# Jahn–Teller Magnets

^{1}

^{2}

## Abstract

**:**

## 1. Introduction

## 2. Anti-Jahn–Teller Disproportionation

## 3. Electron–Hole Dimers

## 4. Spin Structure of EH Dimers

## 5. Possible Phase States of JT Magnets with Instability to Charge Transfer

## 6. Single-Band JT Magnets

#### 6.1. Effective Hamiltonian of a System of Spin–Triplet Composite Bosons: Non-Magnetic Lattice

#### 6.2. ${d}^{1}$, ${d}^{3}$ JT Magnets

#### ${d}^{7}$ JT Magnets

#### 6.3. ${d}^{9}$ JT Magnets

#### 6.3.1. Isoelectronic Quasi-2D Cuprates and Nickelates

#### 6.3.2. “Silver” JT Magnets

## 7. Two-Band JT Magnets

#### 7.1. Effective Hamiltonian of a System of Spin–Triplet Composite Bosons: Magnetic Lattice

#### 7.2. Chromium Cr${}^{2+}$ Compounds

#### 7.3. Manganites RMnO${}_{3}$

#### 7.4. Iron Fe${}^{4+}$ JT Magnets

#### 7.5. JT Ruthenates

#### 7.6. Iron-Based Superconductors

## 8. Summary

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Bersuker, I. The Jahn-Teller Effect, 1st ed.; Cambridge University Press: Cambridge, UK; New York, NY, USA, 2006. [Google Scholar]
- Kugel’, K.I.; Khomskiĭ, D.I. The Jahn-Teller effect and magnetism: Transition metal compounds. Sov. Phys. Uspekhi
**1982**, 25, 231–256. [Google Scholar] [CrossRef] - Sugano, S.; Tanabe, Y.; Kamimura, H. Multiplets of Transition-Metal Ions in Crystals; Number v. 33 in Pure and Applied Physics; Academic Press: New York, NY, USA, 1970. [Google Scholar]
- Moskvin, A. Atomy v Krystallah (Atoms in Crystals), 1st ed.; Ural Federal University: Ekaterinburg, Russia, 2018. (In Russian) [Google Scholar]
- Bednorz, J.G.; Müller, K.A. Possible highTc superconductivity in the Ba-La-Cu-O system. Z. Phys. B Condens. Matter
**1986**, 64, 189–193. [Google Scholar] [CrossRef] - Ionov, S.P.; Ionova, G.V.; Lubimov, V.S.; Makarov, E.F. Instability of Crystal Lattices with Respect to Electron Density Redistributions. Phys. Status Solidi (B)
**1975**, 71, 11–57. [Google Scholar] [CrossRef] - Anderson, P.W. Model for the Electronic Structure of Amorphous Semiconductors. Phys. Rev. Lett.
**1975**, 34, 953–955. [Google Scholar] [CrossRef] - Scheurell, S.; Scholz, F.; Olesch, T.; Kemnitz, E. Electrochemical evidence for Cu
^{3+}-Cu^{2+}-Cu^{+}transitions in the orthorhombic YBa_{2}Cu_{3}O_{7−x}phase. Supercond. Sci. Technol.**1992**, 5, 303–305. [Google Scholar] [CrossRef] - Larsson, S. Mixed valence model for superconductivity. Braz. J. Phys.
**2003**, 33, 744–749. [Google Scholar] [CrossRef] - Wilson, J.A. Again ‘why layered, square-planar, mixed-valent cuprates alone?’—Further pursuit of the ‘chemical’ negative-
**U**Route HTSC Mech. J. Phys. Condens. Matter**2000**, 12, R517–R547. [Google Scholar] [CrossRef] - Hirsch, J.E.; Scalapino, D.J. Double-valence-fluctuating molecules and superconductivity. Phys. Rev. B
**1985**, 32, 5639–5643. [Google Scholar] [CrossRef] - Sleight, A.W. Oxide Superconductors: A Chemist’s View. MRS Proc.
**1987**, 99, 3. [Google Scholar] [CrossRef] - Kulik, I.O.; Pedan, A.G. Phase transition in a model of superconducting glass. Sov. Phys. JETP
**1980**, 52, 742–748. [Google Scholar] - Rice, T.M.; Sneddon, L. Real-Space and $\overrightarrow{\mathrm{k}}$ -Space Electron Pairing in BaPb
_{1−x}Bi_{x}O_{3}. Phys. Rev. Lett.**1981**, 47, 689–692. [Google Scholar] [CrossRef] - David, W.I.F.; Harrison, W.T.A.; Gunn, J.M.F.; Moze, O.; Soper, A.K.; Day, P.; Jorgensen, J.D.; Hinks, D.G.; Beno, M.A.; Soderholm, L.; et al. Structure and crystal chemistry of the high-Tc superconductor YBa
_{2}Cu_{3}O_{7−x}. Nature**1987**, 327, 310–312. [Google Scholar] [CrossRef] - Varma, C.M. Missing valence states, diamagnetic insulators, and superconductors. Phys. Rev. Lett.
**1988**, 61, 2713–2716. [Google Scholar] [CrossRef] [PubMed] - Dzyaloshinskii, I.E. Chemical nature of the pairing of holes in high-temperature superconductors. JETP Lett.
**1989**, 49, 142–144. [Google Scholar] - Geballe, T.; Moyzhes, B.Y. Qualitative understanding of the highest Tc cuprates. Phys. C Supercond.
**2000**, 341–348, 1821–1824. [Google Scholar] [CrossRef] - Mitsen, K.V.; Ivanenko, O.M. Phase diagram of La
_{2–X}M_{x}CuO_{4}Key Underst. Nat. High- T_{c}Supercond. Phys.-Uspekhi**2004**, 47, 493–510. [Google Scholar] [CrossRef] - Tsendin, K.D.; Popov, B.P.; Denisov, D.V. Explanation of the phase diagram of high-temperature superconductors in terms of the model of negative- U Centres Supercond. Supercond. Sci. Technol.
