Coupling of magnetic and lattice collective excitations in the 2D van der Waals antiferromagnet FePS$_{3}$

Alexey Kuzmenko; Dirk van der Marel; Dumitru Dumcenco; Itzik Kapon; Kartik Panda; Nimrod Bachar

REVIEW 2 major objections 6 minor 59 references

Coupling of magnetic and lattice collective excitations in the 2D van der Waals antiferromagnet FePS$_{3}$

T0 review · 2 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Polarized infrared light maps the circular dichroism of the field-split 122 cm-1 magnon in FePS3 and shows lattice phonons acquiring magnetic-field-dependent optical activity.

desk verdict Worth a look: the raw Faraday-rotation dataset is new and likely robust, but the central quantitative claim about reduced dichroism at 129 cm^-1 does not survive scrutiny of the birefringence analysis. read the letter →

arxiv 2507.17238 v3 pith:MR2TJ6YV submitted 2025-07-23 cond-mat.str-el

Kartik Panda , Itzik Kapon , Dumitru Dumcenco , Dirk van der Marel , Alexey Kuzmenko , Nimrod Bachar This is my paper · ORCID

classification cond-mat.str-el

keywords FePS3vanderWaalsantiferromagnetspin-phononcouplingFaradayrotationcircularopticalconductivitymagnoninfraredmagneto-spectroscopy2Dmagnets

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 seeks to establish that the 122 cm-1 (15 meV) excitation of the two-dimensional van der Waals antiferromagnet FePS3 is a magnon whose field-split branches have measurable circular dichroism, and that this dichroism is modified where the magnon meets lattice vibrations. The authors combine polarized infrared transmission with Faraday rotation measurements up to 7 T to reconstruct the circular optical conductivities $\sigma_+$ and $\sigma_-$. They find the lower branch is almost fully dichroic while the upper branch near 129 cm-1 retains about one-third of the opposite circular weight, which they attribute to hybridization with nearby infrared phonons; several phonons also show Faraday rotation, implying lattice vibrations acquire magnetic-field-dependent optical activity. If right, this provides a quantitative look at spin-phonon coupling in a 2D antiferromagnet and a route to probing magnetic order with polarization-resolved infrared light.

What carries the argument

The central objects are the circular optical conductivities $\sigma_\pm(\omega) = (\sigma_{xx}+\sigma_{yy})/2 \pm i\sigma_{xy}$, which the paper obtains by combining absolute polarized transmission with Faraday rotation angle measurements using a full polarizer-rotation protocol at $\pm 7$ T. The reconstruction assumes an effective orthorhombic in-plane dielectric tensor with a single antisymmetric off-diagonal component $\sigma_{xy}$, and uses field reversal so that the linear birefringence term $\delta = (\varepsilon_{xx}-\varepsilon_{yy})/2$ cancels to leading order; the off-diagonal term is then extracted as $\varepsilon_{xy}(\omega) = (2c/\omega d)\, n_0(\omega)\Theta(\omega)$. This is what converts measured rotation angles into the dichroism of the split magnon branches and of the phonon modes.

What would settle it

Measure the zero-field linear birefringence $\delta = (\varepsilon_{xx}-\varepsilon_{yy})/2$ in the same 100-150 cm-1 range and compare it with $\varepsilon_{xy}$ obtained from field reversal; if $\delta$ is comparable to or larger than $\varepsilon_{xy}$, the cancellation no longer isolates the magneto-optical term. A thickness-dependence or in-plane crystal-rotation check of the reconstructed $\sigma_{xy}$ would also show whether residual cross-polarization or monoclinic terms contaminate the result.

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Extended reading notes

Core claim

The central claim is that the 122 cm-1 mode of FePS3 is a genuine magnetic excitation: it is polarization-independent, hardens on cooling with an order-parameter-like temperature dependence around $T_N \approx 118$ K, and splits linearly with magnetic field at a gyromagnetic ratio near $0.94$ cm$^{-1}$/T. Combining absolute polarized transmission with Faraday rotation measured by a full polarizer-rotation protocol at $\pm 7$ T, the authors reconstruct $\sigma_\pm(\omega) = (\sigma_{xx}+\sigma_{yy})/2 \pm i\sigma_{xy}$ and show that the two field-split branches carry opposite circular dichroism. The lower branch is essentially fully dichroic, whereas the upper branch near 129 cm-1 shows a reduced dichroic response, with $\sigma_+$ approximately one-third of $\sigma_-$; this anomaly is attributed to hybridization with nearby infrared-active phonons at 128 and 133 cm-1. Phonon modes at 108, 133.1, and 165.6 cm-1 also exhibit Faraday rotation of up to roughly 50 mrad at 7 T, providing evidence that lattice vibrations acquire magnetic-field-dependent optical activity through spin-phonon coupling.

