Strongly correlated altermagnet CaCrO$_3$

Peng-Jie Guo; Rong-Qiang He; Zhenfeng Ouyang; Zhong-Yi Lu

REVIEW 4 major objections 7 minor 2 cited by

Strongly correlated altermagnet CaCrO$_3$

T0 review · 4 major / 7 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper demonstrates that CaCrO3 is a strongly correlated altermagnet and a Hund's metal, with DFT+DMFT reproducing the measured incoherent metallic behavior that static DFT+U cannot.

desk verdict A solid DFT+DMFT case for CaCrO3 as a strongly correlated altermagnet and Hund's metal, held back mainly by missing numerical parameters and a 'quantitative' claim that is really qualitative. read the letter →

arxiv 2507.14081 v2 pith:5KOCWIL4 submitted 2025-07-18 cond-mat.str-el cond-mat.mtrl-sci

Zhenfeng Ouyang , Peng-Jie Guo , Rong-Qiang He , Zhong-Yi Lu This is my paper · ORCID

classification cond-mat.str-elcond-mat.mtrl-sci

keywords altermagnetismCaCrO3DFT+DMFTHund'smetalnon-Fermiliquidheavyfermionsstronglycorrelatedelectronsperovskiteoxide

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

CaCrO3, a chromium-based perovskite known to be a C-type antiferromagnetic metal below roughly 90 K, is argued here to be a strongly correlated altermagnet: its antiparallel Cr sublattices are connected by rotations rather than by translation or inversion, so the bands are spin-split while the net magnetization stays zero. The paper shows that density functional theory plus dynamical mean-field theory reproduces the measured correlated metallic behavior, including an incoherent photoemission peak near $-0.2$ eV and a magnetic moment of about $1.3\,\mu_B$/Cr, while static DFT+U instead gives an insulator. It further identifies the material as a Hund's metal, a correlated metal whose quasiparticle coherence is suppressed by Hund's coupling, with the incoherent, non-Fermi-liquid state driven by that coupling. The altermagnetism creates incipient flat bands near the Fermi level, and Hundness renormalizes them into a heavy-fermion-like regime with a maximum mass enhancement of about 47. The broader claim is that Hund's metals are a natural platform for studying strongly correlated altermagnetism.

What carries the argument

The carrying machinery is density functional theory plus dynamical mean-field theory (DFT+DMFT): the lattice problem is mapped to a local impurity problem with a frequency-dependent self-energy, which is what permits incoherent spectral weight and non-Fermi-liquid behavior to survive in the calculated spectra. The central diagnostic objects are the local spin-multiplet weights of the Cr-t2g shell, where the dominant high-spin $S_z=1$ weight identifies a Hund's metal; the imaginary-time spin-spin correlation function $C_{ss}(\tau)=\langle S_z(\tau)S_z(0)\rangle$, whose large value at $\tau=\beta/2$ signals a spin-frozen phase with unscreened local moments; and the low-frequency self-energy on the imaginary frequency axis, whose nonlinearity is read as a non-Fermi-liquid signature and, through $m^*/m \approx 1 - \mathrm{Im}\,\Sigma(i\omega_0)/\omega_0$, as the source of the mass enhancement. The symmetry analysis of the C-type magnetic order in the $Pbnm$ structure—where spin-space-group operations protect nodal planes at $k_x=0,\pi$ and $k_y=0,\pi$—is what defines the d-wave altermagnetic character.

What would settle it

Measure the low-temperature electronic specific heat coefficient $\gamma$ of CaCrO3: if it is close to the bare band value rather than roughly 47 times larger, the heavy-fermion claim fails. Angle-resolved photoemission below the Néel temperature that resolves sharp quasiparticles instead of an incoherent hump near $-0.2$ eV, or neutron diffraction that finds a magnetic propagation vector incompatible with the assumed C-type order, would also contradict the central claim.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that CaCrO3 is a strongly correlated altermagnet whose low-energy physics is controlled by Hund's coupling, and that this physics is invisible to static correlation corrections. With dynamical correlations included, the Cr-t2g bands collapse into a narrow window from roughly $-0.2$ to $0.1$ eV around the Fermi level; the symmetry-protected altermagnetic spin splitting remains visible along S-Γ and R-Z, and an incoherent hump near $-0.2$ eV matches the experimental photoemission spectrum. The calculated magnetic moment of about $1.3\,\mu_B$/Cr agrees with the neutron-diffraction value near $1.2\,\mu_B$/Cr. The local multiplet distribution is dominated by the high-spin $S_z=1$ state, and the low-frequency self-energy is nonlinear, both signatures of a spin-frozen, non-Fermi-liquid Hund's metal. The same self-energy gives a maximum mass enhancement $m^*/m \approx 47$, comparable to 4f heavy-fermion systems, which the authors attribute to Hundness promoting the incipient flat bands that altermagnetism already produces. Treated with static DFT+U and $U=5$ eV, the same material becomes insulating, contradicting experiment.