**2006**, 19, 313–318. [Google Scholar] [CrossRef] - Katayama-Yoshida, H.; Kusakabe, K.; Kizaki, H.; Nakanishi, A. General Rule and Materials Design of Negative Effective U System High- T
_{c}Superconductivity. Appl. Phys. Express**2008**, 1, 081703. [Google Scholar] [CrossRef] - Pouchard, M.; Villesuzanne, A. Are Superconductivity Mechanisms a Matter for Chemists? Condens. Matter
**2020**, 5, 67. [Google Scholar] [CrossRef] - Mazin, I.I.; Khomskii, D.I.; Lengsdorf, R.; Alonso, J.A.; Marshall, W.G.; Ibberson, R.M.; Podlesnyak, A.; Martínez-Lope, M.J.; Abd-Elmeguid, M.M. Charge Ordering as Alternative to Jahn-Teller Distortion. Phys. Rev. Lett.
**2007**, 98, 176406. [Google Scholar] [CrossRef] - Ogg, R.A. Bose-Einstein Condensation of Trapped Electron Pairs. Phase Separation and Superconductivity of Metal-Ammonia Solutions. Phys. Rev.
**1946**, 69, 243–244. [Google Scholar] [CrossRef] - Schafroth, M.R. Superconductivity of a Charged Ideal Bose Gas. Phys. Rev.
**1955**, 100, 463–475. [Google Scholar] [CrossRef] - Alexandrov, A.S. High-temperature superconductivity: The explanation. Phys. Scr.
**2011**, 83, 038301. [Google Scholar] [CrossRef] - Müller, K.A. The Polaronic Basis for High-Temperature Superconductivity. J. Supercond. Nov. Magn.
**2017**, 30, 3007–3018. [Google Scholar] [CrossRef] - Pavuna, D.; Dubuis, G.; Bollinger, A.T.; Wu, J.; He, X.; Božović, I. On Local Pairs vs. BCS: Quo Vadis High- T
_{c}Superconductivity. J. Supercond. Nov. Magn.**2017**, 30, 731–734. [Google Scholar] [CrossRef] - Božović, I.; He, X.; Wu, J.; Bollinger, A.T. Dependence of the critical temperature in overdoped copper oxides on superfluid density. Nature
**2016**, 536, 309–311. [Google Scholar] [CrossRef] - Pelc, D.; Popčević, P.; Požek, M.; Greven, M.; Barišić, N. Unusual behavior of cuprates explained by heterogeneous charge localization. Sci. Adv.
**2019**, 5, eaau4538. [Google Scholar] [CrossRef] - Moskvin, A.S. Perspectives of disproportionation driven superconductivity in strongly correlated 3d compounds. J. Phys. Condens. Matter
**2013**, 25, 085601. [Google Scholar] [CrossRef] - Allen, P.B.; Perebeinos, V. Anti-Jahn-Teller polaron in LaMnO
_{3}. Phys. Rev. B**1999**, 60, 10747–10753. [Google Scholar] [CrossRef] - Feng, N.; Han, J.; Lin, C.; Ai, Z.; Lan, C.; Bi, K.; Lin, Y.; Xue, K.H.; Xu, B. Anti-Jahn-Teller effect induced ultrafast insulator to metal transition in perovskite BaBiO
_{3}. Npj Comput. Mater.**2022**, 8, 226. [Google Scholar] [CrossRef] - Kamimura, H.; Araidai, M.; Ishida, K.; Matsuno, S.; Sakata, H.; Shiraishi, K.; Sugino, O.; Tsai, J.S. First-Principles Calculation of Copper Oxide Superconductors That Supports the Kamimura-Suwa Model. Condens. Matter
**2020**, 5, 69. [Google Scholar] [CrossRef] - Moskvin, A.S.; Avvakumov, I.L. Why does the tetrahedrally coordinated Fe drive the superconductivity? In Proceedings of the III International Conference “Fundamental Problems of High-Temperature Superconductivity”, Moscow, Zvenigorod, 13–17 October 2008; p. 215. [Google Scholar]
- Larsson, S. Strong electron correlation and phonon coupling in high Tc superconductors. Phys. C Supercond.
**2007**, 460–462, 1063–1065. [Google Scholar] [CrossRef] - Alonso, J.A.; García-Muñoz, J.L.; Fernández-Díaz, M.T.; Aranda, M.A.G.; Martínez-Lope, M.J.; Casais, M.T. Charge Disproportionation in R NiO
_{3}Perovskites: Simultaneous Metal-Insulator and Structural Transition in YNiO_{3}. Phys. Rev. Lett.**1999**, 82, 3871–3874. [Google Scholar] [CrossRef] - Woodward, P.M.; Cox, D.E.; Moshopoulou, E.; Sleight, A.W.; Morimoto, S. Structural studies of charge disproportionation and magnetic order in CaFeO
_{3}. Phys. Rev. B**2000**, 62, 844–855. [Google Scholar] [CrossRef] - Uchiyama, H.; Baron, A.Q.R.; Tsutsui, S.; Tanaka, Y.; Hu, W.Z.; Yamamoto, A.; Tajima, S.; Endoh, Y. Softening of Cu-O Bond Stretching Phonons in Tetragonal HgBa
_{2}CuO_{4}+ δ. Phys. Rev. Lett.**2004**, 92, 197005. [Google Scholar] [CrossRef] [PubMed] - Vikhnin, V.S.; Kapphan, S.E. New type charge transfer states in ferroelectric oxides: Actual problems. Radiat. Eff. Defects Solids
