Coupling between magnetism and band structure in a 2D semiconductor

Alberto F. Morpurgo; Alessandro Scarfato; Christoph Renner; Fan Wu; Lihuan Sun; Marco Gibertini; Menghan Liao

REVIEW 3 major objections 4 minor 14 references

Coupling between magnetism and band structure in a 2D semiconductor

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read When CrPS4 enters its magnetic state, its conduction and valence bands split by about 0.5 eV into fully spin-polarized copies, and the energy differences between these band edges account for every photoluminescence line observed.

desk verdict Solid STS/PL/DFT study mapping spin-split bands in CrPS4, but the full spin-polarization claim rests on an argument from silence that needs softening or spin-resolved confirmation. read the letter →

arxiv 2505.09946 v2 pith:B7MZW637 submitted 2025-05-15 cond-mat.mtrl-sci cond-mat.mes-hall

Lihuan Sun , Marco Gibertini , Alessandro Scarfato , Menghan Liao , Fan Wu , Alberto F. Morpurgo , Christoph Renner This is my paper · ORCID

classification cond-mat.mtrl-scicond-mat.mes-hall

keywords CrPS4vanderWaalsmagneticsemiconductorspinsplittingexchangeenergyscanningtunnelingspectroscopyphotoluminescencebandstructuretwo-dimensional

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 sets out to show that the semiconducting and magnetic properties of the van der Waals semiconductor CrPS4 are coupled through a single mechanism: when the material enters its magnetic state below 38 K, the electronic bands are split by a large exchange energy of roughly 0.5 eV, leaving the low-energy conduction and valence bands fully spin-polarized. The authors combine scanning tunneling spectroscopy, photoluminescence, and density functional theory to argue that every observed optical transition in the magnetic state is the energy difference between two band edges of the same spin, while the spin-opposite pairs remain dark. What makes this worth caring about is that it explains not only the ordinary optical gap but also a mysterious high-energy photoluminescence line deep in the band continuum, and it identifies CrPS4 as a platform where gate-tunable half-metallic conduction should be achievable. The central claim is that all basic optoelectronic processes in this material are governed by the spin-split band structure that develops on entering the magnetic state.

What carries the argument

The central object is the exchange-split band structure of a single CrPS4 layer in its A-type antiferromagnetic state, in which each layer is ferromagnetically ordered and neighboring layers point oppositely. Bands that are paired in the paramagnetic phase split into two spin copies separated by roughly 0.5 eV, so the lowest conduction band and highest valence band have opposite spins. The argument is carried by matching energy differences between STS-detected band edges to photoluminescence transition energies, then confirming the assignment with spin-resolved density functional theory, which also reproduces the measured spatial pattern of the wavefunctions. Whether a transition is bright or dark is decided by whether the two bands used in the transition have the same spin and share a common point in momentum space.

What would settle it

A decisive test would be a direct measurement of the spin of the bands, for example spin-resolved photoemission or spin-polarized tunneling on the same CrPS4 surface: full spin polarization at the band edges would confirm the claim, and a detectable minority-spin signal would refute it. Alternatively, a broad search for weak, dark or momentum-indirect emission lines in the magnetic state would check the assumption that all spin-allowed transitions would be visible in photoluminescence.

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Extended reading notes

Core claim

In the magnetic state of CrPS4, the paper claims, the conduction and valence bands are each split into two spin copies separated by about 0.5 eV of exchange energy, and the band edges that determine transport and optics are fully spin-polarized over a broad energy interval. This spin splitting reduces the tunneling bandgap to about 0.87 eV, makes the optical gap of about 1.34 eV arise from same-spin transitions, and accounts for a Fano-shaped line at 1.37–1.40 eV and a sharp high-energy photoluminescence line at 1.99 eV. Density functional theory calculations reproduce the relative positions of all detected band edges and the spatial structure of the wavefunctions, and the paper concludes that every basic optoelectronic process in CrPS4 follows from the evolution of the spin-polarized band structure when magnetic order appears.

Load-bearing premise

The claim that the bands are fully spin-polarized rests on the assumption that every allowed optical transition between partially polarized bands would produce a detectable photoluminescence line; if dark excitons, defect states, or momentum mismatch hide such transitions, the absence of extra lines would not prove full spin polarization.

Editorial extensions

If this is right

The tunneling bandgap of about 0.87 eV is invisible in photoluminescence because it connects opposite-spin band edges, so direct radiative recombination is forbidden.
The 1.99 eV photoluminescence line is emitted from a fully spin-polarized conduction band whose same-spin valence counterpart lies deep in the continuum; the electron cannot relax without a rare spin flip, so it survives to recombine radiatively.
The spin-polarized band structure over a broad energy interval makes CrPS4 a candidate platform for gate-tunable half-metallic conductors based on van der Waals magnetic semiconductors.
The same exchange-splitting mechanism explains the exponential gate-voltage dependence of magnetoconductance reported for CrPS4 transistors, because aligning spins shifts the conduction band edge downward.

