Recognition: unknown
Coupled phase transitions in crystalline solids with extreme chemical disorder
Pith reviewed 2026-05-07 16:08 UTC · model grok-4.3
The pith
Compositionally complex oxides undergo coupled symmetry-lowering phase transitions despite extreme chemical disorder.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
In the five-cation spinel [Mn0.2Co0.2Ni0.2Cu0.2Zn0.2]Cr2O4, an orbital-driven structural transition occurs at 100 K and a magnetism-driven transition at 40 K. Both nickel and copper are required; local-structure measurements show distinct and opposing distortions around these two cations while manganese, cobalt and zinc remain largely undistorted. The transitions therefore arise from cooperation via competition among the local distortions inside an otherwise disordered A-site lattice.
What carries the argument
Cooperation via competition among opposing local Jahn-Teller distortions around nickel and copper in the chemically disordered A-site of the spinel lattice, which collectively lowers the global symmetry.
If this is right
- Targeted inclusion of multiple Jahn-Teller active cations can be used to induce symmetry-lowering transitions in other high-entropy oxides.
- Local-structure measurements become essential for uncovering hidden cooperative mechanisms in chemically disordered materials.
- The same competition mechanism can couple structural changes to magnetic or electronic properties at higher temperatures by altering the cation set.
- Design rules for complex oxides now include deliberate use of local-distortion competition beyond average-symmetry constraints.
Where Pith is reading between the lines
- The approach could be extended to other crystal families such as perovskites or pyrochlores to test whether the cooperation mechanism is general to high-entropy systems.
- Quantitative modeling of the energy balance between competing distortions might allow prediction of transition temperatures for chosen cation combinations.
- Functional properties such as magnetoelectric coupling or ionic conductivity could be engineered in these disordered lattices by stabilizing the low-symmetry phases.
Load-bearing premise
The transitions are genuinely produced by coupled orbital and magnetic degrees of freedom acting through local distortions rather than by undetected long-range cation ordering or measurement artifacts.
What would settle it
If high-resolution diffraction or local probes detect long-range A-site cation ordering, or if the transitions disappear in samples containing only one of nickel or copper while overall composition is held fixed, the claim that disorder itself hosts the coupled transitions would be falsified.
Figures
read the original abstract
Structural phase transitions often couple to magnetic and electronic degrees of freedom, enabling emergent phenomena in solids. In high-entropy oxides (HEOs), which typically stabilize in highly symmetric cubic phases, such transitions are considered rare due to the extreme chemical disorder-analogous to the behavior observed in high-entropy alloys. This raises a fundamental question: can the rich physics of coupled phase transitions persist in such disordered systems? Here, we show that targeted design of compositionally complex oxides (CCOs) can trigger symmetry-lowering transitions, with spinel-type materials serving as a representative case. For instance, [Mn$_{0.2}$Co$_{0.2}$Ni$_{0.2}$Cu$_{0.2}$Zn$_{0.2}$]Cr$_2$O$_4$, having two Jahn-Teller (J-T) active ions, undergoes two successive coupled structural transitions upon cooling: an orbital-driven transition at 100 K and a magnetism-driven transition at 40 K. Systematic substitution of $A$-site cations reveals that both Ni and Cu are essential for these transitions. Element specific local structure investigations uncover distinct and opposing local distortions around Ni and Cu, while Mn, Co, and Zn remain largely undistorted. These results establish that CCOs can host coupled phase transitions through `cooperation via competition' among local distortions in a chemically disordered lattice. This discovery expands the design principles for complex oxides, introducing a new paradigm for tuning structural and functional properties in high-entropy systems beyond conventional symmetry constraints.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript claims that targeted design in the compositionally complex spinel [Mn0.2Co0.2Ni0.2Cu0.2Zn0.2]Cr2O4, incorporating two Jahn-Teller active ions (Ni and Cu), induces two successive symmetry-lowering structural transitions upon cooling: an orbital-driven transition near 100 K and a magnetism-driven transition near 40 K. These arise via 'cooperation via competition' among opposing local distortions in an extremely chemically disordered A-site lattice, as evidenced by systematic A-site substitutions showing both Ni and Cu are required and by element-specific local structure probes revealing distinct distortions around Ni versus Cu (with Mn, Co, and Zn largely undistorted).