Load-bearing premise

The calculation presumes the magnetic ground state is the collinear C-type antiferromagnetic order with the same periodicity as the crystal, and it relies on on-site interaction parameters $U$ and $J$ whose values are given only in the supplemental material; if that ordering or those parameters are not representative, the predicted spin splitting, Hund's-metal classification, and mass enhancement of about 47 do not follow.

Editorial extensions

If this is right

CaCrO3 becomes a concrete material where altermagnetism, Hund's coupling, and heavy-fermion behavior coexist, providing a testbed for correlated altermagnet physics.
Static DFT+U misclassifies this material as an insulator, so correlated altermagnets generally may require dynamical-correlation treatments rather than static Hubbard corrections.
The experimentally observed incoherent photoemission peak is explained as a Hundness-driven, spin-frozen non-Fermi-liquid feature rather than a band-structure artifact.
Hundness can transform altermagnetism-induced incipient flat bands into a heavy-fermion regime, with a mass enhancement comparable to that of 4f heavy-fermion compounds.
Hund's metals are proposed as a platform for realizing and tuning strongly correlated altermagnetism.

Reading between the lines

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

If the paper is right, spin-splitting magnitudes and Berry-curvature-derived responses for other strongly correlated altermagnets should be rechecked with dynamical methods, since static DFT+U can misclassify them.
A measurable consequence the authors do not report: the low-temperature specific heat of CaCrO3 should show a Sommerfeld coefficient roughly 47 times the band value.
Because the paramagnetic 290 K calculation already shows non-Fermi-liquid behavior, spin freezing appears to be independent of altermagnetic order; measurements across the ordering temperature could test whether ordering sharpens or suppresses the incoherence scale.
Other perovskites and Hund's metals with two electrons per transition-metal site could be screened computationally for the same coexistence of altermagnetism, Hundness, and heavy-fermion behavior.

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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

Quick take: this is a solid, useful DFT+DMFT paper, not a breakthrough. The altermagnetic classification of CaCrO3 was already known from DFT (Ref [25]); the new content is the correlated treatment and the Hund's metal interpretation. The calculation reproduces two experimental anchors—the local moment (1.3 vs 1.2 μB) and the incoherent PES feature at about -0.2 eV—and it shows clearly why DFT+U fails. The symmetry analysis is careful, and the spin multiplet weights, the spin-frozen phase, and the non-Fermi liquid self-energy make a coherent case for Hundness.

The soft spots are in numerical transparency. The main text does not report the DMFT U and J values or the double-counting scheme; these are deferred to the Supplemental Material. That makes the 'quantitatively capture' claim untestable as posted. The comparison with experiment is really qualitative—a peak at the right energy and a moment within 0.1 μB. There is no sensitivity scan, so we don't know whether the incoherent peak or the m*/m≈47 mass enhancement are robust to U and J choices. Near a Hund's metal crossover these quantities can shift a lot. Using the experimental U estimate as an input is a minor concern, not a flaw. None of these issues is fatal, and I don't see a circularity problem: the C-type order is imposed from experiment, the spin splitting follows from symmetry, and the spectral function and moment are computed, not fitted. The citation pattern looks appropriate.

Bottom line: this paper is a credible candidate benchmark for strongly correlated altermagnetism and deserves a serious referee. The authors should be asked to put the DMFT parameters and double-counting scheme in the main text or a clearly available supplement, add a brief U-J sensitivity check, and soften 'quantitatively capture' to 'capture' or 'reproduce'. For anyone working on Hund's metals or correlated altermagnets, this is worth reading and citing once those pieces are in place.

Referee Report

4 major / 7 minor

Summary. The manuscript reports DFT+DMFT calculations for CaCrO3 in the experimentally established C-type antiferromagnetic phase. The authors find a strongly correlated altermagnet that is also a Hund's metal, with a non-Fermi-liquid self-energy, a large mass enhancement m*/m ~ 47, and incipient flat bands promoted by Hundness. They compare their computed spectral function with photoemission, reporting an incoherent feature at ~ -0.2 eV that matches the experimental energy, and obtain a local moment of ~1.3 muB against the neutron value ~1.2 muB. They further show that DFT+U misdescribes the system as an insulator, and conclude that DFT+DMFT quantitatively captures the correlated metallic and incoherent behavior of CaCrO3.