Reading between the lines

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

A testable extension of the paper's picture: the high-energy line's energy should track the exchange splitting as a function of magnetic field or uniaxial strain, since it is set by the same-spin separation of a deep valence band and a conduction band.
If the bands are truly fully spin-polarized over a broad interval, optical excitation at photon energies well above the gap should generate spin-polarized carriers without any spin-polarized contacts, a property useful for spin injection.
The same STS-to-PL comparison could be applied to other layered magnetic semiconductors to see whether the exchange-split band picture is general or whether excitonic and defect effects mask it in other materials.

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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

The real news here is the first STS mapping of the spin-split band edges in CrPS4, and the unified picture it gives for the previously puzzling PL lines, including the 1.99 eV feature. The data look carefully taken, the comparison across STS, PL, and DFT is systematic, and the STM topography simulations are a nice extra check. The paper earns its keep as an experimental tour de force.

What is genuinely new: above Tc you see a clean gap; below Tc you see extra features that line up with PL transitions if you read them as spin-split band edges. The match between the STS energy differences and the PL lines is impressive, and the DFT calculation, while not perfect, reproduces the relative band positions and the wavefunction maps. Data are deposited, which is good.

Now the soft spots. The claim that individual bands are fully spin-polarized over a broad energy interval is not measured directly. It rests on the statement in the Discussion that if bands were not fully spin-polarized, many more optical transitions should be seen. That is an argument from silence, and in a 2D semiconductor it is fragile: dark excitons, momentum mismatch, and small oscillator strengths can easily hide transitions. The paper also compares single-particle STS band-edge differences directly to PL photon energies, ignoring exciton binding energies, which in 2D can be hundreds of meV. The DFT gap is 0.6 eV versus 0.87 eV measured—about 30% off—so the DFT support is qualitative for the gap size, even if the same-spin transition energies match better. The colored arrows on the DFT bands are placed post hoc, which is fine for illustration but not independent confirmation.

None of this kills the central picture. The evidence that exchange splitting rearranges the band edges and drives the optical response is strong. But the strong conclusion about full spin polarization should be flagged as an inference, not a measurement, and the authors should either tone it down or point to a quantitative exciton/matrix-element calculation. A spin-resolved STS experiment would settle it, and the paper itself notes none has been done.

Who is this for? Anyone working on 2D magnetic semiconductors, especially CrPS4. It deserves a serious referee and, after revision, publication. My recommendation: send it to review, but ask the authors to address the argument-from-silence issue and the exciton-binding-energy point explicitly.

Referee Report

3 major / 4 minor

Summary. The manuscript reports STS, PL, and DFT results on the van der Waals magnetic semiconductor CrPS4. It shows that below the magnetic transition (Tc = 38 K) new features appear in the tunneling spectra, which the authors attribute to spin-split bands with a large exchange energy (about 0.5 eV). The energy differences between the STS features are compared to photoluminescence lines observed in the magnetic state, and a qualitative match is claimed. Spin-polarized DFT calculations are presented that show fully spin-polarized conduction and valence bands, with a calculated gap of 0.6 eV versus the measured 0.87 eV STS gap. Based on the consistency between STS, PL, and DFT, the authors conclude that individual bands are fully spin-polarized over a broad energy interval and that this explains the optoelectronic properties of CrPS4.

Significance. If correct, the paper would provide a comprehensive picture of how magnetism modifies the band structure of a van der Waals semiconductor, with implications for spin-polarized transport and gate-tunable half-metallic devices. The combination of STS, PL, and DFT is strong in principle: the DFT calculation is an independent benchmark, the STM topograph comparison provides a second observable beyond band energies, and the data are deposited in a public repository. The main strength is the multi-technique consistency, but the load-bearing conclusion of full spin polarization is inferred indirectly and needs additional support.

major comments (3)