Significance. If the observed transitions are confirmed to occur in a truly random solid solution without undetected chemical ordering, this would represent a notable advance in the field of high-entropy and compositionally complex oxides. It would demonstrate that coupled orbital-magnetic-structural transitions can persist and be deliberately engineered in highly disordered lattices, expanding design principles beyond conventional symmetry constraints and potentially enabling new routes to functional properties in such systems.
major comments (2)
- [Results and Discussion (local structure and substitution experiments)] The central claim that the transitions result from cooperation among local distortions in a chemically disordered lattice (rather than conventional ordering) is load-bearing and requires explicit validation. The manuscript provides no quantitative metrics—such as Warren-Cowley short-range order parameters, refined site occupancies from diffraction, or analysis of diffuse scattering intensity—to establish the degree of A-site randomness across the relevant temperature range (see results on substitution series and local structure).
- [Methods and Results (element-specific probes)] Element-specific local structure data (likely EXAFS or PDF) are invoked to show opposing distortions around Ni and Cu, but the manuscript lacks reported error bars, data quality metrics, fitting residuals, or exclusion criteria for the temperature-dependent measurements. This undermines assessment of whether the distortions are robustly coupled to the reported transition temperatures.
minor comments (2)
- [Abstract and throughout] Notation for the composition [Mn0.2Co0.2Ni0.2Cu0.2Zn0.2]Cr2O4 should be standardized (e.g., consistent use of subscripts and brackets) throughout the text and figures for clarity.
- [Introduction] The abstract and introduction would benefit from a brief reference to prior work on Jahn-Teller effects in spinels or high-entropy oxides to better contextualize the novelty.
Simulated Author's Rebuttal
We thank the referee for their thorough review and constructive feedback on our manuscript. We appreciate the recognition of the potential significance of our findings in compositionally complex oxides. Below, we address the major comments point by point and outline the revisions we will make to strengthen the manuscript.
read point-by-point responses
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Referee: [Results and Discussion (local structure and substitution experiments)] The central claim that the transitions result from cooperation among local distortions in a chemically disordered lattice (rather than conventional ordering) is load-bearing and requires explicit validation. The manuscript provides no quantitative metrics—such as Warren-Cowley short-range order parameters, refined site occupancies from diffraction, or analysis of diffuse scattering intensity—to establish the degree of A-site randomness across the relevant temperature range (see results on substitution series and local structure).
Authors: We agree that explicitly quantifying the degree of chemical disorder is important to support our central claim. The substitution series and element-specific local structure data provide indirect evidence for a random solid solution, as the observed transitions depend on the specific combination of cations and show distinct local environments without indications of long-range ordering. However, we acknowledge the absence of direct quantitative metrics like Warren-Cowley parameters. In the revised manuscript, we will include an analysis of the X-ray diffraction data to compute short-range order parameters and assess site occupancies, along with any available diffuse scattering information, to better validate the randomness of the A-site lattice. revision: yes
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Referee: [Methods and Results (element-specific probes)] Element-specific local structure data (likely EXAFS or PDF) are invoked to show opposing distortions around Ni and Cu, but the manuscript lacks reported error bars, data quality metrics, fitting residuals, or exclusion criteria for the temperature-dependent measurements. This undermines assessment of whether the distortions are robustly coupled to the reported transition temperatures.
Authors: We thank the referee for pointing out this omission, which is critical for the credibility of the local structure results. The element-specific probes (EXAFS) indeed reveal opposing distortions around Ni and Cu that correlate with the transition temperatures. To address this, we will revise the manuscript to include error bars on the fitted distortion parameters, goodness-of-fit metrics (e.g., R-factors), data quality indicators such as signal-to-noise ratios, and details on the criteria used for including temperature-dependent data points. This will allow readers to better evaluate the robustness and coupling to the phase transitions. revision: yes
Circularity Check
No circularity: purely experimental observations with no derivation chain
full rationale
The manuscript is an experimental study reporting synthesis, XRD, magnetic, and element-specific local structure measurements (e.g., EXAFS or similar) on [Mn0.2Co0.2Ni0.2Cu0.2Zn0.2]Cr2O4 and substituted variants. It identifies two successive symmetry-lowering transitions at ~100 K and ~40 K, attributes them to opposing Jahn-Teller distortions around Ni and Cu, and concludes that both ions are required via substitution experiments. No equations, ansatzes, fitted parameters, or predictive models are presented whose outputs loop back to their own inputs. Claims rest on direct data comparison and chemical substitution, not on self-referential definitions or self-citation chains. Any self-citations (if present) support background context rather than load-bearing steps. The randomness assumption is an experimental premise subject to falsification by additional probes, not a circular reduction.
