Spin-Chirality-Driven Bulk Photovoltaic Effect in van der Waals Magnet CrSBr

Dezhao Wu; Meng Ye; Wenhui Duan; Yong Xu

REVIEW 3 major objections 5 minor 56 references

Spin-Chirality-Driven Bulk Photovoltaic Effect in van der Waals Magnet CrSBr

T0 review · 3 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Vector spin chirality in a canted antiferromagnet drives a switchable, time-reversal-even bulk photovoltaic effect.

desk verdict A clean, novel symmetry mechanism for i-type BPVE via spin chirality, with convincing DFT support in CrSBr; the main caveat is the simplified modeling of the field-induced canted state, which is addressable rather than fatal. read the letter →

arxiv 2608.03492 v1 pith:MIJEDB6R submitted 2026-08-04 cond-mat.mtrl-sci

Dezhao Wu , Yong Xu , Meng Ye , Wenhui Duan This is my paper · ORCID

classification cond-mat.mtrl-sci

keywords bulkphotovoltaiceffectvectorspinchiralitychiralshiftcurrentinjectionCrSBrcantedantiferromagnetspin-orbitcouplingfirst-principlescalculations

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

The paper predicts that vector spin chirality, the cross product of neighboring magnetic moments, can generate an unconventional kind of bulk photovoltaic current in magnetic materials. In bilayer antiferromagnetic CrSBr, a small magnetic field cants the spins, producing a nonzero spin chirality that breaks the combined parity-time symmetry while leaving the crystal centrosymmetric. The authors show that this activates two new photocurrents, a chiral shift current and a chiral injection current, whose magnitudes match conventional shift currents but which can be switched on and off, reversed in direction, and continuously tuned by the applied magnetic field. A careful reader would care because it provides a magnetic, rather than crystallographic, knob for controlling photocurrents, and an experimentally accessible material in which to test it.

What carries the argument

The central object is the vector spin chirality κ = S_A × S_B, the cross product of the moments in the two CrSBr layers. In the centrosymmetric bilayer, the creation of κ by spin canting breaks the combined PT symmetry, converting the material's magnetic point group from one that forbids i-type photocurrents to one that allows selected chiral shift and injection tensor components. The argument then runs through the second-order photoconductivity tensors σ(i) and η(i), computed from first principles, whose symmetry-allowed components (e.g., σ^yyy_CSC, η^xxy_CIC) carry the current and whose k-resolved analysis identifies the deep-valence-band optical channel responsible for the response.

What would settle it

Measure the in-plane photocurrents of bilayer CrSBr under y-polarized light as the field along z is swept through ±0.3 T: the claim requires the y-axis chiral current to switch sign with field reversal while the x-axis magnetic injection current stays put, and requires zero y-channel current in zero field; any other pattern falsifies the mechanism.

Watch

Extended reading notes

Core claim

Using symmetry classification and first-principles calculations on bilayer CrSBr in a canted antiferromagnetic state, the paper establishes that vector spin chirality κ = S_A × S_B acts as a generator of an i-type (time-reversal-even) magnetic bulk photovoltaic effect. This effect consists of a chiral shift current (CSC) under linearly polarized light and a chiral injection current (CIC) under circularly polarized light, both absent in the pristine collinear PT-symmetric antiferromagnet and both activated when spin canting breaks PT symmetry. In addition to showing that the current magnitudes are comparable to conventional shift currents, the paper demonstrates three control features: on/off

Load-bearing premise

The predictions assume that the spin-canting angle of bilayer CrSBr can be treated as a well-defined external control parameter set by the magnetic field, with no spin-flop transitions, domains, or non-rigid spin rearrangements intervening.

Editorial extensions

If this is right

With about 0.3 T producing a 10° canting, bilayer CrSBr should show chiral shift and injection currents of the same order as conventional shift currents while the un-canted state shows none.
Reversing the magnetic field reverses the spin-canting direction and hence the sign of the chiral currents, while leaving intrinsic c-type currents (MIC, MSC) unchanged; this PT-based rule is a clean experimental fingerprint.
Sweeping the field from 0 to about 2 T tunes the canting angle and modulates the currents nonmonotonically, with maximum intensity around 45°, giving a magnetic-field-controlled optical switch.
Under linearly polarized light, the intrinsic MIC and chiral CSC flow along orthogonal directions, so a multiterminal device can measure them separately and confirm the effect without ambiguity.
The low-frequency response is carried by an optical transition channel from deeper valence bands, so the effect will not be captured by band-edge-only models or by the nesting channel that dominates chiral second-harmonic generation in the same material.