Load-bearing premise

The load-bearing premise is that the in-plane optical response is effectively orthorhombic with a single antisymmetric off-diagonal component and that linear birefringence cancels under field reversal, so that if monoclinic off-diagonal terms or birefringence are not negligible, the reconstructed circular conductivities and the reported dichroism would be distorted.

Editorial extensions

If this is right

The 122 cm-1 mode is a magnetic excitation: its frequency hardens on cooling along an order-parameter curve with $T_N \approx 118$ K and its field splitting is linear at about 0.94 cm-1/T up to 7 T.
The lower split branch is essentially fully dichroic, with the $\sigma_-$ spectral weight matching the zero-field mode, so the two branches can be assigned to opposite circular polarizations of the two spin sublattices.
The upper branch's reduced dichroism, with $\sigma_+$ about one-third of $\sigma_-$, is a signature of hybridization with nearby infrared phonons, providing direct evidence of spin-phonon coupling in the collective excitation spectrum.
Phonon modes at 108, 133.1, and 165.6 cm-1 exhibit Faraday rotation up to roughly 50 mrad at 7 T, showing that lattice vibrations acquire magnetic-field-dependent optical activity.
Polarization-resolved infrared magneto-spectroscopy can quantify spin-lattice coupling and circular dichroism in low-dimensional antiferromagnets.

Reading between the lines

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

Beyond the paper, the same full-protocol Faraday technique should be transferable to monolayer FePS3, where the 122 cm-1 mode persists; measuring its circular dichroism would test whether spin-phonon coupling survives the two-dimensional limit.
Beyond the paper, the upper-branch hybridization hypothesis predicts an avoided crossing between the 129 cm-1 magnon and the 133 cm-1 phonon as a function of magnetic field, and resolving that crossing would yield a direct magnon-phonon coupling strength.
Beyond the paper, the authors' tentative crystal-field assignment leaves open whether the 122 cm-1 transition arises from the 6.4 meV or 17.9 meV spin-orbit level; circular-dichroism measurements as a function of field direction relative to the c-axis could distinguish the two.

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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

Worth a look: this is the first polarized IR magneto-transmission and Faraday-rotation study of FePS3 that I know of. The raw observations are credible and new: the 122 cm^-1 magnon splits linearly with field, several phonons show B-odd Faraday rotation at the 10–50 mrad level, and the low-temperature phonon spectrum becomes strongly anisotropic. The authors also did a careful full-protocol measurement rather than the fast four-point scheme, which matters for a monoclinic sample. The DFT phonon table and the MnPS3 control strengthen the paper. Credit where it's due.

The problem is the extraction of σ_xy and the claim that the upper branch at ~129 cm^-1 shows reduced dichroism. Appendix D's derivation assumes δ=0 when it converts Faraday angle to ε_xy (Eq. D29). For δ≠0, the eigenmodes are elliptical and the measured rotation is not simply (ωd/2c) Re(n_+ − n_−). A Jones calculation gives θ_F ≈ −g sin(2kdn0√(δ²+g²))/(2√(δ²+g²)), so δ does not cancel in the field-reversal analysis; it appears as a multiplicative prefactor that is frequency-dependent and potentially large near 129 cm^-1, where two strongly polarization-selective phonons sit. The expansion in Eq. D31 is also mis-stated: the branch used requires δ≫|ε_xy|, not δ≪ε̄. So the reconstructed σ_xy—and the headline reduced-dichroism claim—is not established as presented. This is an internal analysis-chain issue, not a disagreement with outside consensus. The raw Faraday rotation spectra may show the effect, but the paper doesn't provide the Jones-matrix analysis that would validate it.

