Quantum disordered ground state and relative proximity to an exactly solvable model in the frustrated magnet CeMgAl$_{11}$O$_{19}$

A. Eli\'a\v{s}; A. Kancko; C. A. Corr\^ea; D. Sedmidubsk\'y; G. Bastien; J. Prokle\v{s}ka; L. N\'adhern\'y; M. Kratochv\'ilov\'a; M. \v{Z}onda; P. Gegenwart

REVIEW 3 major objections 5 minor 113 references

Quantum disordered ground state and relative proximity to an exactly solvable model in the frustrated magnet CeMgAl$_{11}$O$_{19}$

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper establishes that the disordered ground state of the triangular magnet CeMgAl11O19 is not primarily a quantum spin liquid induced by proximity to the exactly solvable XXZ point, and it points to structural disorder as the…

desk verdict Solid magnetization/DMRG study that revises CeMgAl11O19's Jz/J⊥ to about -0.22, but the fitted ratio lacks an uncertainty and neglects J_c, so the exact distance from the QCP is not pinned down. read the letter →

arxiv 2506.16207 v1 pith:FKCKZMQP submitted 2025-06-19 cond-mat.str-el

G. Bastien , A. Eliáš , V. Anderle , A. Kancko , C. A. Corrêa , S. Kumar , P. Proschek , J. Prokleška

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L. Nádherný D. Sedmidubský T. Treu P. Gegenwart M. Kratochvílová M. Žonda R. H. Colman

This is my paper

classification cond-mat.str-el

keywords triangularlatticeantiferromagnetquantumspinliquidXXZmodelmagnetizationDMRGstructuraldisorderCeMgAl11O19frustratedmagnetism

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 paper studies the triangular-lattice magnet CeMgAl11O19 at temperatures down to 0.03 K and asks why it never orders magnetically. The authors combine magnetization and specific-heat measurements on single crystals with density-matrix renormalization group (DMRG) calculations for the spin-1/2 XXZ model, and they obtain a best-fit exchange anisotropy $J_z/J_\perp = -0.22$. That places the material farther from the exactly solvable quantum critical point at $J_z/J_\perp = -0.5$ than the value $J_z/J_\perp = -0.43$ previously extracted from inelastic neutron scattering. They conclude that the absence of magnetic order is not mainly due to quantum criticality toward a spin liquid, and they propose that structural disorder, identified by single-crystal X-ray diffraction, is the most probable cause. If correct, CeMgAl11O19 becomes a case where disorder, not the proximity to an exactly solvable model, controls the quantum disordered ground state.

What carries the argument

The machinery is the anisotropic XXZ Hamiltonian on the triangular lattice, $\hat{H}=\sum_{\langle i,j\rangle} J_\perp(S^x_iS^x_j+S^y_iS^y_j)+J_z S^z_iS^z_j$, with an exactly solvable spin-liquid point at $J_z/J_\perp=-0.5$ where the ground state is a superposition of umbrella states. The comparison is made through zero-temperature DMRG magnetization curves on a $12 \times 9$ cylindrical lattice, matched to the 0.03 K data along the $c$ axis with the in-plane exchange fixed at $J_\perp=0.056$ meV, $g_c=3.36$, and a demagnetization correction. DMRG structure factors at $J_z/J_\perp=-0.22$ predict a 120-degree coplanar order at zero field evolving into ferromagnetic order along $c$ and an up-up-down plateau near 1.8 T for fields in the $ab$ plane. Single-crystal X-ray diffraction supplies the three structural disorder sources that the clean-lattice calculation cannot capture.

What would settle it

A decisive check would be to grow a stoichiometric, structurally ordered crystal of CeMgAl11O19 and measure its magnetization to dilution temperatures: if the best DMRG fit then returns near $J_z/J_\perp = -0.43$, or if long-range magnetic order appears below 30 mK, the paper's central conclusion fails. On the current crystals, observing the predicted 1/3 magnetization plateau near 1.8 T for fields in the $ab$ plane would support the fitted ratio.