**2002**, 157, 853–856. [Google Scholar] [CrossRef] - Mazumdar, S. Negative charge-transfer gap and even parity superconductivity in Sr
_{2}RuO_{4}. Phys. Rev. Res.**2020**, 2, 023382. [Google Scholar] [CrossRef] - Green, R.J.; Haverkort, M.W.; Sawatzky, G.A. Bond disproportionation and dynamical charge fluctuations in the perovskite rare-earth nickelates. Phys. Rev. B
**2016**, 94, 195127. [Google Scholar] [CrossRef] - Moskvin, A.; Panov, Y. Model of charge triplets for high- Tc cuprates. J. Magn. Magn. Mater.
**2022**, 550, 169004. [Google Scholar] [CrossRef] - Moskvin, A.; Panov, Y. Effective-Field Theory for Model High-Tc Cuprates. Condens. Matter
**2021**, 6, 24. [Google Scholar] [CrossRef] - Moskvin, A.S. Charge transfer excitons in HTSC cuprates and nickelates. Opt. I Spektrosk.
**2023**, 131, 491–501. [Google Scholar] [CrossRef] - Zener, C. Interaction between the d -Shells in the Transition Metals. II. Ferromagnetic Compounds of Manganese with Perovskite Structure. Phys. Rev.
**1951**, 82, 403–405. [Google Scholar] [CrossRef] - Merz, M.; Nücker, N.; Schuppler, S.; Arena, D.; Dvorak, J.; Idzerda, Y.U.; Ustinovich, S.N.; Soldatov, A.G.; Shiryaev, S.V.; Barilo, S.N. X-ray absorption of Ba
_{1−X}K_{x}BiO_{3}BaPb_{1−y}Bi_{y}O_{3}: Competition Bipolaronic Charg.-Density Wave States. Europhys. Lett. (EPL)**2005**, 72, 275–281. [Google Scholar] [CrossRef] - Chaillout, C.; Santoro, A.; Remeika, J.; Cooper, A.; Espinosa, G.; Marezio, M. Bismuth valence order-disorder study in BaBiO
_{3}by powder neutron diffraction. Solid State Commun.**1988**, 65, 1363–1369. [Google Scholar] [CrossRef] - Rodríguez-Carvajal, J.; Hennion, M.; Moussa, F.; Moudden, A.H.; Pinsard, L.; Revcolevschi, A. Neutron-diffraction study of the Jahn-Teller transition in stoichiometric LaMnO
_{3}. Phys. Rev. B**1998**, 57, R3189–R3192. [Google Scholar] [CrossRef] - Huang, Q.; Santoro, A.; Lynn, J.W.; Erwin, R.W.; Borchers, J.A.; Peng, J.L.; Greene, R.L. Structure and magnetic order in undoped lanthanum manganite. Phys. Rev. B
**1997**, 55, 14987–14999. [Google Scholar] [CrossRef] - Moskvin, A.S. Disproportionation and electronic phase separation in parent manganite LaMnO
_{3}. Phys. Rev. B**2009**, 79, 115102. [Google Scholar] [CrossRef] - Moskvin, A.S.; Ovanesyan, N.S.; Trukhtanov, V.A. Angular dependence of the superexchange interaction Fe
^{3}+-O^{2−}-Cr^{3+}. Hyperfine Interact.**1975**, 1, 265–281. [Google Scholar] [CrossRef] - Moskvin, A.S. Dzyaloshinskii Interaction and Exchange-Relativistic Effects in Orthoferrites. J. Exp. Theor. Phys.
**2021**, 132, 517–547. [Google Scholar] [CrossRef] - Moskvin, A. Structure–Property Relationships for Weak Ferromagnetic Perovskites. Magnetochemistry
**2021**, 7, 111. [Google Scholar] [CrossRef] - Alonso, J.A.; Martínez-Lope, M.J.; Casais, M.T.; Fernández-Díaz, M.T. Evolution of the Jahn-Teller Distortion of MnO
_{6}Octahedra in RMnO_{3}Perovskites (R = Pr, Nd, Dy, Tb, Ho, Er, Y): A Neutron Diffraction Study. Inorg. Chem.**2000**, 39, 917–923. [Google Scholar] [CrossRef] - Pangburn, E.; Banerjee, A.; Freire, H.; Pépin, C. Incoherent transport in a model for the strange metal phase: Memory-matrix formalism. Phys. Rev. B
**2023**, 107, 245109. [Google Scholar] [CrossRef] - Moskvin, A.S.; Panov, Y.D. Nature of the Pseudogap Phase of HTSC Cuprates. Phys. Solid State
**2020**, 62, 1554–1561. [Google Scholar] [CrossRef] - Moskvin, A.S.; Panov, Y.D. Phase separation in high-T
_{c}cuprates. J. Phys. Conf. Ser.**2022**, 2164, 012014. [Google Scholar] [CrossRef] - Gong, W.; Greedan, J.; Liu, G.; Bjorgvinsson, M. Crystal structure and magnetic properties of orthorhombic Sr
_{2}VO_{4}with tetrahedral vanadium (IV). J. Solid State Chem.**1991**, 95, 213–219. [Google Scholar] [CrossRef] - Deisenhofer, J.; Schaile, S.; Teyssier, J.; Wang, Z.; Hemmida, M.; Von Nidda, H.A.K.; Eremina, R.M.; Eremin, M.V.; Viennois, R.; Giannini, E.; et al. Electron spin resonance and exchange paths in the orthorhombic dimer system Sr
_{2}VO_{4}. Phys. Rev. B**2012**, 86, 214417. [Google Scholar] [CrossRef] - Wang, Z.; Kamenskyi, D.; Cépas, O.; Schmidt, M.; Quintero-Castro, D.L.; Islam, A.T.M.N.; Lake, B.; Aczel, A.A.; Dabkowska, H.A.; Dabkowski, A.B.; et al. High-field electron spin resonance spectroscopy of singlet-triplet transitions in the spin-dimer systems Sr
