Altermagnetic Perovskites

Hitoshi Seo; Makoto Naka; Yukitoshi Motome

Altermagnetic Perovskites

T0 review · 0 major / 8 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Perovskites with the common GdFeO3-type octahedral rotation are predicted to be altermagnets, exhibiting spin-split bands and spin-current generation without spin-orbit coupling, and a component-specific anomalous Hall effect with it.

desk verdict A solid, honest review that reclassifies known perovskite antiferromagnets as altermagnetic candidates; the symmetry framework is the real value, the quantitative table is softer. read the letter →

arxiv 2411.11025 v1 pith:P6XAT5AM submitted 2024-11-17 cond-mat.str-el

Makoto Naka , Yukitoshi Motome , Hitoshi Seo This is my paper · ORCID

classification cond-mat.str-el

keywords altermagnetismperovskiteoxidesantiferromagnetspincurrentanomalousHalleffectGdFeO3-typedistortionHubbardmodelspin-orbitcoupling

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This review argues that the standard octahedral rotation found in most perovskite oxides — the GdFeO3-type distortion — turns many antiferromagnetic perovskites into altermagnets, a class of magnets with zero net magnetization but broken time-reversal symmetry. Working from a multi-orbital Hubbard model, the authors show that the rotation makes electron hoppings sublattice-dependent and spatially anisotropic, which together with a C-type antiferromagnetic order produces non-relativistic spin-split bands. In the metallic state these bands generate a spin current under an applied electric field without any spin-orbit coupling. When spin-orbit coupling is included, the same distorted structure gives a component-specific anomalous Hall effect that can be read off from the broken mirror and glide symmetries. A sympathetic reader would care because it predicts concrete, measurable cross-correlation phenomena in well-known compounds such as CaCrO3 and LaVO3.

What carries the argument

The load-bearing object is the multi-d-orbital Hubbard model on the distorted perovskite lattice, with transfer integrals evaluated through ligand p orbitals for a rigid-octahedra geometry parametrized by the rotation angle $\varphi$ (the GdFeO3-type distortion). Its key output is the pattern of nearest-neighbor inter-orbital hoppings that are sublattice-dependent — switched between the $[110]$ and $[1\bar{1}0]$ directions on the B1 versus B2 bonds — plus next-nearest-neighbor hoppings through the ligands. The former produce the non-relativistic spin splitting and spin current; the latter, together with spin-orbit coupling, produce the fictitious magnetic flux loops that generate the anomalous Hall effect. A symmetry rule — the anomalous Hall component is fixed by which two of the three mirror and glide operations are broken by the magnetic order — carries the classification in Table II.

What would settle it

Measure the spin current conductivity in CaCrO3 (C-type antiferromagnetic metal, $T_N \approx 90$ K) by applying an electric field along [010] and detecting the transverse spin current along [100]: the predicted symmetric tensor ($\chi_{xy} = \chi_{yx}$, $\chi_{xx} = \chi_{yy} = 0$) and its scaling with the longitudinal conductivity distinguish this mechanism from the spin Hall effect, and their absence below $T_N$ would refute the model.

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Extended reading notes

Core claim

The central claim is that altermagnetism is latent in the perovskite family: the GdFeO3-type distortion, present in many ABX3 compounds, makes the inter-orbital d-d transfer integrals sublattice-dependent and anisotropic in the specific pattern shown for the B1-B2 bonds, so that when the antiferromagnetic order breaks time-reversal symmetry, the band structure acquires a d-wave-like spin splitting even at zero spin-orbit coupling. This splitting yields a spin current conductivity with a symmetric tensor ($\chi_{xy} = \chi_{yx}$, diagonal elements zero) in the C-type antiferromagnetic metallic phase. With spin-orbit coupling, the next-nearest-neighbor hoppings through ligand p orbitals generate a net fictitious magnetic field along one axis, giving an anomalous Hall effect in the perpendicular plane; the rules are summarized in Table II, where breaking two of the three mirror and glide symmetries selects which Hall component is active. The authors therefore assert that the mechanism does not rely on spin-orbit coupling for the spin current, and that the anomalous Hall effect is driven by the collinear antiferromagnetic component with the same symmetry as the weak ferromagnetism, not by the net moment itself.