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Extended reading notes

Core claim

On the paper's own terms, the central claim is that a quantitative comparison of the low-temperature magnetization of CeMgAl11O19 with DMRG ground-state calculations for the nearest-neighbor XXZ Hamiltonian determines the exchange anisotropy ratio to be $J_z/J_\perp = -0.22$, assuming $J_\perp = 0.056$ meV from the earlier neutron study. This ratio still has the same sign structure proposed before, antiferromagnetic in-plane coupling and ferromagnetic out-of-plane coupling, but it is sufficiently far from the quantum critical point at $J_z/J_\perp = -0.5$ that the exactly solvable spin-liquid point cannot be the origin of the observed quantum disordered state. The authors therefore state that the results exclude a quantum spin liquid state induced mainly by magnetic quantum criticality and instead point to the central role of structural disorder, which they document as cerium deficiency, magnesium/aluminium site mixing, and splitting of the Al(5) site. The absence of magnetic order down to 0.03 K is then attributed to the combination of frustration, proximity to quantum criticality, and structural disorder, with short-range 120-degree order suggested as a plausible realization.

Load-bearing premise

The fitted ratio $J_z/J_\perp = -0.22$ depends on accepting the earlier neutron value $J_\perp = 0.056$ meV, the measured $g_c = 3.36$, the demagnetization correction, and the assumption that disorder and the bond-dependent coupling $J_c$ (set to zero) do not reshape the magnetization curve; if any of those move, the conclusion that the material sits away from the quantum critical point moves with it.

Editorial extensions

If this is right

If the fitted ratio is correct, the material is not a quantum-critical spin liquid, and the excitation continuum reported by the neutron study needs a different explanation than proximity to the solvable point.
At $J_z/J_\perp=-0.22$ the clean model predicts 120-degree order, so the discrepancy with the absence of order becomes a direct measure of how strongly structural disorder perturbs the triangular lattice.
The predicted 1/3 magnetization plateau at $\mu_0H\approx1.8$ T for fields in the $ab$ plane is a testable signature of the fitted ratio, although the small $g_{ab}$ currently prevents measuring it.
The material can be used for adiabatic demagnetization cooling to below 0.1 K, as demonstrated by self-cooling from 2 K to 0.09 K.
A random-singlet state is judged unlikely because susceptibility and $C_p/T$ do not show the power-law divergence predicted for such states, leaving short-range 120-degree order or another disorder-induced state as the candidate.

Reading between the lines

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

If structural disorder is indeed the controlling variable, crystals with different cerium deficiency or Al/Mg mixing should show a tunable ordering temperature or correlation length, which is a testable prediction the paper does not make.
The discrepancy between the magnetization fit and the neutron fit might be reduced by including the bond-dependent coupling $J_c$ that the paper sets to zero, so refitting both datasets with the full Hamiltonian would test whether the two probes are actually inconsistent.
The same disorder-sensitive physics may apply to the isostructural Pr and Nd analogs already studied, making the LnMgAl11O19 family a systematic platform for separating frustration from disorder.
A structurally ordered, near-stoichiometric sample would be the decisive experiment: if it orders magnetically, disorder is the dominant mechanism, and if it stays disordered, intrinsic quantum fluctuations are stronger than this fit suggests.

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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

Bottom line: solid experimental paper. Single crystals, magnetization down to 30 mK, no order, DMRG comparison gives Jz/J⊥ ≈ -0.22, a meaningful revision of the INS-based -0.43. The qualitative conclusion—this material is not parked at the XXZ quantum critical point—is likely correct.

What's new and good: the low-T magnetization, the DMRG fitting procedure (with reproducible TeNPy parameters, finite-size scaling, structure factors), the CEF calculation confirming S_eff=1/2, and the detailed structural-disorder analysis (10% Ce deficiency, Mg/Al mixing, Al5 splitting). All of this is solid and documented.