Axiom & Free-Parameter Ledger
Reference graph
Works this paper leans on
-
[1]
S ¨oderlind, P., Eriksson, O., Johansson, B., Wills, J. M. & Bor- ing, A. M. A unified picture of the crystal structures of met- als.Nature374, 524–525 (1995). URLhttps://doi.org/ 10.1038/374524a0
-
[2]
URLhttps://www.science.org/doi/abs/ 10.1126/science.1112453
Heathman, S.et al.A high-pressure structure in curium linked to magnetism.Science309, 110–113 (2005). URLhttps://www.science.org/doi/abs/ 10.1126/science.1112453
-
[3]
& Vincent, A
Cantor, B., Chang, I., Knight, P. & Vincent, A. Microstruc- tural development in equiatomic multicomponent alloys.Mate- 9 rials Science and Engineering: A375-377, 213–218 (2004). URLhttps://www.sciencedirect.com/science/ article/pii/S0921509303009936
2004
-
[4]
URLhttps://advanced.onlinelibrary
Yeh, J.-W.et al.Nanostructured high-entropy alloys with multiple principal elements: Novel alloy design concepts and outcomes.Advanced Engineering Materials6, 299–303 (2004). URLhttps://advanced.onlinelibrary. wiley.com/doi/abs/10.1002/adem.200300567
-
[5]
P., Raabe, D
George, E. P., Raabe, D. & Ritchie, R. O. High-entropy alloys. Nature reviews materials4, 515–534 (2019)
2019
-
[6]
Bhowal, S. & Spaldin, N. A. Polar metals: Prin- ciples and prospects.Annual Review of Materi- als Research53, 53–79 (2023). URLhttps: //www.annualreviews.org/content/journals/ 10.1146/annurev-matsci-080921-105501
-
[7]
& Kovtun, G
V A, F., Glamazda, V . & Kovtun, G. A phase transition in vana- dium.Z. Eksp. Teor. Fiz57, 1065–1068 (1969)
1969
-
[8]
& Spi ˇs´ak, D
Hobbs, D., Hafner, J. & Spi ˇs´ak, D. Understanding the complex metallic element mn. i. crystalline and noncollinear magnetic structure ofα-mn.Physical Review B68, 014407 (2003)
2003
-
[9]
Sewak, R., Dey, C. C. & Toprek, D. Temperature induced phase transformation in co.Scientific Reports12, 10054 (2022)
2022
-
[10]
Magomedov, M. N. Changes in the properties of iron during bcc–fcc phase transition.Physics of the Solid State63, 215– 222 (2021)
2021
-
[11]
& Park, C.-H
Na, S.-H. & Park, C.-H. First-principles study of structural phase transition of sn.J. Korean Phys. Soc56, 494–497 (2010)
2010
-
[12]
M.et al.Entropy-stabilized oxides.Nature communi- cations6, 8485 (2015)
Rost, C. M.et al.Entropy-stabilized oxides.Nature communi- cations6, 8485 (2015)
2015
-
[13]
Schweidler, S.et al.High-entropy materials for energy and electronic applications.Nature Reviews Materials1–16 (2024)
2024
-
[14]
Shahbazi, H.et al.Resiliency, morphology, and entropic trans- formations in high-entropy oxide nanoribbons.Science388, 950–956 (2025)
2025
-
[15]
& Curtarolo, S
Oses, C., Toher, C. & Curtarolo, S. High-entropy ceramics. Nature Reviews Materials5, 295–309 (2020)
2020
-
[16]
S., Oudah, M., Rottler, J
Aamlid, S. S., Oudah, M., Rottler, J. & Hallas, A. M. Under- standing the role of entropy in high entropy oxides.Journal of the American Chemical Society145, 5991–6006 (2023)
2023
-
[17]
Christian, J. W. Mechanism of phase transformations in met- als.Nature177, 419–421 (1956). URLhttps://doi.org/ 10.1038/177419a0
-
[18]
Nature Materials21, 290–296 (2022)
Fu, X.et al.Atomic-scale observation of non-classical nucleation-mediated phase transformation in a titanium alloy. Nature Materials21, 290–296 (2022). URLhttps://doi. org/10.1038/s41563-021-01144-7