_{3}Cr_{2}O_{8}and Ba_{3}Cr_{2}O_{8}. Phys. Rev. B**2014**, 89, 174406. [Google Scholar] [CrossRef] - Barone, P.; Yamauchi, K.; Picozzi, S. Jahn-Teller distortions as a novel source of multiferroicity. Phys. Rev. B
**2015**, 92, 014116. [Google Scholar] [CrossRef] - Hepting, M. The Rare-Earth Nickelates. In Ordering Phenomena in Rare-Earth Nickelate Heterostructures; Series Title: Springer Theses; Springer International Publishing: Cham, Switzerland, 2017; pp. 13–29. [Google Scholar] [CrossRef]
- Chaloupka, J.; Khaliullin, G. Orbital Order and Possible Superconductivity in LaNiO
_{3}/LaMO_{3}Superlattices. Phys. Rev. Lett.**2008**, 100, 016404. [Google Scholar] [CrossRef] - Gawryluk, D.J.; Klein, Y.M.; Shang, T.; Sheptyakov, D.; Keller, L.; Casati, N.; Lacorre, P.; Fernández-Díaz, M.T.; Rodríguez-Carvajal, J.; Medarde, M. Distortion mode anomalies in bulk PrNiO
_{3}: Illustrating the potential of symmetry-adapted distortion mode analysis for the study of phase transitions. Phys. Rev. B**2019**, 100, 205137. [Google Scholar] [CrossRef] - Kumar, D.; Rajeev, K.P.; Alonso, J.A.; Martínez-Lope, M.J. Spin-canted magnetism and decoupling of charge and spin ordering in NdNiO
_{3}. Phys. Rev. B**2013**, 88, 014410. [Google Scholar] [CrossRef] - Bousquet, E.; Cano, A. Non-collinear magnetism & multiferroicity: The perovskite case. Phys. Sci. Rev.
**2023**, 8, 479–508. [Google Scholar] [CrossRef] - Zhang, J.; Zheng, H.; Ren, Y.; Mitchell, J.F. High-Pressure Floating-Zone Growth of Perovskite Nickelate LaNiO
_{3}Single Crystals. Cryst. Growth Des.**2017**, 17, 2730–2735. [Google Scholar] [CrossRef] - Guo, H.; Li, Z.W.; Zhao, L.; Hu, Z.; Chang, C.F.; Kuo, C.Y.; Schmidt, W.; Piovano, A.; Pi, T.W.; Sobolev, O.; et al. Antiferromagnetic correlations in the metallic strongly correlated transition metal oxide LaNiO
_{3}. Nat. Commun.**2018**, 9, 43. [Google Scholar] [CrossRef] [PubMed] - Shamblin, J.; Heres, M.; Zhou, H.; Sangoro, J.; Lang, M.; Neuefeind, J.; Alonso, J.A.; Johnston, S. Experimental evidence for bipolaron condensation as a mechanism for the metal–insulator transition in rare-earth nickelates. Nat. Commun.
**2018**, 9, 86. [Google Scholar] [CrossRef] [PubMed] - Li, B.; Louca, D.; Yano, S.; Marshall, L.G.; Zhou, J.; Goodenough, J.B. Insulating Pockets in Metallic LaNiO
_{3}. Adv. Electron. Mater.**2016**, 2, 1500261. [Google Scholar] [CrossRef] - Wawrzyńska, E.; Coldea, R.; Wheeler, E.M.; Mazin, I.I.; Johannes, M.D.; Sörgel, T.; Jansen, M.; Ibberson, R.M.; Radaelli, P.G. Orbital Degeneracy Removed by Charge Order in Triangular Antiferromagnet AgNiO
_{2}. Phys. Rev. Lett.**2007**, 99, 157204. [Google Scholar] [CrossRef] - Chen, H.; Freeman, C.L.; Harding, J.H. Charge disproportionation and Jahn-Teller distortion in LiNiO
_{2}and NaNiO_{2}: A density functional theory study. Phys. Rev. B**2011**, 84, 085108. [Google Scholar] [CrossRef] - Zhang, F.C.; Rice, T.M. Effective Hamiltonian for the superconducting Cu oxides. Phys. Rev. B
**1988**, 37, 3759–3761. [Google Scholar] [CrossRef] - Moskvin, A.S. True charge-transfer gap in parent insulating cuprates. Phys. Rev. B
**2011**, 84, 075116. [Google Scholar] [CrossRef] - Moskvin, A.S.; Panov, Y.D. Topological Structures in Unconventional Scenario for 2D Cuprates. J. Supercond. Nov. Magn.
**2019**, 32, 61–84. [Google Scholar] [CrossRef] - Moskvin, A.S.; Panov, Y.D. Electron–Hole Dimers in the Parent Phase of Quasi–2D Cuprates. Phys. Solid State
**2019**, 61, 1553–1558. [Google Scholar] [CrossRef] - Moskvin, A.S. Large Variety of the On-Site Order Parameters and Phase States in Quasi-2D HTSC Cuprates. Phys. Met. Metallogr.
**2019**, 120, 1252–1259. [Google Scholar] [CrossRef] - Naito, M.; Krockenberger, Y.; Ikeda, A.; Yamamoto, H. Reassessment of the electronic state, magnetism, and superconductivity in high-Tc cuprates with the Nd
_{2}CuO_{4}structure. Phys. C Supercond. Its Appl.**2016**, 523, 28–54. [Google Scholar] [CrossRef] - Li, D.; Lee, K.; Wang, B.Y.; Osada, M.; Crossley, S.; Lee, H.R.; Cui, Y.; Hikita, Y.; Hwang, H.Y. Superconductivity in an infinite-layer nickelate. Nature
**2019**, 572, 624–627. [Google Scholar] [CrossRef] - Panov, Y.D. Critical Temperatures of a Model Cuprate. Phys. Met. Metallogr.
**2019**, 120, 1276–1281. [Google Scholar] [CrossRef] - Fischer, P.; Roult, G.; Schwarzenbach, D. Crystal and magnetic structure of silver difluoride-II. Weak 4d-ferromagnetism of AgF
_{2}. J. Phys. Chem. Solids**1971**, 32, 1641–1647. [Google Scholar] [CrossRef] - Derzsi, M.; Tokár, K.; Piekarz, P.; Grochala, W. Charge ordering mechanism in silver difluoride. Phys. Rev. B