Soft spots: the headline ratio is essentially a one-parameter fit. J⊥ is taken from the prior INS paper, g_c=3.36 is from their own saturation magnetization (ESR says 3.66–3.74), the demagnetization correction is approximate, and the supplement drops J_c=0 because the minimal model fits well. No uncertainty is quoted on the ratio. A sensitivity scan over J⊥, g_c, and J_c would make the claim sturdier. That said, the saturation field is a strong constraint, and the difference between the -0.43 and -0.22 magnetization curves is clearly visible, so I don't think the stress-test's stronger claim—that the QSL exclusion is unsupported—holds. The exact value may shift; the direction of the revision likely will not.

Who benefits: the triangular-lattice frustrated-magnetism community, especially people interested in disorder-induced mimicry and quantum-critical QSL candidates. It deserves a serious referee, not a desk reject. I'd send it to review with a request for uncertainty/sensitivity analysis and a more nuanced statement of what is excluded.

Referee Report

3 major / 5 minor

Summary. This manuscript reports single-crystal magnetization and specific heat measurements on the triangular-lattice magnet CeMgAl11O19 down to T = 0.03 K, together with DFT crystal-field calculations and DMRG simulations of the XXZ model in Eq. (1). The authors confirm an effective S = 1/2 ground doublet, a strongly anisotropic g-tensor, and the absence of magnetic order down to 0.03 K. Comparing the c-axis magnetization with zero-temperature DMRG results, they extract an exchange ratio Jz/J⊥ = -0.22 (fixing J⊥ = 0.056 meV from the prior INS study), and conclude that the material is farther from the ferromagnetic-to-antiferromagnetic quantum critical point at Jz/J⊥ = -0.5 than suggested by the INS-derived value -0.43. They propose that the absence of order is most probably caused by structural disorder identified in single-crystal X-ray diffraction (10% Ce deficiency, Mg/Al mixing, Al(5) splitting), rather than by proximity to the exactly solvable spin-liquid point.

Significance. If the extracted ratio Jz/J⊥ = -0.22 is robust, the manuscript materially revises the interpretation of CeMgAl11O19 from a quantum-critical spin liquid to a disordered magnet, a distinction that matters for the triangular-lattice QSL debate. The study adds value through the low-temperature magnetization and specific heat data, the DMRG finite-size scaling in the Supplemental Material, the explicit numerical settings for reproducibility, and the detailed structural disorder analysis. The paper also makes a falsifiable prediction: the clean XXZ model at the fitted ratio orders into 120-degree order, which is not observed experimentally, and it predicts a 1/3 magnetization plateau for in-plane fields that could be tested in future experiments.

major comments (3)

[Fig. 3(a) and main text, 'Our best fit value...'] The headline result Jz/J⊥ = -0.22 is presented as a single best-fit value without any uncertainty or robustness analysis. The fit fixes J⊥ = 0.056 meV from Ref. [12], uses gc = 3.36 inferred from saturation (which is 8-11% lower than the ESR values 3.66-3.74 quoted in the manuscript), applies an approximate demagnetization correction with N ≈ 0.32, and compares T = 0 DMRG curves to T = 0.03 K data. Since the saturation field and low-field slope are the main constraints, a systematic shift in gc or J⊥ changes the field-to-energy conversion and can move the inferred ratio toward or away from the quantum critical point at Jz/J⊥ = -0.5. The authors should provide confidence intervals and a parameter-robustness table, for example fitting with gc = 3.66-3.74 and with J⊥ varied within the uncertainty of Ref. [12], to support the claim of a weaker proximity to the QCP.
[Supplemental Material, Section V (Hamiltonian S5 and Jc = 0)] The bond-dependent exchange Jc is set to zero because the minimal model 'fits well' the experimental data. This is not sufficient for the main conclusion, because the exactly solvable spin-liquid point and the QCP at Jz/J⊥ = -0.5 apply to the XXZ Hamiltonian without Jc. If Jc is non-negligible, as analyzed in Ref. [12], then the fitted value of Jz/J⊥ is an effective parameter that can absorb parts of Jc, and the comparison to the exactly solvable point is not apples-to-apples. The authors should either quantify Jc in their model (e.g., by fitting DMRG with finite Jc and showing that M(H) is insensitive to it) or explicitly state the estimated upper bound on Jc and its effect on the inferred ratio.
[Final paragraph and Conclusion] The attribution of the absence of magnetic order to structural disorder is presented as the most probable explanation, but the manuscript offers no quantitative test. The observed disorder (10% Ce deficiency, Mg/Al site mixing, Al(5) splitting) is qualitatively linked to known disorder effects in YbMgGaO4 and NaYbSe2, but the paper does not show that this level of bond or site randomness is sufficient to suppress 120-degree order in the XXZ triangular-lattice model at Jz/J⊥ = -0.22. A disorder-strength estimate (e.g., from local structural variations and the exchange sensitivity) and a comparison with predicted disorder-driven order suppression would turn this proposal into a substantive claim; alternatively, the claim should be explicitly softened to a speculation.

