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Spontaneous in-plane anomalous Hall response observed in a ferromagnetic oxide

T0 review · 2 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Spontaneous anomalous Hall voltage observed at zero field in a ferromagnetic oxide.

desk verdict Genuinely new zero-field Hall observation in SrRuO3, but the in-plane AHE interpretation hinges on an untested assumption about strictly in-plane remanence. read the letter →

arxiv 2502.10018 v1 pith:A5TNWADI submitted 2025-02-14 cond-mat.mtrl-sci cond-mat.str-el

Shinichi Nishihaya , Yuta Matsuki , Haruto Kaminakamura , Yoshiya Murakami , Hiroaki Ishizuka , Masaki Uchida This is my paper · ORCID
classification cond-mat.mtrl-scicond-mat.str-el
keywords anomalousHalleffectin-planemagnetizationSrRuO3thinfilmsspontaneousresponsetrigonaldistortionorbitalferromagnetismzero-fieldtransportferromagneticoxide
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 reports that (111)-oriented SrRuO3 ultrathin films, whose magnetization prefers to lie in the film plane, produce a spontaneous anomalous Hall voltage at zero magnetic field. The signal is hysteretic, switches sign when the in-plane magnetization direction is rotated by 60 degrees, and vanishes at the Curie temperature, so it is tied to the ferromagnetic order itself. The authors interpret it as an off-diagonal transport response: the in-plane spin magnetization generates an out-of-plane orbital ferromagnetic moment through higher-order terms that trigonal distortion makes allowed. If correct, this is the first demonstration of a spontaneous, switchable in-plane anomalous Hall effect in a hard ferromagnet, and it opens a way to engineer Hall responses without applying any magnetic field.

What carries the argument

The load-bearing object is a symmetry-based expansion of the Hall conductivity on the Hall plane in powers of the field or magnetization direction cosines. For a cubic crystal on a (111) plane, the leading term is proportional to $B_{[100]}+B_{[010]}+B_{[001]}$, which vanishes when $B$ lies in the plane and therefore cannot produce the observed in-plane signal. The paper argues that trigonal distortion of the film, which breaks the threefold rotations about the three other $\langle111\rangle$ directions, allows third-order terms such as $B_{[100]}B_{[010]}B_{[001]}$; this term has the right polar-angle shape, including a local maximum at $[11\bar{1}]$ with sign opposite to $[111]$. Replacing $B$ by the magnetization $M$ in the same expansion explains why a spontaneous Hall response survives at zero field. The machinery is therefore a phenomenological higher-order coupling between the in-plane field or spin direction and an out-of-plane Hall vector.

What would settle it

Perform SQUID or polar-MOKE magnetometry at 2 K on the same films using the exact 9 T in-plane polarization protocol, and compare the measured out-of-plane remanent moment with the threshold needed to produce the observed zero-field $\rho_{yx}$ through the out-of-plane anomalous Hall hysteresis of Fig. 2A. If the out-of-plane remanence exceeds that threshold, the spontaneous in-plane interpretation fails; if it is negligible, the claim is supported.

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Extended reading notes

Core claim

On (111)-oriented SrRuO3 films with thicknesses of 4.1 and 7.0 nm, the Hall resistivity $\rho_{yx}$ measured while sweeping an in-plane field reaches values comparable to the conventional out-of-plane anomalous Hall effect, and it remains finite and hysteretic after the field is returned to zero. The zero-field Hall resistivity follows a square-wave pattern with threefold symmetry as the in-plane polarizing-field direction is rotated, and it disappears above the Curie temperature. Because the films have in-plane easy axes, the authors rule out the conventional explanation through an out-of-plane magnetization canting and instead attribute the response to out-of-plane orbital ferromagnetism off-diagonally coupled to the in-plane spin magnetization. The polar-angle scans show a nonmonotonic dependence with a sign change between $[111]$ and $[11\bar{1}]$, which in their analysis requires higher-order terms such as $B_{[100]}B_{[010]}B_{[001]}$ that become allowed under trigonal distortion.

Load-bearing premise

The load-bearing premise is that after a 9 T in-plane field is removed, the film's remanent magnetization remains strictly in the plane, so the zero-field Hall voltage cannot be a conventional out-of-plane anomalous Hall effect from magnetization canting; the paper infers this from transport angle scans, notably the closed hysteresis around the in-plane $[11\bar{2}]$ direction in Fig. 4A, without a direct magnetization measurement.

Editorial extensions

If this is right

  • A zero-field Hall state with memory exists in a conventional ferromagnetic oxide: polarizing along an in-plane easy direction leaves a large $\rho_{yx}$ that persists until the field is reapplied or the temperature approaches $T_C$.
  • The sign of the spontaneous Hall voltage is set by the in-plane magnetization direction, so a 60-degree rotation of the writing field reverses the output without requiring any out-of-plane field.
  • The trigonal-distortion analysis predicts a threefold-symmetric angular pattern for the in-plane anomalous Hall effect, and this pattern is observed in both the azimuthal and polar scans.
  • The response disappears at the Curie temperature and its magnitude follows the ferromagnetic hysteresis, indicating that it is intrinsic to the magnetic order rather than a field-geometry artifact.