Significance. If the central claims hold, CaCrO3 would be a rare material example where altermagnetism, Hund's metallicity, and heavy-fermion-like behavior coexist, and the paper would provide a useful demonstration of DFT+DMFT for strongly correlated altermagnets. The manuscript is significant because studies of altermagnetism with dynamical correlations are still scarce, and it anchors the calculation to two external experimental quantities (the photoemission incoherent peak and the neutron local moment). The explicit failure of DFT+U and the comparison of magnetic and paramagnetic DMFT results are also valuable. However, the quantitative claims are not yet fully supported, as the main text omits the DMFT interaction parameters and provides no sensitivity analysis, and the 'quantitative capture' of the incoherent state is not backed by a quantitative metric. These issues are addressed in the major comments.

major comments (4)

[Results of dynamical electronic correlation; Supplemental Material [32]] The main text never reports the Cr-t2g interaction parameters U and J used in the DFT+DMFT calculation; they are deferred to the Supplemental Material [32]. The central quantitative results - the position of the incoherent feature, the local moment of about 1.3 muB, and the mass enhancement of about 47 - all depend on U, J, and the double-counting scheme. Near a Hund's-metal crossover these observables can vary substantially with U and J. The authors should state U and J, name the double-counting scheme, and provide a sensitivity scan or an explicit robustness argument in the main text before the phrase 'quantitatively capture' can be assessed.
[Results of dynamical electronic correlation; Fig. 2(a) right panel] The claim that DFT+DMFT 'quantitatively capture[s] the incoherent state' is not quantitatively supported. The only comparison made is that both the calculated spectral function and the experimental PES spectrum show an incoherent feature near -0.2 eV. There is no comparison of spectral weight, peak width, or relative intensity, and no uncertainty estimate. The authors should either soften the wording to 'qualitatively reproduces' or provide a quantitative fit (e.g., peak position and width with respect to the experimental spectrum at the same energy).
[Promotion of flat bands; Fig. 4(b)] The mass enhancement m*/m ~ 47 is obtained from m*/m = 1 - ImSigma(i omega0)/omega0, a formula that assumes a Fermi-liquid form of the self-energy. The same paragraph argues that ImSigma(i omega_n) is nonlinear at low frequency, i.e., non-Fermi-liquid. Applying a Fermi-liquid formula to a non-Fermi-liquid self-energy is not obviously justified; the resulting number may overestimate or misrepresent the quasiparticle weight. The authors should either justify the extrapolation or replace this estimate with a quantity appropriate for the non-Fermi-liquid regime, such as a spectral-weight analysis of the coherent part of A(omega).
[Spin frozen phase; Fig. 4(b)] The non-Fermi-liquid classification is inferred from the 'nonlinear' behavior of ImSigma(i omega_n) at low Matsubara frequencies. With only a few low-frequency points, it is difficult to distinguish a true nonlinearity from Fermi-liquid linear behavior with a large slope, especially if the self-energy is sensitive to the analytic continuation or to the fixed C-type magnetic order. The authors should show ImSigma over a wider frequency range and provide a fit or a more systematic finite-temperature analysis to support the NFL claim.

minor comments (7)

[Abstract and Introduction] The abstract and introduction use the phrase 'quantitatively capture' before the supporting comparison is described; consider rewording to 'reproduce' or 'qualitatively capture' until the quantitative metric is provided.
[Promotion of flat bands] The definition of mass enhancement appears to contain typographical issues: 'm*/m = 1 - Im(i omega0)/omega0' should likely read 'm*/m = 1 - ImSigma(i omega0)/omega0'. Please correct the notation and define omega0 consistently with omega_n = (2n+1)pi/beta.
[Results of static electronic correlation] The phrase 'altermagneric CaCrO3' in the paragraph on DFT+U results is a typo for 'altermagnetic CaCrO3'.
[Conclusion and last paragraph] The word 'investiagtions' near the end of the paper is a typo for 'investigations'; also 'self-consistency circle' should be 'self-consistency cycle'.
[Fig. 3 and surrounding text] The manuscript contains a corrupted or uninterpretable inserted passage around the Fig. 3 caption (the string beginning with '/s48/s49/s48 ...'). The authors should ensure the submitted text is clean and free of such artifacts.
[Table I] The table header uses 'N' and 'Sz' without defining N. A sentence explaining that N is the total electron number of the local multiplet and Sz the spin projection would improve readability.
[References] Reference [32] says 'See Supplemental Material at xxx', leaving the URL as a placeholder. This should be updated before publication.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: DFT+DMFT predictions are benchmarked against external experiments, not constructed from them.