Load-bearing premise

The mechanism depends on the tight-binding parametrization in which the rotated octahedra fix the orbital overlaps through ligand p orbitals with a rigid-octahedra geometry; if the real orbital overlap pattern differs, the predicted spin splitting, spin-current sign, and Hall selection rules could fail even though the symmetry analysis remains formally correct.

Editorial extensions

If this is right

CaCrO3 and LaVO3, which show C-type antiferromagnetic order and GdFeO3-type distortion, are predicted to exhibit electric-field-driven spin currents in their metallic antiferromagnetic phases.
Several orthorhombic perovskites (for example LaCrO3, YCrO3, LaFeO3, and doped manganites) are predicted to show anomalous Hall conductivity in specific planes selected by their antiferromagnetic pattern, such as $\sigma_{xy}$ for $G_xA_yF_z$ and $\sigma_{yz}$ for $F_xC_yG_z$.
The spin-current generation is a dissipative effect whose conductivity should scale with the longitudinal electrical conductivity below the Néel temperature, distinguishing it from the spin Hall effect.
The anomalous Hall effect can appear even when the net magnetization is zero, because a single collinear antiferromagnetic component that breaks the required symmetries is sufficient.
The symmetry rule extends beyond perovskites to the organic altermagnet $\kappa$-(ET)2X, which belongs to the same space group Pbnm.

Reading between the lines

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

If the mechanism holds for the listed compounds, many previously ordinary antiferromagnetic perovskites — including doped manganites and ferrites — would be reclassified as altermagnetic candidate materials, and past transport data might already contain unread spin-current or Hall signals.
The same orbital-overlap logic suggests that layered Ruddlesden-Popper perovskites and 4d/5d systems, which also exhibit octahedral rotations, may show altermagnetic responses with altered anisotropy patterns, a testable extension beyond the paper's explicit list.
A direct experimental test would be spin- and angle-resolved photoemission on a cleaved CaCrO3 or LaVO3 surface below $T_N$: the predicted d-wave spin splitting should vanish on the $k_x=0$ and $k_y=0$ mirror planes, a signature not present in conventional Néel antiferromagnets.
The proximity-effect anomalous Hall effect already observed at interfaces of distorted perovskites could be interpreted as the present altermagnetic Hall effect combined with scalar spin chirality, an idea the authors flag as awaiting further analysis.

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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

Short version: this is a review, not a new-results paper, and it says so. The value is in the synthesis: it connects the early first-principles work of Solovyev and Okugawa et al. to the authors' own Hubbard-model calculations, and boils the altermagnetic response down to a clean symmetry table (Table II). That table is internally consistent and matches the earlier ab initio AHE results, so the central classification argument holds up.

What's actually new here is the packaging: a systematic candidate list (Table III) that maps AFM patterns in distorted perovskites onto spin-current and AHE expectations. That's useful for experimentalists. The paper is honest about its own status and about the fact that the spin-current mechanism was predicted in the authors' earlier PRB papers. Self-citation in that context is legitimate; those papers contain parameter sweeps and falsifiable predictions, not fittings of the target result.

Soft spots, in proportion: the quantitative predictions for spin-current conductivity and AHE magnitude rest on the tight-binding parametrization of the GdFeO3 distortion, specifically the sublattice-dependent inter-orbital hoppings in Sec. III. That's a real limitation. The symmetry argument is robust, but the signs and magnitudes in Table III could change if the rigid-octahedra geometry with a single tilt angle miscalculates the actual d-d overlaps. The stress-test note is right about that being the weakest load-bearing point. It's not fatal for a review, because the qualitative altermagnetic behavior is symmetry-protected and the authors say the table is non-exhaustive, but readers should treat the specific compounds as candidates, not confirmed predictions. Also, there's no direct experimental confirmation of spin currents in these perovskites yet; the paper notes that.

Who's this for? Experimentalists working on perovskite oxides and people entering the altermagnetism literature. A serious referee should engage with the symmetry table and check the model-to-material mapping; the paper deserves review rather than desk rejection. My own verdict: send it to review, with the expectation that the authors tighten the discussion of the tight-binding uncertainty.