**2022**, 105, L081113. [Google Scholar] [CrossRef] - Bachar, N.; Koteras, K.; Gawraczynski, J.; Trzciński, W.; Paszula, J.; Piombo, R.; Barone, P.; Mazej, Z.; Ghiringhelli, G.; Nag, A.; et al. Charge-Transfer and d d excitations in AgF
_{2}. Phys. Rev. Res.**2022**, 4, 023108. [Google Scholar] [CrossRef] - Shen, C.; Žemva, B.; Lucier, G.M.; Graudejus, O.; Allman, J.A.; Bartlett, N. Disproportionation of Ag(II) to Ag(I) and Ag(III) in Fluoride Systems and Syntheses and Structures of (AgF
^{+})_{2}AgF_{4}^{−}MF_{6}^{−}Salts (M = As, Sb, Pt, Au, Ru). Inorg. Chem.**1999**, 38, 4570–4577. [Google Scholar] [CrossRef] - Tokár, K.; Derzsi, M.; Grochala, W. Comparative computational study of antiferromagnetic and mixed-valent diamagnetic phase of AgF
_{2}: Crystal, electronic and phonon structure and p-T phase diagram. Comput. Mater. Sci.**2021**, 188, 110250. [Google Scholar] [CrossRef] - Scatturin, V.; Bellon, P.L.; Salkind, A.J. The Structure of Silver Oxide Determined by Means of Neutron Diffraction. J. Electrochem. Soc.
**1961**, 108, 819. [Google Scholar] [CrossRef] - Allen, J.P.; Scanlon, D.O.; Watson, G.W. Electronic structures of silver oxides. Phys. Rev. B
**2011**, 84, 115141. [Google Scholar] [CrossRef] - Hirschfeld, P.J. Using gap symmetry and structure to reveal the pairing mechanism in Fe-based superconductors. Comptes Rendus Phys.
**2016**, 17, 197–231. [Google Scholar] [CrossRef] - Dong, S.; Yu, R.; Yunoki, S.; Liu, J.M.; Dagotto, E. Double-exchange model study of multiferroic RMnO
_{3}perovskites. Eur. Phys. J. B**2009**, 71, 339–344. [Google Scholar] [CrossRef] - Stout, J.W.; DeLassus, P.; Graham, C.D.; Rhyne, J.J. CrF
_{2}, A Canted Antiferromagnet. AIP Conf. Proc.**1972**, 5, 669. [Google Scholar] [CrossRef] - Jiménez-Mier, J.; Olalde-Velasco, P.; Yang, W.L.; Denlinger, J. X-ray absorption and resonant inelastic x-ray scattering (RIXS) show the presence of Cr
^{+}at the surface and in the bulk of CrF_{2}. In Proceedings of the AIP Conference Proceedings, Ciudad Juárez, Mexico, 4–6 March 2015; p. 020002. [Google Scholar] [CrossRef] - Raffaelle, R.; Anderson, H.U.; Sparlin, D.M.; Parris, P.E. Transport anomalies in the high-temperature hopping conductivity and thermopower of Sr-doped La(Cr,Mn)O
_{3}. Phys. Rev. B**1991**, 43, 7991–7999. [Google Scholar] [CrossRef] - Van Roosmalen, J.; Cordfunke, E. The Defect Chemistry of LaMnO
_{3±δ}. J. Solid State Chem.**1994**, 110, 109–112. [Google Scholar] [CrossRef] - Zhou, J.S.; Goodenough, J.B. Paramagnetic phase in single-crystal LaMnO
_{3}. Phys. Rev. B**1999**, 60, R15002–R15004. [Google Scholar] [CrossRef] - Ritter, C.; Ibarra, M.R.; De Teresa, J.M.; Algarabel, P.A.; Marquina, C.; Blasco, J.; García, J.; Oseroff, S.; Cheong, S.W. Influence of oxygen content on the structural, magnetotransport, and magnetic properties of LaMnO
_{3+δ}. Phys. Rev. B**1997**, 56, 8902–8911. [Google Scholar] [CrossRef] - Kim, Y.J. p-Wave Pairing and Colossal Magnetoresistance in Manganese Oxides. Mod. Phys. Lett. B
**1998**, 12, 507–518. [Google Scholar] [CrossRef] - Krivoruchko, V.N. Local spin-triplet superconductivity in half-metallic manganites: A perspective platform for high-temperature topological superconductivity. Low Temp. Phys.
**2021**, 47, 901–907. [Google Scholar] [CrossRef] - Markovich, V.; Fita, I.; Wisniewski, A.; Puzniak, R.; Mogilyansky, D.; Titelman, L.; Vradman, L.; Herskowitz, M.; Gorodetsky, G. Metastable diamagnetic response of 20 nm La
_{1−x}MnO_{3}particles. Phys. Rev. B**2008**, 77, 014423. [Google Scholar] [CrossRef] - Kasai, M.; Ohno, T.; Kanke, Y.; Kozono, Y.; Hanazono, M.; Sugita, Y. Current-Voltage Characteristics of YBa
_{2}Cu_{3}O_{y}/La_{0.7}Ca_{0.3}MnO_{z}/YBa_{2}Cu_{3}O_{y}Trilayered-Type Junctions. Jpn. J. Appl. Phys.**1990**, 29, L2219. [Google Scholar] [CrossRef] - Mitin, A.; Kuz’micheva, G.; Novikova, S. Mixed Oxides of Manganese with Perovskite and Perovskite-related Structures. Russ. J. Inorg. Chem.