Minor: the 320 cm^-1 feature is weak; the symmetry assignments are explicitly approximate (fine, but not to be leaned on); the data repository reference [31] has no accessible link.

Bottom line: this is a serious experimental paper that deserves review, but the referee should insist on a quantitative treatment of birefringence, either by measuring δ(ω) and using a full Jones transfer-matrix fit, or by showing the reduced dichroism survives in the raw B-reversed Faraday spectra. The other observations—magnon splitting, phonon Faraday rotation, anisotropy—are likely robust and should survive revision.

Referee Report

2 major / 6 minor

Summary. The manuscript reports polarization-resolved infrared magneto-transmission and Faraday rotation measurements on a 26 µm FePS3 crystal between 5 and 150 K and up to ±7 T. Below TN ≈ 118 K, the phonon spectrum develops a strong anisotropy between the two principal in-plane polarizations, whereas a mode at 122 cm⁻¹ remains polarization-independent, hardens on cooling with an order-parameter-like temperature dependence (Eq. 2), and splits linearly with applied magnetic field with a gyromagnetic ratio near the free-electron value, identifying it as a magnetic excitation. From absolute transmission and a full-protocol Faraday angle measurement at ±7 T, the authors reconstruct the circular optical conductivities σ± and report a pronounced dichroism of the field-split branches, a reduced dichroic response of the upper branch near 129 cm⁻¹ that they attribute to hybridization with a nearby infrared phonon, and Faraday rotation of several phonon modes (108, 133.1, 165.6 cm⁻¹) interpreted as evidence of spin–phonon coupling. The paper also provides DFT phonon frequencies, Raman data, a MnPS3 comparison, and a public data repository.

Significance. If the quantitative reconstruction were shown to be sound, the paper would provide the first quantitative mapping of the circular optical conductivities of the field-split magnon branches in FePS3 and direct magneto-optical evidence for spin–phonon coupling in a 2D antiferromagnet. The qualitative phenomenology is solid: the field splitting of the 122 cm⁻¹ mode is compared against the free-electron gyromagnetic ratio without adjustment (Fig. 8), the order-parameter-like temperature dependence is fitted consistently for both polarizations, the full-protocol Faraday measurements document a ~2 mrad noise floor with explicit transmission masking, and the polarized dataset is openly archived. The DFT phonon catalog, the MnPS3 control, and the authors' candor about the limitations of the Lorentz fits, the indicative symmetry assignments, and the Appendix C multiplet model are all strengths.

major comments (2)

[Appendix D, Eqs. D17–D31 and Eq. D29] The analysis of the birefringent case in Appendix D is not valid, and the stress-test concern about the cancellation argument lands. Equations D17–D18 give eigenmode refractive indices n²± = ε̄ ± sqrt(δ² − ε_xy²), which are even in ε_xy; the text then argues that the birefringent contribution cancels in the field-reversal analysis because ε_xy² is symmetric under B → −B. This conclusion does not follow, because the measured Faraday angle is not the eigenvalue phase difference: for δ ≠ 0 the propagating eigenmodes are elliptical, and a Jones-matrix treatment of the 26 µm slab gives a B-odd rotation proportional to ε_xy × sin(2kdn0 sqrt(δ² + ε_xy²))/sqrt(δ² + ε_xy²) (transparent limit), which reduces to the δ = 0 result of Eq. D29 only when δ = 0. Field reversal cancels B-even contributions; it does not remove the δ- and thickness-dependent prefactor multiplying ε_xy. In addition, the expansion in Eq. D31 is a power series in ε_xy/δ and therefore requires δ ≫ |ε_xy|, not the stated condition δ ≪ ε̄; conversely, the regime δ ≪ |ε_xy|, which is the one the authors need, is not treated. These are load-bearing for the headline result because δ(ω) is resonantly enhanced near 129 cm⁻¹, where the 128.5 and 133.1 cm⁻¹ modes are strongly polarization-selective in the zero-field transmission (Table I). The reconstructed σ_xy, and with it the reduced-dichroism claim, is therefore not established until the authors either perform an explicit Jones propagation using the independently determined σ_xx(ω) and σ_yy(ω) or quantify δ(ω)/|ε_xy(ω)| at 116 and 129 cm⁻¹.
[Sec. IVB, Figs. 12 and 18] The reduced dichroism of the upper branch (σ+ ≈ σ−/3 at 129 cm⁻¹) is the central quantitative result, but its robustness is not demonstrated. First, the two independent determinations of σ_xy (Pol 1 and Pol 2) disagree locally precisely around 129 cm⁻¹, as acknowledged in Sec. IVB and visible in Fig. 18; averaging the two removes the discrepancy rather than resolving it. The argument that a frequency-local discrepancy cannot be systematic is not compelling, because birefringence-related distortions are themselves resonant and frequency-local near the anisotropic phonons at 128.5 and 133.1 cm⁻¹. The error budget for the σ+/σ− ratio should include the spread between the two polarizations and the sensitivity to the averaging choice. Second, the upper branch sits on the shoulder of the strong 128.5 cm⁻¹ phonon (Pol 1), which contributes an unpolarized background (σ_xx + σ_yy)/2 to both σ+ and σ−; a competing explanation of the reduced ratio is simply that this phonon background fills in σ+, and the paper does not subtract it with an explicit multi-oscillator fit. Establishing the hybridization interpretation therefore requires either a quantitative coupled-mode model or a demonstration that the reduced dichroism persists after phonon baseline subtraction.