Reading between the lines

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

Editor's extension: No external field is needed in materials where noncollinear order is intrinsic; the same CSC/CIC mechanism should make spin spirals and skyrmion lattices produce chiral photocurrents whose sign encodes the handedness of the magnetic texture.
Editor's extension: Because the computed currents scale with spin-orbit coupling strength, chemical substitution or heterostructure engineering of SOC in the CrSX family should provide a second knob, beyond field angle, for designing the chiral photocurrent magnitude.
Editor's extension: The orthogonal-current geometry suggests a simple photocurrent-based magnetometer: measuring the ratio of the y- and x-channel currents under y-polarized light would provide a direct optical readout of the canting angle and hence the local magnetic field.
Editor's extension: The deep-valence-band channel's dominance may be generic for PT-broken magnetic bilayers, implying that full-band calculations, not low-energy models, are needed to predict chiral photocurrents in similar van der Waals magnets.

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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

Two things you should know about arXiv:2608.03492. First, it establishes a genuinely new class of magnetic BPVE: vector spin chirality κ breaks PT symmetry in centrosymmetric magnets and generates i-type shift and injection currents (CSC and CIC), distinct from the usual c-type magnetic BPVE. Second, the symmetry analysis and first-principles evidence in bilayer CrSBr are solid; the paper is worth a serious referee despite a couple of modeling simplifications.

What's new: previous work on magnetic BPVE focused on collinear magnets with time-reversal-odd (c-type) responses. Here, noncollinear spin order gives a time-reversal-even (i-type) response even when the crystal is centrosymmetric. The classification in Tables I-II is clean and useful. The demonstration that SOC is essential and that an unusual deeper-valence-band channel dominates the low-frequency response is concrete and interesting.

What it does well: The magnetic point group analysis is rigorous, and the computed tensor components match the symmetry predictions exactly. The switching/reversal behavior (reversal of canting direction ~ PT operation) is checked numerically. The magnitude is comparable to conventional shift currents.

Soft spots, in order of importance: (1) The field-induced canted state is modeled by simply rotating spins to a fixed angle θ, with no self-consistent spin Hamiltonian or explicit B field. The paper cites experiments for the 0.3 T/10° estimate, which is reasonable for small canting, but the larger-θ tunability curves assume a rigid sequence of magnetic point groups that could be modified by spin-flop, domains, or non-uniform canting. I think this is a modeling caveat, not a fatal flaw: the core mechanism survives for any noncollinear state with the same symmetry. But the authors should be pushed to clarify the mapping to B and discuss robustness. (2) No code or data deposited; 'available upon request' is weak for reproducibility. (3) No excitonic corrections; for CrSBr, where excitons dominate optical properties, this could affect quantitative spectra, though the symmetry-based conclusions stand.

The stress-test note worries that the rigid-canting assumption is load-bearing. I'd push back: the central claim is the existence of the mechanism, not the precise B(θ) relation. Even if real CrSBr's canted state has φ≠0 or a different MPG, the paper's thesis about spin chirality as a BPVE source remains. For this specific material, the symmetry predictions would need updating, but the paper already gives the general classification.

Bottom line: This paper deserves peer review. The referee should focus on the magnetic-state modeling and ask for shared data/code. I'd be happy to cite it for the classification; I'd bring it to a reading group on nonlinear optics in magnets.

Referee Report

3 major / 5 minor

Summary. The paper proposes a new subclass of bulk photovoltaic effect (BPVE) driven by vector spin chirality κ, termed chiral shift current (CSC) and chiral injection current (CIC). These are classified as i-type (time-reversal-even) but of magnetic origin, in contrast to conventional c-type magnetic BPVE. Using bilayer CrSBr as a prototype, the authors combine a magnetic point-group analysis with first-principles PBE+U+SOC calculations. They show that the pristine PT-symmetric AFM state supports only c-type MIC and MSC, while a canted AFM state with κ ≠ 0 breaks PT symmetry and activates CSC/CIC with the predicted nonzero tensor components. They report field-switchable on/off behavior, reversal of photocurrent direction on reversing the canting direction, continuous intensity modulation with canting angle, and identify SOC, interlayer coupling, and an unusual deep-valence-band channel as controlling factors.