**1997**, 42, 1791. [Google Scholar] [CrossRef] - Nath, R.; Raychaudhuri, A.K.; Mukovskii, Y.M.; Mondal, P.; Bhattacharya, D.; Mandal, P. Electric field driven destabilization of the insulating state in nominally pure LaMnO
_{3}. J. Phys. Condens. Matter**2013**, 25, 155605. [Google Scholar] [CrossRef] - Cabassi, R.; Bolzoni, F.; Gilioli, E.; Bissoli, F.; Prodi, A.; Gauzzi, A. Jahn-Teller-induced crossover of the paramagnetic response in the singly valent e
_{g}system LaMn_{7}O_{12}. Phys. Rev. B**2010**, 81, 214412. [Google Scholar] [CrossRef] - Schaile, S.; Von Nidda, H.A.K.; Deisenhofer, J.; Loidl, A.; Nakajima, T.; Ueda, Y. Korringa-like relaxation in the high-temperature phase of A -site ordered YBaMn
_{2}O_{6}. Phys. Rev. B**2012**, 85, 205121. [Google Scholar] [CrossRef] - Takano, M.; Nakanishi, N.; Takeda, Y.; Naka, S.; Takada, T. Charge disproportionation in CaFeO
_{3}studied with the Mössbauer effect. Mater. Res. Bull.**1977**, 12, 923–928. [Google Scholar] [CrossRef] - Takeda, T.; Kanno, R.; Kawamoto, Y.; Takano, M.; Kawasaki, S.; Kamiyama, T.; Izumi, F. Metal–semiconductor transition, charge disproportionation, and low-temperature structure of Ca
_{1-x}Sr_{x}FeO_{3}synthesized under high-oxygen pressure. Solid State Sci.**2000**, 2, 673–687. [Google Scholar] [CrossRef] - Reehuis, M.; Ulrich, C.; Maljuk, A.; Niedermayer, C.; Ouladdiaf, B.; Hoser, A.; Hofmann, T.; Keimer, B. Neutron diffraction study of spin and charge ordering in SrFeO
_{3−δ}. Phys. Rev. B**2012**, 85, 184109. [Google Scholar] [CrossRef] - Chakraverty, S.; Matsuda, T.; Ogawa, N.; Wadati, H.; Ikenaga, E.; Kawasaki, M.; Tokura, Y.; Hwang, H.Y. BaFeO
_{3}cubic single crystalline thin film: A ferromagnetic insulator. Appl. Phys. Lett.**2013**, 103, 142416. [Google Scholar] [CrossRef] - Fujioka, J.; Ishiwata, S.; Kaneko, Y.; Taguchi, Y.; Tokura, Y. Variation of charge dynamics upon the helimagnetic and metal–insulator transitions for perovskite AFeO
_{3}(A = Sr and Ca). Phys. Rev. B**2012**, 85, 155141. [Google Scholar] [CrossRef] - Kuzushita, K.; Morimoto, S.; Nasu, S.; Nakamura, S. Charge Disproportionation and Antiferromagnetic Order of Sr
_{3}Fe_{2}O_{7}. J. Phys. Soc. Jpn.**2000**, 69, 2767–2770. [Google Scholar] [CrossRef] - Kim, J.H.; Peets, D.C.; Reehuis, M.; Adler, P.; Maljuk, A.; Ritschel, T.; Allison, M.C.; Geck, J.; Mardegan, J.R.L.; Bereciartua Perez, P.J.; et al. Hidden Charge Order in an Iron Oxide Square-Lattice Compound. Phys. Rev. Lett.
**2021**, 127, 097203. [Google Scholar] [CrossRef] - Adler, P. Properties of K
_{2}NiF_{4}-Type Oxides Sr_{2}FeO_{4}. J. Solid State Chem.**1994**, 108, 275–283. [Google Scholar] [CrossRef] - Adler, P.; Reehuis, M.; Stüßer, N.; Medvedev, S.A.; Nicklas, M.; Peets, D.C.; Bertinshaw, J.; Christensen, C.K.; Etter, M.; Hoser, A.; et al. Spiral magnetism, spin flop, and pressure-induced ferromagnetism in the negative charge-transfer-gap insulator Sr
_{2}FeO_{4}. Phys. Rev. B**2022**, 105, 054417. [Google Scholar] [CrossRef] - Itoh, M.; Shikano, M.; Shimura, T. High- and low-spin transition of Ru
^{4+}in the perovskite-related layered system Sr_{n+1}Ru_{n}O_{3n+1}(N = 1, 2, ∞) Change n. Phys. Rev. B**1995**, 51, 16432–16435. [Google Scholar] [CrossRef] - Grutter, A.J.; Wong, F.J.; Arenholz, E.; Vailionis, A.; Suzuki, Y. Evidence of high-spin Ru and universal magnetic anisotropy in SrRuO
_{3}thin films. Phys. Rev. B**2012**, 85, 134429. [Google Scholar] [CrossRef] - Cao, G.; Song, W.; Sun, Y.; Lin, X. Violation of the Mott–Ioffe–Regel limit: High-temperature resistivity of itinerant magnets Sr
_{n+1}Ru_{n}O_{3n+1}(n = 2,3,∞) and CaRuO_{3}. Solid State Commun.**2004**, 131, 331–336. [Google Scholar] [CrossRef] - Nakatsuji, S.; Maeno, Y. Quasi-Two-Dimensional Mott Transition System Ca
_{2−x}Sr_{x}RuO_{4}. Phys. Rev. Lett.**2000**, 84, 2666–2669. [Google Scholar] [CrossRef] [PubMed] - Nobukane, H.; Yanagihara, K.; Kunisada, Y.; Ogasawara, Y.; Isono, K.; Nomura, K.; Tanahashi, K.; Nomura, T.; Akiyama, T.; Tanda, S. Co-appearance of superconductivity and ferromagnetism in a Ca
_{2}RuO_{4}nanofilm crystal. Sci. Rep.**2020**, 10, 3462. [Google Scholar] [CrossRef] [PubMed] - Maeno, Y.; Hashimoto, H.; Yoshida, K.; Nishizaki, S.; Fujita, T.; Bednorz, J.G.; Lichtenberg, F. Superconductivity in a layered perovskite without copper. Nature
