Magnetic-Field Dependence of Paramagnetic Properties Investigated by 63/65Cu-NMR on the Yb Zigzag-Chain Semiconductor YbCuS2

Fumiya Hori; Kenji Ishida; Shunsaku Kitagawa; Takahiro Onimaru; Yudai Ohmagari

REVIEW 3 major objections 5 minor 43 references

Magnetic-Field Dependence of Paramagnetic Properties Investigated by 63/65Cu-NMR on the Yb Zigzag-Chain Semiconductor YbCuS2

T0 review · 3 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read Magnetic fields suppress the broad 50 K maximum of the nuclear spin-lattice relaxation rate in the paramagnetic state of YbCuS2 and, above 3 T, induce a new low-temperature enhancement of spin fluctuations.

desk verdict A careful NMR study of YbCuS2 with genuinely new observations, but the central field-suppression claim is entangled with a frequency dependence the paper never tests. read the letter →

arxiv 2502.00830 v1 pith:EA7UDR33 submitted 2025-02-02 cond-mat.str-el

Fumiya Hori , Shunsaku Kitagawa , Kenji Ishida , Yudai Ohmagari , Takahiro Onimaru This is my paper · ORCID

classification cond-mat.str-el

keywords YbCuS2zigzagchain63CuNMRnuclearspin-latticerelaxationKnightshiftfield-inducedparamagneticstatefrustratedmagnet50Kanomaly

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 uses 63/65Cu nuclear magnetic resonance to ask how magnetic fields alter the paramagnetic state of the zigzag-chain semiconductor YbCuS2. The authors find that the broad maximum of the nuclear spin-lattice relaxation rate 1/T1 near 50 K, which is robust against pressure and chemical substitution at zero field, is rapidly suppressed by applied fields. Above 3 T, a new low-temperature enhancement of 1/T1 appears, signaling that magnetic fields modify the spin fluctuations well above the antiferromagnetic ordering temperature of about 1 K. The results imply that the field-induced phases seen below TN have a precursor in the paramagnetic state. A sympathetic reader would care because the field-driven changes suggest the Yb zigzag chains host competing ground-state tendencies that a field can tilt.

What carries the argument

The central observable is the 63Cu nuclear spin-lattice relaxation rate 1/T1, measured by spin-echo NMR on a powdered sample at fields from 0.1 T to 10 T. The Knight shift is extracted from field-swept spectra using the second-order quadrupolar relation δν/(γHres) ≈ K + D/(1+K)(γHres)^2, with the quadrupolar coefficient D assumed temperature-independent at its 50 K value of 12.81 MHz². The 1/T1 data are fitted with relaxation functions appropriate for spin I = 3/2, including a matrix-diagonalization form at low fields. These measurements probe low-energy spin fluctuations and their field dependence.

What would settle it

Measure the field-swept NMR spectra at multiple frequencies at several fixed temperatures (for example, 10 K, 50 K, and 100 K) and extract D(T) directly as the slope of δν/(γHres) versus (γHres)^{-2}; if D varies by more than a few percent over the measured temperature range, the reported K(T) and the field-independence conclusion are not robust. A single-crystal NMR measurement that resolves the orientation of the ac plane would also independently test the easy-plane assignment.

Watch

Extended reading notes

Core claim

In the paramagnetic state of YbCuS2, the broad 50 K anomaly in the nuclear spin-lattice relaxation rate is field-dependent: increasing magnetic fields suppress the 1/T1 maximum, and for fields above roughly 3 T the maximum becomes indistinct and a new low-temperature upturn appears instead. The Knight shift K is proportional to the bulk magnetic susceptibility and is independent of magnetic field, with a hyperfine coupling of about 0.14 T/μB. Spectral simulations of the partially oriented powder sample indicate that the ac plane is the easy plane. The authors interpret the 1/T1 behavior as evidence that a magnetic-field-driven modification of the paramagnetic state occurs above TN, likely related to the field-induced phases observed below TN, including the 1/3 magnetization plateau and the high-field phase.

Load-bearing premise

The extraction of the Knight shift relies on assuming that the second-order quadrupolar coefficient D is independent of temperature and equal to its 50 K value of 12.81 MHz²; if D changes with temperature, the reported Knight shift values would be systematically shifted and the conclusion that K is field-independent would need to be revisited.