Significance. If the central claims hold, this would establish a genuinely new mechanism for i-type BPVE arising from noncollinear magnetism, with symmetry-based switching properties that are distinct from both conventional shift currents and previously studied c-type magnetic BPVE. The paper's strengths include a clean symmetry classification (Tables I–III), a consistent first-principles verification of the nonzero tensor components and their switching rules, and a plausible experimental protocol using the orthogonal directions of MIC and CSC under y-polarized light. The calculation pipeline (Wannier interpolation, 400×400 k-mesh, standard shift/injection-current formulas) is appropriate and reproducible in principle. However, the quantitative magnitude claims and the central tunability story rest on an assumption about how an applied magnetic field realizes the assumed rigid spin-canting states, which is not demonstrated in the manuscript.

major comments (3)

[CSC and CIC in BL CrSBr, paragraph beginning 'We took the out-of-plane canting state...'] The central claims of on/off switching and continuous modulation assume that a small applied field B along z realizes the rigid spin configuration (θ, φ) = (10°, 0°) and more generally the sequence in Table III up to θ=90°. No self-consistent Zeeman calculation, spin model, or energy minimization is presented; the '0.3 T for 10°' statement is qualitative and not derived. If field-induced spin-flop, non-uniform canting, or domain formation occurs, the magnetic point group would differ and the predicted zero/nonzero tensor components and their reversals would not apply. This is load-bearing for the 'exceptional tunability' claim. Please either compute the field-dependent magnetic ground state (e.g., with a classical spin model fitted to CrSBr parameters) or explicitly reframe the results as predictions for an idealized rigid-canting model and temper the experimental protocol claims.
[Fig. 5 and Discussion, intensity modulation claim] The continuous intensity modulation of σ_yyy_CSC and η_xxy_CIC as a function of θ is computed by manually rotating all spins at fixed θ. In reality, the equilibrium canting angle under an external field is determined by the competition between Zeeman energy, exchange, and anisotropy, and the angle–field relation B(θ) is not necessarily monotone or single-valued. The claim that the photocurrent can be 'continuously and dynamically modulated by an external magnetic field' therefore goes beyond what the calculations show. The computed θ-dependence is a valid model response, but the mapping to B should be treated as an assumption or supported by a microscopic model.
[Methods and Fig. 2(a), magnitude comparison] The statement that CSC/CIC magnitudes are 'comparable to' conventional NSC in other 2D magnets is based on PBE+U independent-particle optics without excitonic effects. CrSBr is known to have strong excitonic physics, and the 0.98 eV resonance analyzed here is close to exciton-dominated spectral regions. The symmetry and switching conclusions are unaffected, but the quantitative magnitude comparison should be qualified, or a BSE/GW-level check for at least one representative peak should be provided if the magnitude claim is retained.

minor comments (5)

[Table III caption] The sentence 'The notations of MPGs follow the direction sequence of x, y and z' is opaque. Please spell out an example, e.g., m'2'm' means the m' plane is perpendicular to x and the m' plane to z.
[Fig. 2(d)] The caption says 'all independent in-plane tensor components' but the main text only discusses σ_yyy_CSC and η_xyy_MIC. Please identify each component in the panel or in the caption.
[Reference [17]] The DOI string '10.1038/s41563-026-02593-8' appears to contain an extra hyphen or an unusual volume marker. Please verify the bibliographic data.
[Eq. (1) and surrounding text] The phrase 'the last two indices' when stating abc=acb could be misread as a=b; it means interchange the second and third Cartesian indices. Consider writing 'abc is symmetric under b↔c'.
[General presentation] The term 'time-reversal-even magnetic BPVE' in the abstract may confuse readers because the i-type nature is defined by PT symmetry, not by T alone. A brief clarification in the introduction would help.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the first-principles photocurrents are not equivalent to their inputs; only minor non-load-bearing self-citations appear.

full rationale

The central derivation is self-contained. The paper begins from the standard decomposition of rectification currents (Eq. 1) and computes the i-type shift/injection photoconductivities from first-principles Wannier-interpolated wavefunctions for explicitly prescribed spin-canted CrSBr magnetic configurations. The predicted CSC and CIC components are not fitted to any experimental photocurrent or to the claimed effect; they emerge from the calculated band structure and from symmetry analysis (Table III), and the numerical results (Figs. 2-5) confirm the nonzero components. The only self-referential elements are the authors' own computational implementation (refs. 44-46) and a comparison with their prior SHG study (ref. 30); neither feeds the target result into the photocurrent calculation. The statement that a canting angle of 10 degrees corresponds to B approximately 0.3 T is a physical modeling input, not a fitted or derived prediction; while it may carry empirical uncertainty (e.g., spin-flop or domain effects), it is not a circularity. Therefore no step of the derivation reduces to its own input by construction.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central quantitative predictions rest on the standard BPVE formalism, the assumed magnetic point group of the canted state, and the fixed-spin approximation that maps an experimental magnetic field to a prescribed canting angle. No new physical entities are introduced; CSC and CIC are labels for existing photocurrent types arising from a new symmetry-breaking channel.