minor comments (5)

[Title and Abstract] There is a typo in the title and abstract: 'a n exactly solvable model' should read 'an exactly solvable model'.
[Main text, DMRG fitting paragraph] The text states that the strongest interaction is kept at 'J⊥ = -0.056 meV', while the Hamiltonian in Eq. (1) and Fig. 3 use J⊥ = 0.056 meV; the sign is inconsistent and should be corrected.
[Fig. 4 cross-reference] The text describing Cp/T refers to 'Fig. 4(b)' when discussing the data shown in the top panel; the figure panels should be cross-checked and referenced correctly.
[Supplemental Material, Eq. (S5)] The notation for the bond-dependent term Jc(Si·eij)(Sj·eij) is ambiguous because eij is not defined; please define the bond unit vectors and the sign convention.
[Demagnetization correction] The demagnetization factor N ≈ 0.32 is described as an average for a nearly cubic crystal, but the correction is applied only to the c-axis magnetization; it would be helpful to state explicitly the assumed sample dimensions and whether the same correction is used for the in-plane curves.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the fitted Jz/J_perp ratio is openly a fit to magnetization data, and the DMRG 120-degree order statement is an independent model output, not a repackaged input.

full rationale

The paper's central quantitative claim is an openly labeled fit: experimental M(H) at T = 0.03 K is compared with DMRG ground-state magnetization curves for the XXZ Hamiltonian (Eq. 1), with J_perp fixed at 0.056 meV from the prior INS study (Ref. [12]) and g_c = 3.36 from saturation magnetization. The text states 'Our best fit value, Jz/J_perp = -0.22' and explicitly contrasts it with the INS-derived value -0.43. No equation in the paper makes the fitted ratio equal to the input data by construction; the ratio is a parameter extracted from the data, not a quantity claimed to be derived from first principles. The later statement that DMRG 'predict[s] the formation of a 120 degree' order for Jz/J_perp = -0.22 is a genuine model output computed from the fitted Hamiltonian, and it is not equivalent to the experimental observation of no ordering; the authors explicitly treat the discrepancy as evidence for structural disorder, which is an additional interpretation rather than a circular repackaging. The only imported numerical coupling, J_perp, comes from an external INS paper by a different group, not from the present authors, so no load-bearing self-citation or uniqueness-imported-from-authors pattern is present. Parameter sensitivity, neglected J_c, and g_c uncertainty are legitimate experimental/modeling concerns, but they concern robustness, not circularity. The derivation chain is therefore self-contained and non-circular.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The headline ratio is a one-parameter fit to magnetization with J⊥ fixed from prior INS; the DFT-CEF confirmation of S_eff = 1/2 uses an empirical hybridization shift; the clean XXZ model and the disorder attribution are assumptions rather than derived results.

free parameters (3)

Jz/J⊥ ratio = -0.22
Best fit of zero-temperature DMRG magnetization curves to the T = 0.03 K c-axis M(H) data; no uncertainty is quoted.
J⊥ exchange scale = 0.056 meV
Fixed input taken from the prior INS study Ref. [12]; it sets the energy scale for the fitted ratio and is not independently measured in this work.
DFT orbital-dependent shift Δ = 20 eV for O-2s, 8 eV for O-2p
Empirical parameter in the DFT/Wannier crystal-field calculation that controls Ce-4f to O-2p/2s hybridization and shapes the CEF splitting used to justify S_eff = 1/2.