Referee Report

0 major / 8 minor

Summary. This manuscript reviews the authors' and others' theoretical work on altermagnetism in perovskite-structure oxides, with emphasis on the microscopic mechanism by which GdFeO3-type octahedral rotations combine with collinear antiferromagnetic order (particularly C-type order in d2 systems) to produce non-relativistic spin splitting and electric-field-driven spin currents, and, in the presence of spin-orbit coupling, component-specific anomalous Hall effects. The review introduces a multiorbital Hubbard model with nearest- and next-nearest-neighbor ligand-mediated d-d hoppings, summarizes model results for the C-type antiferromagnetic phase, establishes a symmetry-based selection rule for the anomalous Hall effect in the four AFM patterns compatible with Pbnm symmetry (Table II), and compiles a candidate-material table with predicted cross-correlation phenomena (Table III).

Significance. The review's main contribution is a clear synthesis: the symmetry-based Table II connects the four allowed AFM patterns in the Pbnm perovskite structure to the corresponding anomalous Hall conductivity components, and it is consistent both with the earlier ab initio results of Solovyev (Ref. [30]) and with the authors' own model calculations. The paper also makes a useful pedagogical point by separating the symmetry-allowed existence of spin splitting and AHE from the model-dependent microscopic mechanisms (anisotropic sublattice-dependent hoppings for spin currents; next-nearest-neighbor triangular-loop fictitious flux for the AHE). The candidate table (Table III) provides a practical guide for experimental searches. A notable strength is that the model calculations are parameter sweeps rather than circular fits, so they yield falsifiable predictions (nonzero χ_xy in metallic C-type AFM phases, σ_yz in the FxCyGz state, and so on). The main limitation is that the quantitative magnitudes and signs of χ_xy and σ_yz are derived from a rigid-octahedra tight-binding parametrization (Sec. III, Eq.

minor comments (8)

[Abstract and throughout] The abstract contains the typo "Altermagneticsm" and the main text contains several misspellings (e.g., "orbtial" in Sec. I, "perovkite" in Sec. I, "interation" in Sec. IV, "canditate" in Sec. VII, "comoponents" in the Table III caption, "electic" in Sec. VIII); these should be corrected.
[Sec. III, Eq. (1)] The notation "NN∑" and "NNN∑" is unconventional and potentially confusing; please replace it with standard sums over nearest-neighbor and next-nearest-neighbor pairs, such as Σ_{⟨ij⟩} and Σ_{⟨⟨ij⟩⟩}, with a brief definition.
[Sec. III, after Eq. (1)] The statement that "the additional tilting ψ is uniquely determined by φ [32]" is a strong geometric simplification; real perovskites often exhibit independent rotation and tilting amplitudes, so the manuscript should specify the assumed Glazer tilt system or justify why a single-parameter description is adequate for the model.
[Sec. V, Fig. 5] Please replace "constantly zero" with "identically zero" when describing χ_xy at φ = 0, and clarify that the displayed χ_xy values are model results for a representative parameter set, not first-principles predictions.
[Sec. VI, Fig. 6] The definition of the tilde quantities (σ̃_yz and σ̃_zx) is given only in the text; the caption of Fig. 6(a) should also state that these are obtained by artificially keeping only the major collinear AFM component in the mean-field solution.
[Sec. VII, Table III] The table caption says "whose deviation from 180° indicates the degree of the GdFeO3-type distortion," but for A-site-substituted compounds the B-X-B angle depends on composition; please state the composition to which each listed angle refers or note that the angle is representative.
[References] Reference [68] lists the authors "A. Birk Hellenes" and "Z. Jansa" twice each; please correct the author list.
[Sec. VII and Summary] The manuscript would benefit from an explicit caveat that the quantitative values (magnitudes and signs) of the spin-current conductivity and anomalous Hall conductivity shown in Figs. 5 and 6 are model-dependent and may be revised by future first-principles calculations; the qualitative existence and the choice of tensor components follow from symmetry and are the robust predictions.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the model outputs (spin splitting, spin-current conductivity, anomalous Hall effect) are parameter-sweep results from a stated Hubbard model, not fits to or restatements of the target predictions.