minor comments (6)

[Sec. IIIC, last two paragraphs] The identification of the 122 cm⁻¹ (15 meV) and 320 cm⁻¹ (40 meV) features with magnon excitations is justified by comparison with neutron-scattering energies measured at finite wave vectors, while optical spectroscopy probes q ≈ 0; the text acknowledges this tension but should state explicitly how the zone-center status of these excitations is established (e.g., magnetic-supercell folding, as in Refs. [43, 45, 46]) before describing the reconstruction as a mapping of the magnon circular conductivity.
[Sec. IVB, paragraph after Fig. 12] The sentence 'the lower mode is completely dichroic since the spectral weight of σ− in that excitation is the same magnitude as that of σ1 at zero field while σ+ shows a clear peak' is internally confusing, since a peak in σ+ at 116 cm⁻¹ would contradict complete dichroism; please specify which channel carries the 116 cm⁻¹ peak and which is suppressed.
[Eq. (4) and Fig. 12] Please state the sign convention that connects σ+ and σ− to the spin-sublattice and to the sign of the applied field; as written, the assignment of the upper and lower branches to specific circular polarizations is implicit and cannot be checked against Fig. 9.
[Fig. 8 and Sec. IIIB] The relation between the quoted gyromagnetic ratio γ ≈ 0.94 cm⁻¹/T and the plotted splitting should be clarified: the text quotes branch positions near 116 and 129 cm⁻¹ at 7 T, implying a full splitting of ≈13 cm⁻¹ = 2 × 0.94 × 7, so if γ denotes the per-branch Zeeman shift, the 'expected linear dependence' in Fig. 8 should be drawn with slope 2γ for the full splitting.
[Fig. 10] The 320 cm⁻¹ feature is described as a dip; please specify how the baseline was defined for this feature and whether the 1% transmission mask affects this spectral region at 7 T.
[various] Please correct 'the the optical phonons' (Sec. IID), the inconsistent 'Drude-Lorenz'/'Drude-Lorentz' spelling, 'Sibolometer' (Sec. IIB), and the missing space in 'The fitting yieldsa=' (Fig. 6 caption).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the central extraction is a model-based transform of independent transmission and Faraday measurements.

full rationale

The paper's central quantitative step is not circular: the off-diagonal conductivity sigma_xy is extracted from measured Faraday rotation via Eq. D29, and the circular optical conductivities are formed by combining that independently measured off-diagonal response with the averaged diagonal conductivity (Eq. 4). The reported dichroism between sigma_plus and sigma_minus is therefore a direct representation of the measured magneto-optical signal rather than a prediction fitted back to itself. The interpretation of the reduced dichroism of the upper branch near 129 cm^-1 is presented as an inference from mode proximity and spectral-weight comparison, not as a parameter fitted to the same data. The method citations (Refs. [19] and [32]) include a co-author of the present paper, but the Appendix D derivation is re-derived in the paper and the cited tools are open methods; they are not invoked as an unverified uniqueness theorem or as a substitute for the analysis. The assumption that linear birefringence cancels in the field-reversal analysis is a robustness concern about the extraction, not a case where the output reduces to the input by construction; under the stated rules, an unquantified systematic effect does not constitute circularity. No fitted parameter is renamed as a prediction, and no load-bearing self-citation replaces an independent derivation.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central results rest on standard experimental modeling (Drude-Lorentz slab fits, magneto-optical tensor analysis) plus domain assumptions about FePS3's structure and the validity of the orthorhombic approximation. No new particles or mediators are introduced. The largest burden is the unquantified birefringence cancellation and the tentative crystal-field assignment, both flagged by the authors.

