulator with strong spin-orbit coupling, ba2na1−xcaxoso6. Phys. Rev. Mater .7, 084409, DOI: 10.1103/PhysRevMaterials.7.084409 (2023)

2023 doi
[268]

E., Smith, M

Stitzer, K. E., Smith, M. D. & zur Loye, H.-C. Crystal growth of ba2moso6 (m=li, na) from reactive hydroxide fluxes. Solid State Sci. 4, 311–316, DOI: https://doi.org/10.1016/S1293-2558(01)01257-2 (2002)

2002 doi
[269]

Erickson, A. S. et al. Ferromagnetism in the mott insulator ba2naoso6. Phys. Rev. Lett. 99, 016404, DOI: 10.1103/PhysRevLett.99.016404 (2007)

2007 doi
[270]

Steele, A. J. et al. Low-moment magnetism in the double perovskites ba2moso6 (m = Li,Na). Phys. Rev. B 84, 144416, DOI: 10.1103/PhysRevB.84.144416 (2011)

2011 doi
[271]

Carlo, J. P. et al. Triplet and in-gap magnetic states in the ground state of the quantum frustrated fcc antiferromagnet ba2ymoo6. Phys. Rev. B 84, 100404, DOI: 10.1103/PhysRevB.84.100404 (2011)

2011 doi
[272]

& Hinatsu, Y

Yamamura, K., Wakeshima, M. & Hinatsu, Y . Structural phase transition and magnetic properties of double perovskites ba2camo6 (m=w, re, os). J. Solid State Chem. 179, 605–612, DOI: https://doi.org/10.1016/j.jssc. 2005.10.003 (2006)

2005 doi
[273]

Ishikawa, H. et al. Phase transition in the 5d1 double perovskite ba2careo6 induced by high magnetic field. Phys. Rev. B 104, 174422, DOI: 10.1103/PhysRevB.104.174422 (2021)

2021 doi
[274]

Marjerrison, C. A. et al. Cubic re6+ (5d1) double perovskites, ba2mgreo6, ba2znreo6, and ba2y2/3reo6: Magnetism, heat capacity, µsr, and neutron scattering studies and comparison with theory. Inorg. Chem. 55, 10701–10713, DOI: 10.1021/acs.inorgchem.6b01933 (2016). https://doi....

2016 doi
[275]

& Hiroi, Z

Hirai, D. & Hiroi, Z. Successive symmetry breaking in a jeff = 3/2 quartet in the spin–orbit coupled insulator ba2mgreo6. J. Phys. Soc. Jpn. 88, 064712, DOI: 10.7566/JPSJ.88.064712 (2019). https://doi.org/10.7566/ JPSJ.88.064712

2019 doi
[276]

Liu, W. et al. Phase diagram of ba2naoso6, a mott insulator with strong spin orbit interactions. Phys. B: Condens. Matter 536, 863–866, DOI: https://doi.org/10.1016/j.physb.2017.08.062 (2018)

2017 doi
[277]

Willa, K. et al. Phase transition preceding magnetic long-range order in the double perovskiteba2naoso6. Phys. Rev. B 100, 041108, DOI: 10.1103/PhysRevB.100.041108 (2019). 40/45

2019 doi
[278]

Kesavan, J. K. et al. Doping evolution of the local electronic and structural properties of the double perovskite ba2na1–xcaxoso6. The J. Phys. Chem. C 124, 16577–16585, DOI: 10.1021/acs.jpcc.0c04807 (2020). PMID: 33643515, https://doi.org/10.1021/acs.jpcc.0c04807

2020 doi
[279]

The impact of structural distortions on the magnetism of double perovskites containing 5d1 transition-metal ions

da Cruz Pinha Barbosa, V .et al. The impact of structural distortions on the magnetism of double perovskites containing 5d1 transition-metal ions. Chem. Mater. 34, 1098–1109, DOI: 10.1021/acs.chemmater.1c03456 (2022). https://doi.org/10.1021/acs.chemmater.1c03456

2022 doi
[280]