free parameters (3)

Hubbard U_eff on Cr 3d = 3 eV
An empirical correction from prior CrSBr studies (refs 32-43) that influences the band gap and photocurrent line shape; not fitted to BPVE data here but chosen by hand.
Broadening width for optical response = 0.05 eV
Applied to the Dirac delta in the response formulas; affects peak heights and spectral smoothness, chosen as a typical value.
Spin-canting angle θ = varied 0°-90°, representative 10°
External control parameter; the paper assumes the experimental B field maps to this angle (about 0.3 T for 10°). Not fitted, but the central tunability claim depends on it.

assumptions (5)

domain assumption The microscopic shift-current and injection-current formulas in Eq. (1) and SI Section IB correctly describe second-order photocurrents in 2D magnets with SOC.
The paper relies on the formalism of refs 44 and 45 but does not re-derive it; the entire quantitative prediction depends on these expressions.
domain assumption The crystal and magnetic symmetries of BL CrSBr, and the magnetic point groups listed in Table III, accurately describe the canted AFM state.
The selection rules and allowed tensor components are obtained from this symmetry classification; if the actual canted state has a different point group, the predicted current components could vanish or change.
ad hoc to paper The spin-canting angle θ, once fixed, is the sole order parameter for PT-breaking; the electronic structure at that fixed spin configuration represents the experimental field-induced state.
The paper uses a fixed-spin approximation rather than a self-consistent Zeeman-field calculation; the mapping to B is taken from experiments (refs 32-43).
domain assumption PBE+U (U=3 eV) and DFT-D3 give a sufficiently accurate ground state for computing BPVE spectra.
Standard DFT approximations are used; band gaps and wavefunctions are approximate, and excitonic effects are neglected.
standard math The i-type/c-type classification in Tables I and II is exhaustive; no other symmetry-breaking mechanism contributes to the photocurrents at the same order.
This is a group-theoretic classification based on P, T, and PT symmetries.

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Cite this review

Pith. "Pith review of Spin-Chirality-Driven Bulk Photovoltaic Effect in van der Waals Magnet CrSBr." pith.science (2026). https://pith.science/paper/MIJEDB6R

@misc{pith2026260803492,
  author       = {Pith},
  title        = {Pith review of: Spin-Chirality-Driven Bulk Photovoltaic Effect in van der Waals Magnet CrSBr},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MIJEDB6R}},
  note         = {Machine review of arXiv:2608.03492}
}

read the original abstract

The bulk photovoltaic effect (BPVE) can be greatly enriched in magnetic materials. Here, we establish vector spin chirality as a tunable knob for generating an unconventional time-reversal-even magnetic BPVE, comprising the chiral shift current (CSC) and chiral injection current (CIC). Using bilayer antiferromagnetic (AFM) CrSBr as a prototype, we theoretically demonstrate the emergence of CSC and CIC. Compared with conventional photovoltaic currents arising from noncentrosymmetric crystal structures or collinear magnetic orderings, CSC and CIC not only possess comparable magnitudes but also exhibit exceptional tunability. Specifically, they can be switched on and off by magnetic-field-induced spin canting, reversed in direction upon canting-direction reversal, and continuously modulated in intensity via canting-angle variation. Furthermore, we reveal an unusual optical transition channel governing both currents in CrSBr. Our work establishes an unconventional magnetic BPVE with remarkable controllability, paving the way for applications in optoelectronics and magnetic sensing in noncollinear magnets.

Figures

Figures reproduced from arXiv: 2608.03492 by the authors.

**Figure 2.** FIG. 2. Generation and switching of LPGE in BL CrSBr. (a) Spin-canting-induced changes in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3. CPGE in BL CrSBr. (a) Schematic of the intrinsic MSC [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: FIG. 4. Mechanism of CSC and CIC in BL cAFM CrSBr exemplified by the ( [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: FIG. 5. Continuous intensity modulation of CSC and CIC in BL cAFM CrSBr under different spin-canting angles. (a)-(b) [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

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