**1994**, 372, 532–534. [Google Scholar] [CrossRef] - Mackenzie, A.P.; Maeno, Y. The superconductivity of Sr
_{2}RuO_{4}and the physics of spin-triplet pairing. Rev. Mod. Phys.**2003**, 75, 657–712. [Google Scholar] [CrossRef] - Mackenzie, A.P.; Scaffidi, T.; Hicks, C.W.; Maeno, Y. Even odder after twenty-three years: The superconducting order parameter puzzle of Sr
_{2}RuO_{4}. Npj Quantum Mater.**2017**, 2, 40. [Google Scholar] [CrossRef] - Leggett, A.J.; Liu, Y. Symmetry Properties of Superconducting Order Parameter in Sr
_{2}RuO_{4}: A Brief Review. J. Supercond. Nov. Magn.**2021**, 34, 1647–1673. [Google Scholar] [CrossRef] - Ruf, J.P.; Paik, H.; Schreiber, N.J.; Nair, H.P.; Miao, L.; Kawasaki, J.K.; Nelson, J.N.; Faeth, B.D.; Lee, Y.; Goodge, B.H.; et al. Strain-stabilized superconductivity. Nat. Commun.
**2021**, 12, 59. [Google Scholar] [CrossRef] - Uchida, M.; Nomoto, T.; Musashi, M.; Arita, R.; Kawasaki, M. Superconductivity in Uniquely Strained RuO
_{2}Films. Phys. Rev. Lett.**2020**, 125, 147001. [Google Scholar] [CrossRef] - Stewart, G.R. Superconductivity in iron compounds. Rev. Mod. Phys.
**2011**, 83, 1589–1652. [Google Scholar] [CrossRef] - Chubukov, A.; Hirschfeld, P.J. Iron-based superconductors, seven years later. Phys. Today
**2015**, 68, 46–52. [Google Scholar] [CrossRef] - Si, Q.; Yu, R.; Abrahams, E. High-temperature superconductivity in iron pnictides and chalcogenides. Nat. Rev. Mater.
**2016**, 1, 16017. [Google Scholar] [CrossRef] - Kreisel, A.; Hirschfeld, P.; Andersen, B. On the Remarkable Superconductivity of FeSe and Its Close Cousins. Symmetry
**2020**, 12, 1402. [Google Scholar] [CrossRef] - Carlo, J.P.; Uemura, Y.J.; Goko, T.; MacDougall, G.J.; Rodriguez, J.A.; Yu, W.; Luke, G.M.; Dai, P.; Shannon, N.; Miyasaka, S.; et al. Static Magnetic Order and Superfluid Density of R FeAs (O, F) (R = La, Nd, Ce) and LaFePO Studied by Muon Spin Relaxation: Unusual Similarities with the Behavior of Cuprate Superconductors. Phys. Rev. Lett.
**2009**, 102, 087001. [Google Scholar] [CrossRef] [PubMed] - Adamski, A.; Krellner, C.; Abdel-Hafiez, M. Signature of multigap nodeless superconductivity in fluorine-doped NdFeAsO. Phys. Rev. B
**2017**, 96, 100503. [Google Scholar] [CrossRef] - Liu, J.; Savici, A.T.; Granroth, G.E.; Habicht, K.; Qiu, Y.; Hu, J.; Mao, Z.Q.; Bao, W. A Triplet Resonance in Superconducting Fe
_{1.03}Se_{0.4}Te_{0.6}. Chin. Phys. Lett.**2018**, 35, 127401. [Google Scholar] [CrossRef] - Xie, T.; Gong, D.; Ghosh, H.; Ghosh, A.; Soda, M.; Masuda, T.; Itoh, S.; Bourdarot, F.; Regnault, L.P.; Danilkin, S.; et al. Neutron Spin Resonance in the 112-Type Iron-Based Superconductor. Phys. Rev. Lett.
**2018**, 120, 137001. [Google Scholar] [CrossRef] - Lee, P.A.; Wen, X.G. Spin-triplet p -wave pairing in a three-orbital model for iron pnictide superconductors. Phys. Rev. B
**2008**, 78, 144517. [Google Scholar] [CrossRef] - Baek, S.H.; Grafe, H.J.; Hammerath, F.; Fuchs, M.; Rudisch, C.; Harnagea, L.; Aswartham, S.; Wurmehl, S.; Van Den Brink, J.; Büchner, B.
^{75}As NMR-NQR study in superconducting LiFeAs. Eur. Phys. J. B**2012**, 85, 159. [Google Scholar] [CrossRef] - Hänke, T.; Sykora, S.; Schlegel, R.; Baumann, D.; Harnagea, L.; Wurmehl, S.; Daghofer, M.; Büchner, B.; van den Brink, J.; Hess, C. Probing the Unconventional Superconducting State of LiFeAs by Quasiparticle Interference. Phys. Rev. Lett.
**2012**, 108, 127001. [Google Scholar] [CrossRef] - Brydon, P.M.R.; Daghofer, M.; Timm, C.; Van Den Brink, J. Theory of magnetism and triplet superconductivity in LiFeAs. Phys. Rev. B
**2011**, 83, 060501. [Google Scholar] [CrossRef] - Brand, J.; Stunault, A.; Wurmehl, S.; Harnagea, L.; Büchner, B.; Meven, M.; Braden, M. Spin susceptibility in superconducting LiFeAs studied by polarized neutron diffraction. Phys. Rev. B
**2014**, 89, 045141. [Google Scholar] [CrossRef] - Gifford, J.A.; Chen, B.B.; Zhang, J.; Zhao, G.J.; Kim, D.R.; Li, B.C.; Wu, D.; Chen, T.Y. Determination of spin polarization using an unconventional iron superconductor. AIP Adv.
**2016**, 6, 115023. [Google Scholar] [CrossRef] - Hirsch, J.E. Why only hole conductors can be superconductors. In Proceedings of the Oxide-Based Materials and Devices VIII, San Francisco, CA, USA, 29 January–1 February 2017; p. 101051V. [Google Scholar] [CrossRef]
- Hirsch, J.; Marsiglio, F. Understanding electron-doped cuprate superconductors as hole superconductors. Phys. C Supercond. Its Appl.
**2019**, 564, 29–37. [Google Scholar] [CrossRef]