[Discussion and conclusions] The central claim that individual bands are fully spin-polarized over a broad energy interval rests on the argument in the second paragraph: 'if the bands were not fully spin polarized, optical transition at many more different energies should be detected in the experiments.' This is an argument from silence. In a 2D semiconductor, many interband transitions are dark or very weak because of exciton binding, symmetry selection rules, momentum mismatch, or small oscillator strength, and photoluminescence is dominated by excitons rather than free-carrier interband recombination. Without a quantitative calculation of optical matrix elements and exciton energies for the proposed band structure, the absence of additional PL lines cannot rule out the presence of unpolarized or partially polarized bands. The DFT calculation alone is not decisive because it uses a specific exchange-correlation functional whose spin splitting is not experimentally validated. The paper should either soften the claim to 'consistent with full spin polarization' or provide a quantitative estimate of the brightness of all competing transitions.
[Tunneling spectroscopy and its interpretation] The quantitative comparison of STS band-edge differences to PL photon energies, summarized in Table I and Fig. 3c, implicitly neglects exciton binding energies. In a 2D semiconductor, exciton binding energies can be hundreds of meV, so the energy of a PL line is not simply the difference between two single-particle band edges. This is not a small correction in the present data: in the paramagnetic state the STS gap is reported as 1.25 eV (Table I) while the optical gap is 1.34 eV, meaning the single-particle gap is smaller than the optical gap, which is unphysical for a direct semiconductor with positive exciton binding. The manuscript should address this discrepancy explicitly, for example by discussing whether the STS features are true band edges or whether the optical transition in the paramagnetic state is not the fundamental gap. Without such a discussion, the claimed 'virtually perfect quantitative match' between STS energy differences and PL energies is not reliable evidence for the band-edge identification.
[Comparison with first-principles simulations] The statement that the DFT calculated bandgap of 0.6 eV is 'very close' to the measured STS gap of 0.87 eV overstates the agreement; the discrepancy is about 30 percent. Moreover, the colored arrows in Fig. 4 are placed onto the DFT band structure post hoc, connecting extrema of the same spin at the same k-point that match the PL energies. This procedure selects the transitions that reproduce the experimental values, so the agreement does not constitute an independent prediction of the optical spectrum. To support the claim that DFT 'quantitatively predicts the relative positions of all detected bands' and explains which pairs of bands radiate, the authors should compute the optical transition strength (e.g., dipole matrix elements) and, ideally, the exciton spectrum, and show that the predicted bright transitions match the observed PL lines. As written, the validation loop is partly circular.

minor comments (4)

[Magnetic and semiconducting properties] The text says 'Exfoliation exposes a buckled selenium surface', but CrPS4 contains sulfur, not selenium; this should be corrected to 'sulfur'.
[Tunneling spectroscopy and its interpretation] The text states 'a bandgap just smaller than 1.5 eV is clearly visible' at 78 K, but Table I reports the PM bandgap as 1.25 eV. Please reconcile these values or state the uncertainty in the gap determination.
[Data availability] In reference 52 the author list appears garbled ('L. Sun, R. Gibertini, A. Scarfato, ...'); the second author should be 'M. Gibertini' to match the other references.
[Discussion and conclusions] The statement that electrons in the high-energy spin-split band 'can only relax by flipping their spin or by hopping to adjacent layers' overlooks other relaxation channels such as phonon-assisted scattering within the same spin manifold, which may affect the radiative lifetime argument. This is a minor point because the qualitative conclusion is unaffected.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: matching STS, PL, and DFT are independent benchmarks; the full-spin-polarization inference rests on an absence-of-lines argument that is an evidentiary gap, not a circular reduction.

full rationale

The paper's central derivation is a triangulation among three independent datasets: (i) STS spectra measured here, (ii) photoluminescence spectra from the external literature (refs 34–38), and (iii) parameter-free DFT band-structure and STM-image simulations. The energy differences among STS features (A–E in Fig. 3c) are compared with PL transition energies; the agreement is a matching of independently measured numbers, not a fitting step, since no STS or PL energy is adjusted to force agreement. The DFT calculation (Quantum ESPRESSO, spin-polarized vdW-DF-cx functional, SSSP pseudopotentials) contains no parameters fitted to the STS or PL data; its calculated gaps (0.6 eV vs STS 0.87 eV; 1.3 eV same-spin separation vs optical gap ~1.34 eV) are used as an external benchmark. The coloured arrows overlaid on Fig. 4 are drawn from experimental STS energy differences, and their consistency with allowed same-spin, same-k DFT transitions is a prediction check, not an input. The one logically fragile step is the inference that absence of extra PL lines proves full spin polarization ('if the bands were not fully spin polarized, optical transition at many more different energies should be detected'); this is an argument from silence that assumes all competing transitions are bright, but it is an evidentiary weakness, not a circular reduction of the conclusion to the input. Self-citations (refs 3, 22, 41, 43) supply context and prior CrPS4 transport results; none is load-bearing in the band-structure derivation. No fitted parameter is renamed as a prediction, and no uniqueness theorem or ansatz is imported from the authors' prior work to force the interpretation.