Editorial extensions

If this is right

The 50 K anomaly is a field-tunable feature, unlike its robustness under pressure and chemical substitution, so magnetic field provides a distinct control parameter for the frustrated zigzag-chain physics.
Above 3 T, the paramagnetic state enters a field-induced spin-fluctuating regime that appears to be the finite-temperature counterpart of the up-up-down ordered phase seen below TN.
The Knight shift being field-independent and proportional to the bulk susceptibility indicates a single uniform spin response, with the hyperfine coupling exceeding the classical dipolar estimate and thus implying transferred hyperfine contributions.
The similarity of the 1/T1 behavior to that of one-dimensional spin-ladder systems suggests that a field-driven crossover from a gapped, dimer-like state to a gapless, Tomonaga-Luttinger-like fluctuating state may be relevant to YbCuS2.

Reading between the lines

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

If the quadrupolar coefficient D actually varies with temperature, the reported temperature dependence of the Knight shift, and hence the conclusion that K is field-independent, could be systematically off; a direct multi-frequency measurement of D(T) would settle this.
The identification of the ac plane as the easy plane rests on a two-dimensional powder-pattern simulation of partially oriented grains; a single-crystal NMR study would confirm the orientation and refine the hyperfine coupling tensor.
The onset of the 1/T1 upturn near 3 T coincides with the field where the antiferromagnetic phase boundary changes slope, suggesting that thermodynamic measurements in the paramagnetic regime (such as magnetostriction or specific heat) might reveal a crossover feature at this field.
The theoretical zigzag-chain model with competing J1 and J2 interactions predicts field-induced gapless states; the observed 1/T1 upturn could be a finite-temperature signature of such a state, testable by comparing with numerical calculations of the relaxation rate.

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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

Colleague,

Quick take: this is a competent, honest NMR paper from a group that clearly knows this material. The new results are real observations: the field suppression of the 50 K 1/T1 anomaly, the low-temperature upturn above 3 T, and the partial-orientation evidence for the ac easy plane. The Knight shift analysis is standard and the K-χ proportionality with bulk susceptibility is clean. The paper also does a good job situating the work in the existing YbCuS2 literature and in the broader frustrated-chain context. Credit where due: the 1/T1 data are directly measured, not model-extracted, and the phase diagram update with Tmax and T* is useful.

Now the soft spots, in order of real weight.

The biggest one is the field-frequency entanglement. Because the H-swept method fixes ν = γH, each field point in Fig. 5 is also a different frequency: 0.1 T corresponds to NQR (low frequency), 1.7 T to 19.5 MHz, 10 T to 113 MHz. The paper rejects the BPP frequency-dependent form only for the zero-field temperature dependence of the anomaly; it never asks whether the field dependence of 1/T1 at 50 K could be a frequency dependence. This matters because the central claim—that the 50 K anomaly is suppressed by H—rests on comparing points at very different frequencies. The fact that the anomaly is still visible at 19.5 and 31.4 MHz but gone at 40.4 MHz suggests a sharp frequency cutoff, which is not impossible but needs an explicit check. A 63Cu/65Cu isotope comparison at the same field would disentangle field and frequency cleanly, and its absence is the main gap.

The other weaknesses are minor by comparison. There are no statistical error bars on 1/T1, and the single-component fit quality is asserted rather than shown with residuals. The D(T) independence assumption in Eq. (3) is untested, but it only affects the absolute K values, and the H-independence of K is already supported by the multi-frequency consistency in Fig. 3(b). The orientation conclusion depends on a simulation with fixed η and νzz, but the linear D plot in Fig. 3(b) suggests the spectral assignment is stable.

The interpretation linking the paramagnetic changes to the field-induced ordered phases is speculative, and the authors say so. That is fine. The paper is not overclaimed.

Who is this for? Experimentalists working on Yb-based frustrated magnets and anyone building the H-T phase diagram of YbCuS2. It deserves a serious referee, but the referee should ask for the isotope test or an explicit frequency-dependence analysis before the suppression claim is taken as settled. I would not cite the suppression claim as established in its current form, but I would read the follow-up.

Recommendation: send to peer review, with the field/frequency issue raised as the main required revision.

Referee Report

3 major / 5 minor

Summary. This manuscript reports 63/65Cu-NMR measurements on the Zigzag-chain semiconductor YbCuS2 in magnetic fields up to 10 T. The authors analyze H-swept spectra to extract a Knight shift K(T), find K proportional to bulk susceptibility with a hyperfine coupling of 0.14 T/μB, and deduce that the ac plane is an easy plane from partial sample orientation. The central relaxation result is that the broad maximum of 1/T1 at ~50 K (the 50 K anomaly) is suppressed by magnetic fields, and that for fields above 3 T a low-temperature upturn of 1/T1 appears, indicating field-induced modification of the paramagnetic state. The paper also compares with the H-T phase diagram and discusses possible connections to a field-induced spin-fluctuating state.