full rationale

The paper is a review built around the authors' prior model studies Refs. [5,6], but the central derivation is not circular. The microscopic Hamiltonian in Sec. III, Eq. (1), takes as input only the multiband d-p Hubbard hoppings through ligand p orbitals in a rigid-octahedra geometry, plus U, J, I, and spin-orbit coupling; the target quantities, the spin-current conductivity chi_xy in Fig. 5(a) and the Hall conductivity sigma_yz in Fig. 6(a), are computed outputs that are shown to vanish at phi=0 and to have nontrivial U and phi dependence. No target observable is used to fix the hopping parameters, and the spin splitting is a band-structure consequence rather than a definitional restatement of the anisotropic-hopping input. The requirement of NNN hoppings for the AHE is a calculated finding, not an assumed equivalence. The symmetry rule in Table II is independently backed by the earlier ab initio results of Solovyev (Ref. [30]) and by the group-theoretic analysis. Candidate assignments in Table III are tied to experimentally determined AFM patterns and Neel temperatures with external references, and the CaCrO3 AHE is cross-checked against the independent DFT calculation of Nguyen and Yamauchi (Ref. [47]). Thus the heavy self-citation is normal for a review of the authors' own line of work and does not reduce any prediction to its input by construction.

Assumptions & free parameters 6 free parameters · 8 assumptions · 0 invented entities

The review rests on the authors' earlier multi-orbital Hubbard model studies and on independent first-principles calculations. The quantitative predictions depend on model parameters chosen from the perovskite literature rather than fitted to the target effects, and on a rigid-octahedra parametrization of the lattice distortion. No new physical entities are introduced; the fictitious magnetic flux in Sec. VI is an emergent gauge description of hopping phases, not a new force or conserved quantity. The symmetry-based selection rules are the most robust part, while the numerical magnitudes of the spin-current and Hall conductivities are the least robust.

free parameters (6)

U (intra-orbital Coulomb repulsion) = ~0.6 to 1.2 eV scanned; main results near 0.725 eV
Chosen as typical for 3d transition-metal oxides, not fitted to the spin-current or Hall data; the phase diagram in Fig. 5(a) depends on it.
U' (inter-orbital Coulomb repulsion) = not stated in text
Enters the Hubbard interaction in Eq. (2); a standard Kanamori parameter set is assumed.
J (Hund coupling) = not stated in text
Enters Eq. (2); affects the stability of the C-type AFM state and orbital order.
I (pair-hopping interaction) = not stated in text
Enters Eq. (2); part of the standard rotationally invariant interaction, usually taken equal to J.
zeta (spin-orbit coupling strength) = not stated in text
Needed for the anomalous Hall effect in Sec. VI; treated as small, typical for 3d elements.
phi (GdFeO3 rotation angle) = 0 to 25 degrees in Figs. 5 and 6
Structural input from experiment and geometry, not fitted; the spin splitting and AHE vanish at phi equals zero, so it is load-bearing.

assumptions (8)

domain assumption The GdFeO3-type tilting angle psi is uniquely determined by the rotation angle phi for the orthorhombic perovskite structure (Sec. III, Ref. [32]).
This rigid-octahedra relation fixes the geometry from which all transfer integrals in Eq. (1) are computed.
domain assumption NN and NNN d-d transfer integrals are obtained from ligand p-orbital mediated d-p-d and d-p-p-d hopping processes on the rotated octahedra (Sec. III, Eq. (1)).
The sublattice-dependent anisotropy that produces altermagnetism enters through these integrals; their quantitative accuracy is assumed.
standard math The Hubbard interaction Hint is treated at the Hartree-Fock mean-field level (Secs. V and VI).
Used to obtain the C-type AFM phases and the spin-dependent band structure; ignores fluctuations.
standard math The spin-current conductivity is computed with Boltzmann transport theory in the metallic C-AFM phase (Sec. V).
Assumes a well-defined Fermi surface and dissipative transport; the paper notes that the effect scales with longitudinal conductivity.
domain assumption The AHE calculation is restricted to a three-band t2g model (Sec. VI).
Assumes eg orbitals do not change the qualitative Hall response in the C-type AFM phases with GdFeO3 distortion.
standard math The four spin patterns FxCyGz, CxFyAz, GxAyFz, and AxGyCz exhaust the possible AFM configurations under Pbnm/Pnma (Sec. IV).
This symmetry classification, taken from Treves and Bertaut, underlies Table II and the AHE selection rules.
domain assumption The (3d)^2 C-type AFM state with G-type orbital order is the relevant ground state over the studied U-phi region (Sec. V, Fig. 5(a)).
The spin-current predictions are made in the C-AFM metallic phase; phase boundaries come from the same mean-field calculation.
domain assumption The experimental AFM patterns and Neel temperatures compiled in Table III are correctly assigned to the listed candidate materials.
The expected spin-current and Hall signals depend on the actual magnetic ground state of each compound.