full rationale

The paper's load-bearing chain is a DFT+DMFT calculation: it starts from the experimentally established C-type AFM structure, builds a correlated impurity model, solves it self-consistently, and obtains spectral functions, local moments, spin-spin correlations, and self-energies. The d-wave altermagnet classification is a symmetry consequence of the neutron-diffraction-determined magnetic order, not a fitted output. The key quantitative comparisons—the incoherent spectral weight near -0.2 eV, the ~1.3 micro_B moment versus 1.2 micro_B neutron value, and m*/m ~ 47 from the Matsubara self-energy—are outputs of the DMFT self-consistency rather than inputs. The Hubbard U ~ 4.8 eV is taken from an experimental PES estimate, but it is a model parameter, not the same quantity as the predicted incoherent peak or mass enhancement; this reduces the strength of the benchmark but does not make the comparison circular by construction. The authors' self-citations (Refs 14, 15, 30, 36-39) are contextual or corroborative and are not used as the justification for the central result. The main text defers U/J values and the double-counting scheme to the Supplemental Material, which is a transparency and robustness concern, not a circularity. No equation is recycled as its own output, and no fitted parameter is relabeled as a prediction.

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

The central claim rests on a standard but approximate many-body method, on a specific magnetic order taken from experiment, and on interaction parameters that are not fully disclosed. No new physical entities are introduced.

free parameters (2)

U (Cr t2g on-site Coulomb interaction) = not stated in main text (experimental estimate 4.8 eV from Ref [24])
Controls the correlation strength in both DFT+U and DFT+DMFT; the metal/insulator competition and the Hund's metal classification depend on it, but the actual DMFT value is deferred to the Supplemental Material.
J (Hund's coupling) = not stated in main text
Hund's coupling is the claimed driver of the non-Fermi liquid and heavy-fermion behavior; its value in the DMFT impurity model is not reported in the main text.

assumptions (4)

domain assumption DFT+DMFT with a local self-energy is an adequate approximation for CaCrO3.
All many-body results in Fig. 2 and Fig. 4 rely on treating dynamic correlations through a local impurity model; nonlocal correlations are neglected.
domain assumption The magnetic ground state of CaCrO3 is collinear C-type AFM with the magnetic primitive cell identical to the crystal primitive cell.
This order, taken from neutron scattering Refs [23,24], is the basis for the altermagnetic symmetry classification and the spin-polarized DFT+DMFT setup.
domain assumption The Cr t2g subspace with the chosen U and J (values in the Supplemental Material) faithfully represents the local Coulomb physics.
The Hund's metal and incoherence results are sensitive to these parameters; the main text quotes only the experimental U estimate, not the actual DMFT values.
standard math Analytic continuation of imaginary-time quantum Monte Carlo data via maximum entropy yields a reliable real-frequency spectral function.
The spectral functions in Fig. 2 and the location of the incoherent peak at about -0.2 eV depend on the MaxEnt procedure, which is inherently ill-posed.

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Cite this review

Pith. "Pith review of Strongly correlated altermagnet CaCrO$_3$." pith.science (2026). https://pith.science/paper/5KOCWIL4

@misc{pith2026250714081,
  author       = {Pith},
  title        = {Pith review of: Strongly correlated altermagnet CaCrO$_3$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5KOCWIL4}},
  note         = {Machine review of arXiv:2507.14081}
}

abstract

Altermagnetism, a newly discovered magnetic phase, has spurred growing research activity. Studies from a perspective of dynamical electronic correlation still remain scarce. Employing density functional theory plus dynamical mean-field theory (DFT+DMFT) that incorporates dynamical electronic correlation, we demonstrate that CaCrO$_3$ is a strongly correlated altermagnet. Our DFT+DMFT calculations successfully reproduce the correlated metallic behavior of CaCrO$_3$ and quantitatively capture the incoherent state observed experimentally. We also identify that the altermagnetic CaCrO$_3$ is a Hund's metal. The incoherent state is attributed to Hund's coupling, which gives rise to a non-Fermi liquid behavior. Moreover, we find that altermagnetism can induce flat bands, and these incipient flat bands are further promoted by the strong renormalization from Hundness, which further drives a heavy-fermion behavior. Hence, we establish CaCrO$_3$ as a strongly correlated altermagnet and propose that Hund's metals provide an ideal platform for investigating the interplay between electronic correlation and altermagnetism. Our work will promote the study of strongly correlated altermagnetism physics.

Figures

Figures reproduced from arXiv: 2507.14081 by the authors.

**Figure 2.** FIG. 2. Band structures of CaCrO [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** FIG. 3. (a) DFT+DMFT calculated imaginary-time spin-spin c [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: FIG. 4. (a) Initial and converged spectral functions [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

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Forward citations

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