**Figure 1.**(Color online): Spin structure of the EH dimer, or self-trapped CT exciton with a step-by-step inclusion of the one- and two-particle charge transfer. Arrows point to electric dipole moments for bare site-centered dimer configurations.

**Figure 2.**(Color online): Angular dependencies of $J\left({d}^{5}{d}^{3}\right)$ and $\frac{1}{10}\left|{t}_{B}\right|$, which define the effective integral ${J}_{eff}=J\left({d}^{5}{d}^{3}\right)-0.1\left|{t}_{B}\right|$.

**Figure 3.**(Color online): Model phase T - n-diagrams of hole-doped CuO${}_{2}$/NiO${}_{2}$ planes in cuprates/nickelates calculated in the effective field approximation ($n=p$ for hole doping), with the phase separation taken into account using Maxwell’s construction; J is the exchange integral, $\Delta =U/2$ is the local correlation parameter, V is the nonlocal correlation parameter, ${t}_{p},{t}_{n},{t}_{pn}$ are three independent integrals of the correlated single-particle transfer, ${t}_{B}$ is the effective transfer integral of the composite boson (see insets), assuming competition between “monophases” NO (disordered), AFMI, BS, FL, and CO. The boundaries between the phases represent lines of equal free energies. The dashed curves (

**a**–

**d**) indicate the lines of equal volume fractions of two neighboring phases, the yellow curves represent the lines of phase transitions of the “third” kind, limiting the regions with maximal 100% volume fractions of one of the phases. See Refs. [43,44] for more details. Pay attention to the strong change in the phase diagram, even with a very small change in the parameters of the Hamiltonian (compare panels

**a**–

**c**).

JT Configuration JT Ions | Symm. | LS/HS | Local Boson | Lattice | Representative Compounds |
---|---|---|---|---|---|

$3{d}^{1}$(${e}_{g}^{1}$):${}^{2}E$ Ti${}^{3+}$, V${}^{4+}$, Cr${}^{5+}$ | tetra | - | ${e}_{g}^{2}$:${}^{3}{A}_{2g}$ s = 1 | A${}_{1g}$ S = 0 | $\beta $-Sr${}_{2}$VO${}_{4}$ (Sr,Ba)${}_{3}$Cr${}_{2}$O${}_{8}$ |

$3{d}^{3}$(${e}_{g}^{3}$):${}^{2}E$ V${}^{2+}$, Cr${}^{3+}$, Mn${}^{4+}$ | tetra | LS | ${\underline{e}}_{g}^{2}$:${}^{3}{A}_{2g}$ s = 1 | A${}_{1g}$ S = 0 | Ba${}_{2}$VGe${}_{2}$O${}_{7}$ (?) |

$3{d}^{4}$(${t}_{2g}^{3}{e}_{g}^{1}$):${}^{5}E$ Cr${}^{2+}$, Mn${}^{3+}$, Fe${}^{4+}$ | octa | HS | ${e}_{g}^{2}$:${}^{3}{A}_{2g}$ s = 1 | A${}_{2g}$ S = 3/2 | CrO, CrF${}_{2}$ Sr${}_{2}$FeO${}_{4}$ (Ca,Sr,Ba)FeO${}_{3}$ (Ca,Sr,Ba)${}_{3}$Fe${}_{2}$O${}_{7}$ RMnO${}_{3}$, LaMn${}_{7}$O${}_{12}$ |

$4{d}^{4}$(${t}_{2g}^{3}{e}_{g}^{1}$):${}^{5}E$ Ru${}^{4+}$ | octa | HS | ${e}_{g}^{2}$:${}^{3}{A}_{2g}$ s = 1 | A${}_{2g}$ S = 3/2 | (Ca,Sr)${}_{2}$RuO${}_{4}$ (Ca,Sr)RuO${}_{3}$, RuO${}_{2}$ (Ca,Sr)${}_{3}$Ru${}_{2}$O${}_{7}$ |

$3{d}^{6}$(${e}_{g}^{3}{t}_{2g}^{3}$):${}^{5}E$ Fe${}^{2+}$, Co${}^{3+}$ | tetra | HS | ${\underline{e}}_{g}^{2}$:${}^{3}{A}_{2g}$ s = 1 | A${}_{2g}$ S = 3/2 | FePn, FeCh, Na${}_{5}$CoO${}_{4}$ |

$3{d}^{7}$(${t}_{2g}^{6}{e}_{g}^{1}$):${}^{2}E$ Co${}^{2+}$, Ni${}^{3+}$ | octa | LS | ${e}_{g}^{2}$:${}^{3}{A}_{2g}$ s = 1 | A${}_{1g}$ S = 0 | RNiO${}_{3}$ (Li,Na,Ag)NiO${}_{2}$ |

$3{d}^{9}$(${t}_{2g}^{6}{e}_{g}^{3}$):${}^{2}E$ Cu${}^{2+}$, Ni${}^{+}$ | octa | - | ${\underline{e}}_{g}^{2}$:${}^{3}{A}_{2g}$ s = 1 | A${}_{1g}$ S = 0 | CuF${}_{2}$, KCuF${}_{3}$, K${}_{2}$CuF${}_{4}$ |

$4{d}^{9}$(${t}_{2g}^{6}{e}_{g}^{3}$):${}^{2}E$ Pd${}^{+}$, Ag${}^{2+}$ | octa | - | ${\underline{e}}_{g}^{2}$:${}^{3}{A}_{2g}$ s = 1 | A${}_{1g}$ S = 0 | AgO (Ag${}^{1+}$Ag${}^{3+}$O${}_{2}$) |

$3{d}^{9}$(${t}_{2g}^{6}{e}_{g}^{3}$):${}^{2}{B}_{1g}$ Cu${}^{2+}$, Ni${}^{+}$ | octa*square | - | ${\underline{b}}_{1g}^{2}$:${}^{1}{A}_{1g}$ s = 0 | A${}_{1g}$ S = 0 | HTSC cuprates RNiO${}_{2}$, CuO |

$4{d}^{9}$(${t}_{2g}^{6}{e}_{g}^{3}$):${}^{2}{B}_{1g}$ Pd${}^{+}$, Ag${}^{2+}$ | octa*square | - | ${\underline{b}}_{1g}^{2}$:${}^{1}{A}_{1g}$ s = 0 | A${}_{1g}$ S = 0 | AgF${}_{2}$, KAgF${}_{3}$ Cs${}_{2}$AgF${}_{4}$, LaPdO${}_{2}$ (?) |

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Moskvin, A.
Jahn–Teller Magnets. *Magnetochemistry* **2023**, *9*, 224.
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Jahn–Teller Magnets. *Magnetochemistry*. 2023; 9(11):224.
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2023. "Jahn–Teller Magnets" *Magnetochemistry* 9, no. 11: 224.
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