Significance. If the central claim holds, the paper provides microscopic evidence that magnetic fields modify the paramagnetic state of a frustrated Yb zigzag-chain material at temperatures far above TN, which is relevant for understanding the field-induced phases below TN (1/3 plateau, up-up-down order, and the high-field phase). Strengths of the paper include direct relaxation measurements without a fitted model for the main 1/T1 trends, the reproduction of the spectra with powder-pattern simulations, the demonstration of H-independence of the Knight shift across several frequencies, and a clear comparison with the published H-T phase diagram. However, the main claim rests on an uncontrolled frequency/field correlation in the H-swept 1/T1 measurements, as detailed below, so the significance can only be assessed after that issue is addressed.

major comments (3)

[Sec. 3, Fig. 5] The central claim that the 50 K anomaly is suppressed by magnetic fields and that a low-T upturn appears above 3 T is based on measurements at different Larmor frequencies. Because the H-swept method fixes the frequency at ν = γH, the data at 0.1, 1.7, 2.7, 3.5, 5.6, and 10 T correspond to 63Cu frequencies of 1.1, 19.5, 31.4, 40.4, 64.2, and 113 MHz, respectively. The observed decrease of 1/T1 at 50 K with increasing nominal field could thus be a frequency dependence rather than a Zeeman-driven modification of the paramagnetic state. The paper discusses the Bloembergen-Purcell-Pound frequency-dependent form only to reject it for the zero-field temperature dependence, and it never tests the field dependence against a frequency dependence. A 63Cu-only measurement cannot separate these two variables. This is load-bearing because the suppression of the 50 K anomaly is the main result. The authors should either present data at a fixed frequency for different fields (e.g., by using both 63Cu and 65Cu at the same Larmor frequency, or by using a different NMR nucleus), or at minimum explicitly quantify the possible frequency dependence of 1/T1 over this range using the same sample and temperature.
[Sec. 3, Eq. (3)] The temperature dependence of the Knight shift is extracted using the assumption that the second-order quadrupole coefficient D is temperature-independent and equal to D(50 K) = 12.81 MHz^2. If D varies with temperature, the K(T) values would be systematically shifted, and the conclusion that K is proportional to bulk susceptibility and H-independent would need revision. The assumption is stated without an experimental test. Although the reported H-independence of K at fixed T (Fig. 3(b)) partially mitigates this concern for the H-dependence, it does not test the T-dependence. The authors should verify the constancy of D by performing the multi-frequency analysis at at least one low temperature (e.g., 10 K or 4.2 K) and comparing with the 50 K value, or provide an estimate of the systematic error in K from a plausible T-dependence of D.
[Sec. 3, Fig. 4 and Fig. 5] The 1/T1 data in Figs. 5(a) and 5(b) are presented without statistical error bars, and the text states that 'T1 was evaluated from the reliable fitting of the relaxation curve with the single component of T1' without showing residuals or goodness-of-fit parameters. The relaxation functions in Eqs. (7) and (8) are sums of multiple exponentials, so a single-component fit is nontrivial. The authors should provide at least representative fit residuals and error bars on the plotted 1/T1 values, especially for the low-temperature upturn points that support the central claim. Without these, it is difficult to assess whether the observed field-induced changes are statistically significant.

minor comments (5)

[Title and affiliations] There are several typographical errors in the title and abstract: 'Inv estigated' and 'Depertment' in the header, and 'e ﬀect' with a stray ligature. These should be corrected.
[Sec. 2] The text says '63/65Cu-NMR 1/T1 was also measured at the peak with the highest intensity', but only 63Cu T1 data are shown. Please specify whether 65Cu T1 was measured and, if not, which isotope was used throughout.
[Sec. 3, Fig. 2] The label 'Se' in Fig. 1(a) appears to be a typo for 'S'. Also, in the caption of Fig. 2(a), the simulation parameters (K = 1%, 63νzz = 9.14 MHz, 65νzz = 8.48 MHz, η = 0.32) are given, but the range of the frequency axis in the simulations is not stated; please add this or refer to the text for details.
[Sec. 3] The paper uses the term 'H-swept' but in the experimental section describes 'H-swept 63/65Cu-NMR spectra at several different frequencies'. It would be clearer to explicitly state that the field was swept at constant frequency, so that each field value corresponds to a distinct Larmor frequency (as noted in the major comments).
[Sec. 3, Fig. 1(b)] The phase diagram in Fig. 1(b) includes the newly determined Tmax and T* points, but the figure is reproduced from a previous work. Please ensure the new data points are clearly distinguished (e.g., by different symbols or color) and that the figure caption explains the added points.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the 1/T1 field-dependence findings are direct measurements, and the Knight-shift analysis uses a standard linear fit with independent bulk-susceptibility data.