Reading between the lines

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

  • Editorial extension: if the higher-order $M$-term mechanism is general, other trigonally distorted ferromagnetic films with in-plane easy axes and Berry-curvature-rich band structures should show the same spontaneous in-plane Hall effect, making it a design handle rather than an SrRuO3-specific accident.
  • Editorial extension: the paper treats the higher-order terms phenomenologically and does not quantify their relative weights, so a first-principles calculation of the anomalous Hall conductivity as a function of in-plane magnetization direction is the natural next test.
  • Editorial extension: the remanent, switchable Hall voltage suggests a magnetic-field-free Hall memory, but the paper does not address switching speed, cycling endurance, or whether the threefold pattern survives in patterned device geometries.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper reports magnetotransport measurements on (111)-oriented SrRuO3 ultrathin films (4.1 and 7.0 nm) at low temperature. It shows that Hall resistivity measured under an in-plane magnetic field is nonzero and hysteretic, has threefold azimuthal symmetry, and persists at zero field after in-plane polarization; the zero-field signal disappears near the Curie temperature and is reproduced in two samples and for two current directions. The authors interpret this as a spontaneous in-plane anomalous Hall effect coupled to the in-plane spin magnetization through higher-order terms allowed by trigonal distortion, and they support this with polar-angle scans that show a nonmonotonic θ dependence and a sign change near [11-1].

Significance. If confirmed, the observation would be the first spontaneous in-plane anomalous Hall effect in a hard ferromagnet, extending the recently studied field-induced in-plane AHE to a hysteretic material with a zero-field response. The experimental data are internally consistent: the zero-field signal tracks ferromagnetic order, appears in two samples and two current directions, and the azimuthal angular dependence matches the C3 symmetry of the (111) SrRuO3 film. The interpretation uses a standard symmetry expansion without fitted parameters. The main weakness is that the attribution of the zero-field signal to in-plane magnetization, rather than to a conventional out-of-plane AHE from a canted remanent state, is not backed by a direct magnetization measurement.

major comments (2)
  1. [§4, Fig. 4A and Supplementary Note S4] The central claim that the zero-field Hall signal is a spontaneous in-plane AHE rests on excluding out-of-plane canting of the remanent magnetization. The only evidence presented is the closed hysteresis loop near the in-plane [112] direction and the inference of in-plane easy axes from transport data. Fig. 4A itself shows a substantial ρyx,0T plateau for polarization near the out-of-plane [111] direction, with magnitude comparable to the in-plane value; for a hard ferromagnet with competing ⟨111⟩ magnetocrystalline and shape anisotropies, this is the signature expected if a partially out-of-plane remanent component survives. A direct vector magnetization measurement (SQUID or MOKE) at remanence, or an angle-resolved remanent-moment determination, is required to rule out a conventional out-of-plane AHE contribution from a canted or multi-domain remanent state. This is load-bearing for the title and abstract claims.
  2. [Discussion, Eqs. (1)-(2) and Fig. 4D] The higher-order term B[100]B[010]B[001], introduced to explain the sign change near [11-1], is an ad hoc symmetry-allowed term: it is not derived from the trigonal distortion parameters of the film and no fit or quantitative comparison with the measured ρyx(θ) is shown. Because the agreement in Fig. 4D is only qualitative, the statement that the zero-field response is shaped by this term is plausible but not quantitatively supported. The central claim does not depend on this term alone, but the interpretation would be substantially strengthened by a comparison of the calculated curves with the data, with stated magnitudes or an estimate of the relative weight of the linear and third-order terms.
minor comments (4)
  1. [Eqs. (1)-(2)] The notation is ambiguous: B is used both as a vector (B = B α_i e_i) and as a magnitude in the prefactors B, B^3, and B^5. Using B_i or m_i for vector components would make the expansion and the terms B^3_[100] etc. easier to follow.
  2. [Fig. 2 caption] The caption for the right panel of Fig. 2 appears to label the geometry as "B // [111]", which is the out-of-plane configuration shown in panel A; the in-plane configuration in panel B should be labeled with the in-plane field direction to avoid confusion.
  3. [§3, antisymmetrization procedure] The antisymmetrization ρyx(ϕ) = (ρyx,raw(ϕ) − ρyx,raw(ϕ+180°))/2 is used repeatedly but never explained; the text should state that this removes even-in-field longitudinal and planar-Hall contributions and isolates the odd Hall response.
  4. [Abstract and Discussion] The phrase "out-of-plane orbital ferromagnetism" is used as a conclusion, but no direct measurement of orbital magnetization is presented. It would be helpful to define the term operationally and to distinguish the inferred out-of-plane orbital moment from the measured transport signal.