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Cite this review

Pith. "Pith review of Altermagnetic Perovskites." pith.science (2026). https://pith.science/paper/P6XAT5AM

@misc{pith2026241111025,
  author       = {Pith},
  title        = {Pith review of: Altermagnetic Perovskites},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/P6XAT5AM}},
  note         = {Machine review of arXiv:2411.11025}
}

abstract

Altermagnet is a class of antiferromagnets, which shows a staggered spin ordering with wave vector ${\bm q}=0$, while its net magnetization is canceled out in the limit of zero relativistic spin-orbit coupling. The simplest case is when the up and down spins are ordered on two crystallographically equivalent sublattice sites within the unit cell that are not connected by translation, and consequently, the system breaks the macroscopic time-reversal symmetry. Accordingly, it exhibits non-relativistic spin splitting in the energy band and characteristic cross-correlation phenomena between spin, charge, and lattice (orbital) degrees of freedom. This is in contrast to conventional N\'{e}el-type antiferromagnets with ${\bm q} \neq 0$ conserving the macroscopic time-reversal symmetry, where the time-reversal operation flipping of spins combined with translation can make the system identical to the original state. Altermagneticsm is universally latent in various magnetic materials that have been considered as simple collinear-type antiferromagnets. In this article, we focus on perovskites with chemical formula {\it ABX}$_3$, which are typical playgrounds for strongly correlated electron systems, and overview their altermagnetic aspects that have been overlooked in the past researches, based on microscopic model studies revealing the mechanisms of their properties. We display that a combination of a variety of antiferromagnetic ordering and the commonly-seen lattice distortions in perovskites gives rise to a non-relativistic spin splitting whose mechanism does not rely on the spin-orbit coupling and its consequent spin current generation, and the anomalous Hall effect in the presence of the spin-orbit coupling.

Figures

Figures reproduced from arXiv: 2411.11025 by the authors.

**Figure 3.** FIG. 3. (a) Perovskite structure with the GdFeO [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 2.** FIG. 2. (a) Optical Hall conductivity at finite [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: FIG. 4. (a) Schematic illustration of the collinear [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: FIG. 5. Spin current conductivity [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

**Figure 6.** Figure 6: (a) shows the U dependence of the dc Hall conductivity σyz in the Cy phase for φ = 25◦ . Since there is the ferromagnetic component Fx and the AHE appears in the plane perpendicular to its direction, one might recall the case for conventional ferromagnets. However, t…

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Third-order and fifth-order nonlinear spin-current generation in $g$-wave and $i$-wave altermagnets, and perfectly nonreciprocal spin-current in $f$-wave magnets
cond-mat.mes-hall 2024-11 conditional novelty 6.0 of 10

In two-band models of higher-wave magnets, the only nonzero nonlinear spin Drude conductivity has order equal to one less than the number of Fermi-surface nodes.

Reference graph

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[110] - B1 B2 B1 B2 B3 B4 FIG. 3. (a) Perovskite structure with the GdFeO 3-type distor- tion. B1-B4 denote the BX6 octahedra contained in the unit cell, connected by symmetry operations thus crystallographical ly equiva- lent. The x′y′z′ axes represent the local coordinate de...
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altermagnet

Figure 1(b) shows the schematic spin-split band struc - ture in altermagnets, which occurs even in the absence of the SOC, in stark contrast to the relativistic spin momentum loc k- ing, e.g., the Rashba effect. As discussed in Ref. [8] based o n the Hubbard model, the splitti...

2020

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

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