& Matsubayashi, K

Arima, H., Oshita, Y ., Hirai, D., Hiroi, Z. & Matsubayashi, K. Interplay between quadrupolar and magnetic interactions in 5d1 double perovskite ba2mgreo6 under pressure. J. Phys. Soc. Jpn. 91, 013702, DOI: 10.7566/JPSJ.91.013702 (2022). https://doi.org/10.7566/JPSJ.91.013702

2022 doi
[281]

Frontini, F. I. et al. Spin-orbit-lattice entangled state in A2MgReO6 (A = Ca, Sr, Ba) revealed by resonant inelastic x-ray scattering (2023). 2311.01621

2023 arXiv
[282]

Živkovi´c, I. et al. Dynamic jahn-teller effect in the strong spin-orbit coupling regime. Nat. Commun. 15, 8587, DOI: 10.1038/s41467-024-52935-w (2024)

2024 doi
[283]

Aharen, T. et al. Magnetic properties of the geometrically frustrated s = 1 2 antiferromagnets, la2limoo6 and ba2ymoo6, with the b-site ordered double perovskite structure: Evidence for a collective spin-singlet ground state. Phys. Rev. B 81, 224409, DOI: 10.1103/PhysRevB.81.2...

2010 doi
[284]

M., ˘Zivkovi´c, I., Spaldin, N

Pásztorová’, J., Tehrani, A. M., ˘Zivkovi´c, I., Spaldin, N. A. & Rønnow, H. M. Experimental and theoretical thermodynamic studies in ba2mgreo6—the ground state in the context of jahn-teller effect.J. Physics: Condens. Matter 35, 245603, DOI: 10.1088/1361-648X/acc62a (2023)

2023 doi
[285]

D., Gaulin, B

V oleti, S., Maharaj, D. D., Gaulin, B. D., Luke, G. & Paramekanti, A. Multipolar magnetism in d-orbital systems: Crystal field levels, octupolar order, and orbital loop currents. Phys. Rev. B 101, 155118, DOI: 10.1103/PhysRevB.101.155118 (2020)

2020 doi
[286]

& Kee, H.-Y

Churchill, D. & Kee, H.-Y . Competing multipolar orders in a face-centered cubic lattice: Application to the osmium double perovskites. Phys. Rev. B 105, 014438, DOI: 10.1103/PhysRevB.105.014438 (2022)

2022 doi
[287]

& Kee, H.-Y

Rayyan, A., Liu, X. & Kee, H.-Y . Fate of multipolar physics in 5d2 double perovskites. Phys. Rev. B 108, 045149, DOI: 10.1103/PhysRevB.108.045149 (2023)

2023 doi
[288]

Aharen, T. et al. Magnetic properties of the s = 3 2 geometrically frustrated double perovskites la2liruo6 and ba2yruo6. Phys. Rev. B 80, 134423, DOI: 10.1103/PhysRevB.80.134423 (2009)

2009 doi
[289]

Carlo, J. P. et al. Spin gap and the nature of the 4d3 magnetic ground state in the frustrated fcc antiferromagnet ba2yruo6. Phys. Rev. B 88, 024418, DOI: 10.1103/PhysRevB.88.024418 (2013)

2013 doi
[290]

Paddison, J. A. M. et al. Cubic double perovskites host noncoplanar spin textures (2023). 2301.11395

2023 arXiv
[291]

Kermarrec, E. et al. Frustrated fcc antiferromagnet ba2yoso6: Structural characterization, magnetic properties, and neutron scattering studies. Phys. Rev. B 91, 075133, DOI: 10.1103/PhysRevB.91.075133 (2015)

2015 doi
[292]

& Kindo, K

Ishikawa, H., Yajima, T., Matsuo, A. & Kindo, K. Ligand dependent magnetism of theJeff = 3/2 Mott insulator Cs2MX6 (M = Ta, Nb, X = Br, Cl).J. Physics: Condens. Matter 33, 125802, DOI: 10.1088/1361-648X/abd7b5 (2021)

2021 doi
[293]