full rationale

The paper's central results are experimental: 63Cu-NMR 1/T1 is measured directly and reported versus T and H; no fitted parameter is renamed as a prediction. The 50 K anomaly suppression and the low-temperature upturn are read off the data, so the derivation chain is self-contained. The Knight shift extraction uses Eq. (2), a standard linear relation in (gamma*Hres)^-2, with D(50K)=12.81 MHz^2 fixed in Eq. (3); the T-independence of D is an untested assumption that could bias K(T), but it is not circular because K is obtained from measured resonance-line positions, not from a model whose output equals its input. The K-chi linearity compares new NMR shifts with previously published bulk susceptibility, which is independent external evidence. Self-citations to prior NQR, neutron, and phase-diagram work supply context and supporting data rather than a uniqueness argument or an ansatz. The field/frequency entanglement in the H-swept NMR method (each field point at a different Larmor frequency) is a possible confound for the interpretation of the field dependence and is not settled by an isotope test; however, it is an experimental-design limitation, not a circular reduction by construction. The ac-plane orientation conclusion is an inference from powder-pattern simulations with stated parameters, not a definitional equivalence. Overall, no load-bearing step reduces to its own input.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central 1/T1 claims are direct measurements and require no free parameters. The spectrum simulations and Knight shift extraction depend on fitted quadrupole parameters and the T-independent D assumption; the K-chi scaling depends on previously published susceptibility data. No invented entities are introduced.

free parameters (6)

63Cu quadrupole frequency 63νzz = 9.14 MHz
Determined from fitting the NMR powder pattern; used in spectrum simulations and low-field relaxation fits.
65Cu quadrupole frequency 65νzz = 8.48 MHz
Determined from fitting the 65Cu NMR powder pattern; used in the spectral simulations.
EFG asymmetry parameter η = 0.32
Fitted to reproduce the observed NMR powder pattern; used in the quadrupole Hamiltonian.
Knight shift K used in simulations = 1%
An input value for the powder pattern simulations in Fig. 2; a fuller K(T) is later extracted from the data.
Second-order quadrupole coefficient D(50K) = 12.81 MHz^2
Extracted from the intercept/slope plot in Fig. 3(b) and then assumed T-independent for all K(T) determinations.
Hyperfine coupling constant Ahf = 0.14 T/μB
Obtained from the slope of the K-chi plot in Fig. 3(d), using bulk susceptibility measured previously by the same group.

assumptions (5)

standard math The NMR Hamiltonian is the sum of Zeeman and quadrupole terms, Eq. (1), with the quadrupole interaction treated as a perturbation for HZ >> HQ.
This is the standard NMR Hamiltonian and is used throughout the analysis.
ad hoc to paper D is T-independent in Eq. (3), so the Knight shift can be obtained by fixing D at its 50 K value.
This is an untested assumption stated without discussion; if D varies with T, the reported K(T) shifts.
domain assumption The relaxation curve for the central transition of I = 3/2 nuclei is given by Eq. (7), and the low-field relaxation by the matrix-diagonalization form in Eq. (8).
These are standard forms for quadrupolar nuclei and are used for T1 extraction.
domain assumption The WIEN2k DFT calculation places Vzz nearly parallel to the b axis.
This external DFT result is used to convert the fitted orientation into the statement that the ac plane is the easy plane.
domain assumption The observed NMR spectrum is a sum of a 3D powder pattern and a 2D powder pattern with φ = 90 degrees.
This two-component model is used to infer partial sample orientation; alternative orientation distributions are not tested.