-
[19]
I.Transition metal compounds(Cambridge Uni- versity Press, 2014)
Khomskii, D. I.Transition metal compounds(Cambridge Uni- versity Press, 2014)
2014
-
[20]
& Tokura, Y
Imada, M., Fujimori, A. & Tokura, Y . Metal-insulator transitions.Rev. Mod. Phys.70, 1039–1263 (1998). URLhttps://link.aps.org/doi/10.1103/ RevModPhys.70.1039
1998
-
[21]
Tokura, Y ., Kawasaki, M. & Nagaosa, N. Emergent functions of quantum materials.Nature Physics13, 1056–1068 (2017). URLhttps://doi.org/10.1038/nphys4274
-
[22]
Keimer, B., Kivelson, S. A., Norman, M. R., Uchida, S. & Za- anen, J. From quantum matter to high-temperature supercon- ductivity in copper oxides.Nature518, 179–186 (2015). URL https://doi.org/10.1038/nature14165
-
[23]
Post, K.et al.Coexisting first-and second-order electronic phase transitions in a correlated oxide.Nature Physics14, 1056–1061 (2018)
2018
-
[24]
Ahn, C.et al.Designing and controlling the properties of tran- sition metal oxide quantum materials.Nature materials20, 1462–1468 (2021)
2021
-
[25]
Middey, S.et al.Physics of ultrathin films and heterostructures of rare-earth nickelates.Annual Review of Materials Research 46, 305–334 (2016)
2016
-
[26]
N.et al.High-entropy oxides: Harnessing crys- talline disorder for emergent functionality.Journal of the Amer- ican Ceramic Society106, 5587–5611 (2023)
Kotsonis, G. N.et al.High-entropy oxides: Harnessing crys- talline disorder for emergent functionality.Journal of the Amer- ican Ceramic Society106, 5587–5611 (2023)
2023
-
[27]
URLhttps: //doi.org/10.1038/nature00964
Lee, S.-H.et al.Emergent excitations in a geometrically frus- trated magnet.Nature418, 1476–4687 (2002). URLhttps: //doi.org/10.1038/nature00964
-
[28]
Bord ´acs, S.et al.Magnetic-order-induced crystal symmetry lowering in a cr 2 o 4 ferrimagnetic spinels.Physical review letters103, 077205 (2009)
2009
-
[29]
Jaubert, L. D. C., Iqbal, Y . & Jeschke, H. O. Spin-peierls transi- tion in the frustrated spinelszncr 2o4 andmgcr 2o4.Phys. Rev. Lett.134, 086702 (2025). URLhttps://link.aps.org/ doi/10.1103/PhysRevLett.134.086702
-
[30]
R., Shoemaker, D
Suchomel, M. R., Shoemaker, D. P., Ribaud, L., Kemei, M. C. & Seshadri, R. Spin-induced symmetry breaking in orbitally or- dered nicr 2 o 4 and cucr 2 o 4.Physical Review B—Condensed Matter and Materials Physics86, 054406 (2012)
2012
-
[31]
Recent developments of the program fullprof, in commission on powder diffraction (iucr).Newslet- ter26, 12–19 (2001)
J.Rodr ´ıguez-Carvajal. Recent developments of the program fullprof, in commission on powder diffraction (iucr).Newslet- ter26, 12–19 (2001)
2001
-
[32]
Nevgi, R.et al.Local structural distortions drive magnetic molecular field in compositionally complex spinel oxide.Na- ture Communications16, 2041–1723 (2025)
2041
-
[33]
S., Yeh, J.-W., Ranganathan, S
Murty, B. S., Yeh, J.-W., Ranganathan, S. & Bhattacharjee, P. P. High-entropy alloys(Elsevier, 2019)
2019
-
[34]
Kennedy, B. J. & Zhou, Q. The role of orbital ordering in the tetragonal-to-cubic phase transition in cucr2o4.Journal of Solid State Chemistry181, 2227–2230 (2008)
2008
-
[35]
Rehr, J. J. & Albers, R. C. Theoretical approaches to x- ray absorption fine structure.Rev. Mod. Phys.72, 621–654 (2000). URLhttps://link.aps.org/doi/10.1103/ RevModPhys.72.621