free parameters (3)

Order-parameter temperature fit parameters a and c (Eq. 2) = a = 33.39 +/- 0.87, c = 89.13 +/- 0.80 cm-1 (Pol 1); a = 33.94 +/- 1.01, c = 87.98 +/- 0.94 cm-1 (Pol 2)
Used to model the temperature dependence of the 122 cm-1 mode; because a and c are free, the order-parameter-like curve is a fit, not a first-principles prediction.
Gyromagnetic ratio for field splitting = gamma ~ 0.94 cm-1/T
Dashed line in Fig. 8 representing the expected linear splitting of the 122 cm-1 mode; close to the free-electron value and used to compare with measured splitting.
Drude-Lorentz oscillator parameters (omega_0, omega_p, gamma) for all IR modes = Values listed in Table I and extracted by fits
Transmission spectra are fitted with a plane-parallel slab model and Drude-Lorentz oscillators; these per-mode parameters determine the optical conductivity and mode frequencies used throughout the paper.

assumptions (6)

domain assumption Slab transmission modeled with Drude-Lorentz dielectric function and magnetic permeability mu ~ 1
Sec. IIIA states 'this analysis assumes mu ~ 1'; the validity of neglecting permeability in the far-infrared is assumed, and the authors defer a fuller treatment.
domain assumption Effective orthorhombic dielectric tensor with antisymmetric off-diagonal component and negligible monoclinic off-diagonal elements
Sec. IVB and App. D adopt sigma with sigma_xy only and an effective orthorhombic approximation; the claim that monoclinic contributions are small is not quantified.
domain assumption Linear birefringence delta cancels in Faraday angle extraction under field reversal
App. D shows delta does not contribute to leading order in epsilon_xy/epsilon_xx for the field-reversal procedure; this requires delta to be small or epsilon_xy small, which is not quantitatively demonstrated.
domain assumption FePS3 zigzag antiferromagnetic structure with spins along c and preserved inversion symmetry
Used to interpret the 122 cm-1 mode as a magnetic excitation and to separate it from folded phonons; based on prior neutron and Raman literature, not re-established here.
domain assumption Local Fe2+ 3d^6 crystal-field multiplet model with trigonal field Delta < 0
Appendix C uses this Tanabe-Sugano-style model to argue the 122 cm-1 mode is inherent to the Fe 3d6 multiplet, but the authors caution that orbital mixing with ligands was omitted and energy spacings cannot be fully accurate.
domain assumption Principal polarization axes identified from 5 K optical spectra, without X-ray alignment to crystal axes
Sec. IIB: 'these two principal polarizations were not associated with the a-b plane crystal axis using X-ray diffraction apparatus'; subsequent assignment of Pol 1/Pol 2 to b/a axes relies on DFT matching.

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Pith. "Pith review of Coupling of magnetic and lattice collective excitations in the 2D van der Waals antiferromagnet FePS$_{3}$." pith.science (2026). https://pith.science/paper/MR2TJ6YV