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

The central claim rests on two pillars: the mapping from STS features to band edges, and the DFT validation. The DFT calculation is independent with no fitted parameters, keeping the circularity burden low. The main burden is the inference that absence of extra PL lines proves full spin polarization.

assumptions (5)

domain assumption DFT with the vdW-DF-cx functional provides a quantitatively accurate electronic structure for CrPS4.
The DFT result is used as validation for the experimental band edges; the authors themselves remark that such good agreement is unexpected and unexplained.
domain assumption STS on a multilayer flake measures the band structure of an isolated, fully ferromagnetically ordered monolayer.
The paper assumes interlayer hopping is negligible in the A-type AFM state so that the top layer dominates the tunnel current; stated in the results section.
domain assumption Optical transitions are direct in k-space and occur between same-spin band extrema at the same k-point.
This assumption is used to place the colored arrows on the DFT band structure in Fig. 4 and to identify allowed transitions.
ad hoc to paper The absence of additional PL lines implies that all bands in the energy window are fully spin-polarized.
This argument from silence is the basis for the central conclusion and is not independently tested.
domain assumption The top layer of the multilayer CrPS4 flake is fully ferromagnetically ordered at 4.5 K.
The paper cites ref 42 for layer-dependent ferromagnetism in CrPS4.

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Pith. "Pith review of Coupling between magnetism and band structure in a 2D semiconductor." pith.science (2026). https://pith.science/paper/B7MZW637

@misc{pith2026250509946,
  author       = {Pith},
  title        = {Pith review of: Coupling between magnetism and band structure in a 2D semiconductor},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/B7MZW637}},
  note         = {Machine review of arXiv:2505.09946}
}

abstract

Van der Waals semiconducting magnets exhibit a cornucopia of physical phenomena originating from the interplay of their semiconducting and magnetic properties. However, a comprehensive understanding of how semiconducting processes and magnetism are coupled is lacking. We address this question by performing scanning tunneling spectroscopy (STS) measurements on the magnetic semiconductor CrPS$_4$, and by comparing the results to photoluminescence experiments and density functional theory (DFT) calculations. Below the magnetic transition, STS exhibit multiple features absent in the paramagnetic state, caused by the proliferation of electronic bands due to spin splitting with a large ($\simeq 0.5$ eV) exchange energy. The energetic differences between the band edges determined by STS match all observed photoluminescence transitions, which also proliferate in the magnetic state. DFT calculations quantitatively predict the relative positions of all detected bands, explain which pairs of bands lead to radiative transitions, and also reproduce the measured spatial dependence of electronic wavefunctions. Our results reveal how all basic optoelectronic processes observed in CrPS$_4$ can be understood in terms of the evolution of the electronic band structure when entering the magnetic state, and allow us to conclude that individual bands are fully spin-polarized over a broad energy interval.

Figures

Figures reproduced from arXiv: 2505.09946 by the authors.

**Figure 1.** Crystal structure and STM characterization of CrPS4. a, Top view and b, side view of the CrPS4 crystal structure. Chromium is colored dark purple, phosphorus light purple, and sulphur yellow. c, Optical image of exfoliated CrPS4 flakes on a platinum film on a SiO2/Si substrate. d, High-resolution STM topography measured at 4.5 K, −1.1 V and 30 pA. e, Line profiles along the 2 traces depicted in d illustrating the co… view at source ↗

**Figure 2.** STM topography and STS tunneling spectroscopy of CrPS4 acquired at 78 K (a-b) and at 4.5 K (c-d). a, Topographic image (V = 1 V, I = 30 pA). b, Color plot of 38 dI/dV (V ) spectra measured along the green arrow in a. c, Topographic image (V = 1 V, I = 30 pA). d, Color plot of 60 dI/dV (V ) spectra measured along the green arrow in c. The conductance data in b and d are normalized to 1/(I/V ), which yields peaked co… view at source ↗

**Figure 4.** DFT calculations of the band structure of monolayer CrPS4. Blue and red lines identify spin-up and spin-down states. The color-dotted arrows are taken from the STS data and represent exactly the same energy differences as in Fig. 3c. They are positioned into the band structure according to allowed optical transitions, i.e. connecting a minimum of an empty band to the maximum of a filled band with the same spin at … view at source ↗

Figures from the paper (1 more)

**Figure 5.** Figure 5: Energy dependent topographic STM images of CrPS4. Experimental topography measured in constant current mode at a, 0.9 V, b, 0.7 V, and c, -1.1 V, with a tunneling current of I = 0.1 nA. DFT simulated topography at d, 1.1 V, e, 0.8 V, and f, -1.1 V. Apart from a slight…

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

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