Mansouri Tehrani, A. et al. Charge multipole correlations and order in Cs2TaCl6. Phys. Rev. Res. 5, L012010, DOI: 10.1103/PhysRevResearch.5.L012010 (2023)

2023 doi
[294]

Morgan, E. E. et al. Hybrid and inorganic vacancy-ordered double perovskites a2wcl6. Chem. Mater. 35, 7032–7038, DOI: 10.1021/acs.chemmater.3c01300 (2023)

2023 doi
[295]

& Saha-Dasgupta, T

Pradhan, K., Paramekanti, A. & Saha-Dasgupta, T. Multipolar magnetism in 5d2 vacancy-ordered halide double perovskites. Phys. Rev. B 109, 184416, DOI: 10.1103/PhysRevB.109.184416 (2024)

2024 doi
[296]

D., Cheetham, A

Li, Y ., Seshadri, R., Wilson, S. D., Cheetham, A. K. & Valenti, R. Microscopic origin of temperature-dependent magnetism in spin-orbit-coupled transition metal compounds (2024). 2402.14064. 41/45

2024 arXiv
[297]

Spin-orbital-lattice entanglement in the ideal j=1/2 compound k2ircl6 (2024)

Warzanowski, P.et al. Spin-orbital-lattice entanglement in the ideal j=1/2 compound k2ircl6 (2024). 2407. 12133

2024
[298]

Osborne, D. W. & Westrum, E. F. The heat capacity of thorium dioxide from 10 to 305 k. the heat capacity anomalies in uranium dioxide and neptunium dioxide. The J. Chem. Phys. 21, 1884–1887, DOI: 10.1063/1. 1698683 (1953)

1953 doi
[299]

& Frazer, B

Cox, D. & Frazer, B. A neutron diffraction study of NpO 2. J. Phys. Chem. Solids 28, 1649 – 1650, DOI: https://doi.org/10.1016/0022-3697(67)90137-0 (1967)

1967 doi
[300]

& Brodsky, M

Dunlap, B., Kalvius, G., Lam, D. & Brodsky, M. Hyperfine field of 237Np in NpO2. J. Phys. Chem. Solids 29, 1365 – 1367, DOI: 10.1016/0022-3697(68)90188-1 (1968)

1968 doi

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [1]

Landau, L. D. & Lifshitz, E. M. Quantum Mechanics: Non-relativistic Theory (Pergamon Press, Oxford, 1965)

1965

[2] [2]

Khomskii, D. I. Transition Metal Compounds (Cambridge University Press, Cambridge, 2014)

2014

[3] [3]

Properties of semiconductors with an extremum loop

Rashba, E. Properties of semiconductors with an extremum loop. i. cyclotron and combinational resonance in a magnetic field perpendicular to the plane of the loop. Sov. Phys.-Solid State 2, 1109 (1960)

1960

[4] [4]

V ., Chulkov, E

Bihlmayer, G., Noël, P., Vyalikh, D. V ., Chulkov, E. V . & Manchon, A. Rashba-like physics in condensed matter. Nat. Rev. Phys. 4, 642–659, DOI: 10.1038/s42254-022-00490-y (2022)

doi:10.1038/s42254-022-00490-y 2022

[5] [5]

Hirsch, J. E. Spin hall effect. Phys. Rev. Lett. 83, 1834 (1999). 26/45

1999

[6] [6]

Maciejko, J., Hughes, T. L. & Zhang, S.-C. The quantum spin hall effect. Annu. Rev. Condens. Matter Phys. 2, 31–53, DOI: https://doi.org/10.1146/annurev-conmatphys-062910-140538 (2011)

work page doi:10.1146/annurev-conmatphys-062910-140538 2011

[7] [7]

& Cros, V

Fert, A., Reyren, N. & Cros, V . Magnetic skyrmions: Advances in physics and potential applications. Nat. Rev. Mater .2, 17031 (2017)

2017

[8] [8]

Mott, N. F. & Peierls, R. Discussion of the paper by de boer and verwey. Proc. Phys. Soc. 49, 72, DOI: 10.1088/0959-5309/49/4S/308 (1937)

work page doi:10.1088/0959-5309/49/4s/308 1937