@misc{pith2026250717238,
  author       = {Pith},
  title        = {Pith review of: Coupling of magnetic and lattice collective excitations in the 2D van der Waals antiferromagnet FePS$_3$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MR2TJ6YV}},
  note         = {Machine review of arXiv:2507.17238}
}

abstract

We combine polarized infrared magneto-transmission and Faraday angle rotation measurements to map the collective excitations of the van der Waals antiferromagnet FePS$_3$. Below the N\'{e}el temperature ($T_\mathrm{N} \approx 118~\mathrm{K}$), the phonon spectrum becomes strongly anisotropic, reflecting the underlying zigzag antiferromagnetic order. In contrast, a prominent excitation at $122~\mathrm{cm}^{-1}$ ($15$~meV) is polarization-independent, hardens on cooling, and splits linearly with magnetic field, identifying its magnetic origin. From absolute transmission and Faraday rotation, we reconstruct the circular optical conductivities and reveal a pronounced dichroism of the field-split excitations. The upper branch near $129~\mathrm{cm}^{-1}$ exhibits a reduced dichroic response, consistent with hybridization with a nearby infrared phonon. Several phonon modes exhibit sizable Faraday rotation, providing evidence for spin-phonon coupling and demonstrating that lattice vibrations acquire magnetic-field-dependent optical activity. In addition, additional excitations appear in the infrared spectra and a broad mid-infrared feature near $900~\mathrm{cm}^{-1}$ emerges only below $T_\mathrm{N}$, consistent with a modified lattice response in the magnetic state. These results highlight the anisotropic nature of spin--phonon coupling in FePS$_3$ and establish polarization-resolved magneto-optical spectroscopy as a powerful probe of coupled spin and lattice dynamics in two-dimensional antiferromagnets.

Figures

Figures reproduced from arXiv: 2507.17238 by the authors.

**Figure 3.** Transmission spectra in the FIR range (black symbols) along with the Drude-Lorentz fit (gray line) from which the [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Real part of the optical conductivity σ1 at 150 K and 5 K in zero magnetic field, extracted via the Variable Dielectric Function of the Drude–Lorentz modeling of transmission data for the two principal polarizations. the IR mode at 128 cm−1 is prominent in Pol. 1, while a distinct mode at 160 cm−1 appears only in Pol. 2. We present in Table I the full list of modes obtained at 5 K. The modes discussed in the text a… view at source ↗

Figures from the paper (12 more)

**Figure 6.** Figure 6: Central frequency of the 122 cm−1 excitation as a function of reduced temperature (TN /T) at zero magnetic field. The red line shows a fit to an order parameter temperature dependence (Eq. 2). The fitting yields a = 33.39±0.87, c = 89.13±0.80 (Pol 1-the solid red line…

**Figure 7.** Figure 7: Polarized magneto-transmission color maps of [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

**Figure 8.** Figure 8: Magnetic-field dependence of the energy splitting [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

**Figure 9.** Figure 9: Faraday rotation angle (top panels) and corresponding magneto-transmission spectra (bottom panels) of FePS [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]

**Figure 10.** Figure 10: Temperature evolution of the Faraday rotation [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]

**Figure 11.** Figure 11: Top panel: Color map of polarized infrared trans [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]

**Figure 12.** Figure 12: shows the circular optical conductivity obtained from the analysis of the Magneto-Optical Kerr/Faraday Effect [32] and by taking into account the in-plane optical conductivity tensor as described above. As expected from a collinear antiferromagnetic resonance, there …

**Figure 13.** Figure 13: Colormap plot of the transmission spectra as a [PITH_FULL_IMAGE:figures/full_fig_p013_13.png]

**Figure 14.** Figure 14: Transmission spectra of FePS3 (TN = 118 K) for two polarizations at (a) 150 K (T > TN ) and (b) 5 K (T ≪ TN ). (c) Zero-field transmission spectra at 100 K (T > TN ) and 10 K (T ≪ TN ) for MnPS3 (TN = 78 K). No additional phonon modes emerge in the antiferromagnetic s…

**Figure 16.** Figure 16: Local crystal field environment of Fe2+ in FePS3 and orientation of the eg (top) and t2g (bottom) orbitals. The eg states have one protuberance pointing toward the negative sulfur ions and one away from it. The t2g states point away from the negative ions. If we call …

**Figure 17.** Figure 17: Tanabe-Sugano diagram of the d 6 energy levels in a trigonal crystal field adapted from Ref. [57]. The black arrow on the right is from the original paper. The green arrow on the left is our tentative assignment [PITH_FULL_IMAGE:figures/full_fig_p016_17.png]

**Figure 18.** Figure 18: Top panel: Circular optical conductivities [PITH_FULL_IMAGE:figures/full_fig_p020_18.png]

Discussion (0). Continue with ORCID to comment.

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