assumptions (4)

domain assumption The magnetic Hamiltonian is the nearest-neighbor XXZ model (Eq. 1) with no bond-dependent exchange or Dzyaloshinskii-Moriya terms.
Mirror planes cancel off-diagonal symmetric exchange and constrain DM along c, but the bond-dependent J_c and DM terms are set to zero in the fit. Invoked in the main text and SM Eq. S5; if J_c is sizable, the fitted Jz/J⊥ could shift.
domain assumption Zero-temperature DMRG results are directly comparable to the T = 0.03 K magnetization data.
The lowest measured temperature is treated as the ground state; the paper does not quantify residual thermal rounding or disorder-induced broadening of the magnetization.
ad hoc to paper The absence of magnetic order, despite the clean-model DMRG prediction of 120-degree order, is attributed to structural disorder.
This attribution reconciles the theory-experiment contradiction but is not derived from a microscopic disorder model; the paper presents structural evidence but no quantitative disorder-inclusive simulation.
domain assumption The DFT/Wannier crystal-field calculation reliably determines the ground doublet as Jz = ±5/2.
Used to confirm S_eff = 1/2; the calculation depends on the empirical orbital-dependent shift and on the chosen exchange-correlation functional, so it is not a parameter-free result.

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Cite this review

Pith. "Pith review of Quantum disordered ground state and relative proximity to an exactly solvable model in the frustrated magnet CeMgAl$_{11}$O$_{19}$." pith.science (2026). https://pith.science/paper/FKCKZMQP

@misc{pith2026250616207,
  author       = {Pith},
  title        = {Pith review of: Quantum disordered ground state and relative proximity to an exactly solvable model in the frustrated magnet CeMgAl$_11$O$_19$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FKCKZMQP}},
  note         = {Machine review of arXiv:2506.16207}
}

abstract

The magnetic properties of the triangular magnet CeMgAl$_{11}$O$_{19}$ were investigated by magnetization and specific heat measurements down to $T=0.03\,$K on single crystals grown by the floating zone method. The formation of effective spins $S_\mathrm{eff}= 1/2$ below $T < 10$\,K was confirmed both by DFT calculations and specific heat measurements. No magnetic order was found down to $T=0.03\,$K despite the formation of magnetic correlations observed in specific heat. The measured magnetization was compared with DMRG computation and their agreement supports the proposal of a strongly anisotropic magnetic interaction antiferromagnetically coupling the spin components in the $ab$ plane and ferromagnetically coupling the spin component along the $c$ axis. However, our quantitative study of the magnetization indicates a weaker proximity to quantum criticality between ferromagnetism and antiferromagnetism than the previous inelastic neutron scattering study. Finally, we propose that the absence of magnetic order in CeMgAl$_{11}$O$_{19}$ would most probably be related to the structural disorder revealed by single-crystal X-ray diffraction.

Figures

Figures reproduced from arXiv: 2506.16207 by the authors.

**Figure 1.** (a) Magnetic susceptibility of CeMgAl11O19 along the easy magnetization axis c as a function of temperature combining data from the MPMS magnetometer and the Hall sensor. Data point obtained upon temperature scan at a magnetic field of µ0H = 0.1 T (discs) are confirmed by direct measurement of the derivative ∂M/∂H (black squares) (b) Magnetic susceptibility of CeMgAl11O19 under magnetic field applied both along the… view at source ↗

**Figure 2.** (a) Magnetization at T = 2 K in CeMgAl11O19 along the c axis and in the ab plane as a function of Magnetic field. The dashed line indicates approximation of the magnetization by Brillouin functions giving the g factor values: gc = 3.4 and gab ≈ 0.6. (b) Magnetization of CeMgAl11O19 along the c axis at different temperatures from T = 0.03 K to T = 1.8 K. using DMRG calculations based on Hamiltonian (1) for various s… view at source ↗

**Figure 3.** (a) Comparison of the experimental magnetization [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

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