Circularity Check

0 steps flagged · score 1.0 of 10

No constructional circularity: the symmetry expansion is parameter-free and the trigonal term is a post-hoc symmetry selection, not a fitted prediction; the main risk is the transport-only exclusion of out-of-plane canting, which is an evidential gap rather than a self-referential tautology.

full rationale

The paper's claimed derivation chain is an experimental observation interpreted with a general symmetry expansion, not a calculation that returns its own inputs. Equations (1) and (2) are stated as a general cubic-crystal expansion of the anomalous Hall conductivity in powers of B or M; no coefficients are fitted and no parameter is later relabeled as a prediction. The trigonal-distortion term B[100]B[010]B[001] is introduced only after the paper states that the cubic B^3 term 'cannot be fitted well' with the data (Discussion, Fig. 4D); this is a post-hoc symmetry selection whose angular dependence is fixed by symmetry, not a fitted quantity masquerading as a derivation. The self-citations ([6], [29], [30]) are background or growth-method references and are not load-bearing for the central claim. The one genuine weakness is evidentiary, not circular: the exclusion of out-of-plane canting rests on transport-inferred in-plane easy axes (Fig. 4A and Supplementary Fig. S4), and no independent magnetization measurement is provided. The paper itself flags the danger in the Introduction ('spin canting or reorientation derived by magnetocrystalline or shape magnetic anisotropy in ferromagnets may complicate observations') and later asserts 'All of these observations evidence ... spins aligned to the in-plane [112] direction' before concluding the zero-field response is not out-of-plane canting. That is under-support for the most load-bearing interpretation, and it should be weighed as a robustness/correctness concern, but it does not make the result equivalent to its inputs by construction. Thus the appropriate circularity finding is no significant circularity, with a low score reflecting only minor non-load-bearing self-citations and an interpretive inference that would benefit from independent magnetization data.

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

The paper introduces no fitted numerical parameters, but its symmetry-based interpretation relies on several domain assumptions: the exact crystal symmetry of the films, the strictly in-plane remanent magnetization, and the ad hoc inclusion of a trigonal-distortion-allowed third-order Hall term. These assumptions are not independently verified by direct measurements or calculations in the main text.

assumptions (4)
  • domain assumption The (111) SrRuO3 films possess C3 symmetry about [111] and related C2 axes and mirror planes, with trigonal distortion.
    Invoked in Fig. 2 and the Discussion to decide which Hall terms are allowed. Structural support is said to be in Supplementary Note S1, which is not fully provided in the main text.
  • domain assumption At zero field, the remanent spin magnetization is strictly in-plane when the polarizing field was applied in the plane, with no out-of-plane canting.
    This is load-bearing for ruling out conventional out-of-plane AHE. It is inferred from transport angle scans rather than from direct magnetization measurements.
  • standard math The Hall conductivity can be expanded as odd powers of the magnetic field B or magnetization M, as in Eqs. (1) and (2).
    This is a standard symmetry-based expansion used to interpret the theta dependence. It is not proved in the paper but is conventional in Hall effect analysis.
  • ad hoc to paper The trigonal distortion allows an additional third-order term B[100]B[010]B[001] that explains the sign change near [11-1].
    This term is introduced to match the observed nonmonotonic theta dependence. No microscopic derivation for SrRuO3 is given, and the authors state that the individual contributions are difficult to quantify.

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Pith. "Pith review of Spontaneous in-plane anomalous Hall response observed in a ferromagnetic oxide." pith.science (2026). https://pith.science/paper/A5TNWADI

@misc{pith2026250210018,
  author       = {Pith},
  title        = {Pith review of: Spontaneous in-plane anomalous Hall response observed in a ferromagnetic oxide},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/A5TNWADI}},
  note         = {Machine review of arXiv:2502.10018}
}
abstract

Recent observation of anomalous Hall effect (AHE) induced by magnetic field or spin magnetization lying in the Hall deflection plane has sparked interest in diverse mechanisms for inducing the Hall vector component perpendicular to the applied magnetic field. Such off-diagonal coupling, which is strictly constrained by symmetry of the system, provides new degrees of freedom for engineering Hall responses. However, spontaneous response as extensively studied for out-of-plane AHE remains unexplored. Here we elucidate in-plane AHE in a typical ferromagnetic oxide SrRuO$_3$. The (111)-orientated ultrathin films with in-plane easy axes of spin magnetization exhibit spontaneous AHE at zero field, which is intrinsically coupled to the in-plane spin magnetization and controllable via its direction. Systematic measurements by varying azimuthal and polar field angles further reveal complex Hall responses shaped by higher-order terms allowed by trigonal distortion of the films. Our findings highlight versatile and controllable in-plane Hall responses with out-of-plane orbital ferromagnetism.

Figures

Figures reproduced from arXiv: 2502.10018 by the authors.

Figure 1
Figure 1. Anomalous Hall effect by in-plane magnetic field. [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. Out-of-plane and in-plane AHE with a hysteresis loop [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. In-plane AHE at zero magnetic field. (A) ρyx of the SrRuO3 film (sample A), taken with continuously changing ϕ of various in-plane magnetic fields at 2 K. (B) Hall resistivity at zero magnetic field ρyx,0T, measured after applying the in-plane field of 9 T and then lowering it to 0 T at each ϕ. The measurements were performed at 2, 50, and 100 K. (C) ρyx,0T measured for another (111) SrRuO3 film with thickness of 7.… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Nonmonotonic polar angle dependence of AHE. [PITH_FULL_IMAGE:figures/full_fig_p016_4.png]

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