2000
-
[36]
H.et al.Direct relationship between magnetism andmno 6 distortions inla 1−xcaxmno3.Phys
Booth, C. H.et al.Direct relationship between magnetism andmno 6 distortions inla 1−xcaxmno3.Phys. Rev. Lett.80, 853–856 (1998). URLhttps://link.aps.org/doi/ 10.1103/PhysRevLett.80.853
-
[37]
Downward, L.et al.Universal relationship between magne- tization and changes in the local structure ofla 1−xcaxmno3: Evidence for magnetic dimers.Phys. Rev. Lett.95, 106401 (2005). URLhttps://link.aps.org/doi/10.1103/ PhysRevLett.95.106401
2005
-
[38]
Roy, S. B. First order magneto-structural phase transition and associated multi-functional properties in magnetic solids.Jour- nal of Physics: Condensed Matter25, 183201 (2013)
2013
-
[39]
& Langridge, S
Lewis, L., Marrows, C. & Langridge, S. Coupled magnetic, structural, and electronic phase transitions in ferh.Journal of Physics D: Applied Physics49, 323002 (2016)
2016
-
[40]
Yamasaki, Y .et al.Magnetic reversal of the ferroelectric polarization in a multiferroic spinel oxide.Phys. Rev. Lett. 96, 207204 (2006). URLhttps://link.aps.org/doi/ 10.1103/PhysRevLett.96.207204
-
[41]
& Palstra, T
Mufti, N., Nugroho, A., Blake, G. & Palstra, T. Magnetodi- electric coupling in frustrated spin systems: the spinelsmcr2o4 (m= mn, co and ni).Journal of Physics: Condensed Matter22, 075902 (2010)
2010
-
[42]
Sharma, N.et al.Large exchange bias effect and complex magnetism in a tetragonal high entropy spinel oxide.Applied Physics Letters123, 161901 (2023)
2023
-
[43]
Music ´o, B.et al.Tunable magnetic ordering through cation selection in entropic spinel oxides.Physical Review Materials 10 3, 104416 (2019)
2019
-
[44]
Sampathkumaran, E. V . & Niazi, A. Superparamagnetic-like ac susceptibility behavior in the partially disordered antifer- romagnetic compoundca 3corho6.Phys. Rev. B65, 180401 (2002). URLhttps://link.aps.org/doi/10.1103/ PhysRevB.65.180401
2002
-
[45]
Das, A.et al.Origin of the long-range ferrimagnetic ordering in cubic mn (co) cr 2 o 4 spinels.Physical Review B107, L100414 (2023)
2023
-
[46]
Reehuis, M.et al.Competing jahn-teller distortions and ferri- magnetic ordering in the geometrically frustrated system n i 1-x c ux c r 2 o 4.Physical Review B91, 024407 (2015)
2015
-
[47]
Reehuis, M.et al.Coexisting antiferromagnetic phases on the frustrated pyrochlore sublattice of the mixed jahn- teller systemni 1−xcuxcr2o4.Phys. Rev. Mater.8, 054414 (2024). URLhttps://link.aps.org/doi/10.1103/ PhysRevMaterials.8.054414
2024
-
[48]
& Siegmann, H
St ¨ohr, J. & Siegmann, H. C.Magnetism: from fundamentals to nanoscale dynamics(Springer, 2006)
2006
-
[49]
Zhang, J.et al.Long-range antiferromagnetic order in a rock- salt high entropy oxide.Chemistry of Materials31, 3705–3711 (2019)
2019
-
[50]
& Newville, M
Ravel, B. & Newville, M. Athena, artemis, hephaestus: data analysis for x-ray absorption spectroscopy using ifeffit.Journal of synchrotron radiation12, 537–541 (2005). METHODS The polycrystalline compositionally complex chromate spinel compositions were synthesized by the conventional solid-state reaction starting with stoichiometric amounts of Cr2O3 and ...
2005
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