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Cite this review

Pith. "Pith review of Magnetic-Field Dependence of Paramagnetic Properties Investigated by 63/65Cu-NMR on the Yb Zigzag-Chain Semiconductor YbCuS2." pith.science (2026). https://pith.science/paper/EA7UDR33

@misc{pith2026250200830,
  author       = {Pith},
  title        = {Pith review of: Magnetic-Field Dependence of Paramagnetic Properties Investigated by 63/65Cu-NMR on the Yb Zigzag-Chain Semiconductor YbCuS2},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EA7UDR33}},
  note         = {Machine review of arXiv:2502.00830}
}

read the original abstract

To investigate the paramagnetic properties of YbCuS2 under magnetic fields, we have performed the 63/65Cu-nuclear magnetic resonance (NMR) measurements. The NMR spectra can be reproduced by the simulations of the three-dimensional powder pattern and the additional two-dimensional powder pattern, indicating the partial sample orientation due to the anisotropy of the magnetic properties. These simulations suggest that the ac plane is the easy plane in YbCuS2. The Knight shift K is proportional to the bulk magnetic susceptibility and field-independent. The broad maximum of the nuclear spin-lattice relaxation rate 1/T1 at Tmax ~ 50 K (50 K anomaly) observed at zero magnetic field is quickly suppressed by the magnetic fields. This indicates that the 50 K anomaly is field-dependent. Furthermore, an anomalous enhancement of 1/T1 at low temperatures was observed above 3 T. This field seemingly corresponds to the magnetic field at which a field-induced phase transition occurs below the antiferromagnetic transition temperature TN ~ 1 K. The changes in 1/T1 observed in the paramagnetic state suggest the presence of the complex quantum phenomena under magnetic fields in YbCuS2.

Figures

Figures reproduced from arXiv: 2502.00830 by the authors.

**Figure 1.** (Color online) (a) Crystal structure of YbCuS2. The solid line represents the unit cell. (b) H-T phase diagram of YbCuS2; the circles and hexagons are the transition temperatures TN obtained from the highest peaks of the specific heat C(T) data and the kinks of the magnetization M(T) data, respectively.13) The ordered phase is divided into at least three phases as indicated by the triangles given by the peaks of dM(… view at source ↗

**Figure 2.** (Color online) (a) 3D powder pattern simulation with K = 1%, 63νzz = 9.14 MHz, 65νzz = 8.48 MHz, and η = 0.32. (b) Observed NMR spectrum at a fixed frequency of 64.2 MHz and 4.2 K in YbCuS2; the narrow lines in the NMR spectrum are signals from the Cu coil used for the NMR measurements and Al as an impurity arising from the NMR probe. (c) 2D powder pattern simulation fixing the azimuthal angle of φ = 90◦ (H ⊥ Vxx) w… view at source ↗

**Figure 3.** (Color online) (a) Temperature variations of the 63Cu-NMR spectrum of powdered YbCuS2 obtained by H-swept method at a frequency of 64.2 MHz for 4.2 K ≤ T ≤ 75 K; the temperature dependence of the Knight shift was estimated at the peak with the highest intensity as indicated in the arrows. (b) Field variations of the 63Cu-NMR spectrum (left hand) and (63γHres) −2 for different NMR frequency (right hand); the horizont… view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: (Color online) 63Cu relaxation curve R(t) at (a) µ0H = 5.6 T, T = 4.2 K, (b) µ0H = 3.5 T, T = 4.2 K, (c) µ0H = 1.7 T, T = 4.2 K, and (d) µ0H = 0.1 T, T = 1.5 K. The dashed line represents the fitting with the single component of T1. region µ0H < 0.5 T, we used the theo…

**Figure 5.** Figure 5: (Color online) (a) Temperature dependence of 63Cu-NMR 1/T1 on YbCuS2 at several magnetic fields; the downarrows represent Tmax obtained from the maximum of 1/T1 below 3 T. The uparrows indicates T ∗ , below which 1/T1 deviates from the extrapolation line below 30 K. Th…

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Introduction Recently, there has been signiﬁcant attention on mag- netic frustration in insulating or semiconducting compoun ds based on rare-earth ions from Ce (4 f 1) to Yb(4 f 13).1–18) The interplay of the strong spin–orbit coupling and the crys - talline electric ﬁeld (CEF) e ﬀect of 4 f electrons leads to the anisotropic exchange interactions, leadi...

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Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.

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Introduction Recently, there has been signiﬁcant attention on mag- netic frustration in insulating or semiconducting compoun ds based on rare-earth ions from Ce (4 f 1) to Yb(4 f 13).1–18) The interplay of the strong spin–orbit coupling and the crys - talline electric ﬁeld (CEF) e ﬀect of 4 f electrons leads to the anisotropic exchange interactions, leadi...

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12, 13) The polycrystalline samples were coarsely powdered to increase the surface area for bet- ter thermal contact

Experimental Polycrystalline samples of YbCuS 2 were synthesized by the melt-growth method. 12, 13) The polycrystalline samples were coarsely powdered to increase the surface area for bet- ter thermal contact. A conventional spin-echo technique wa s used for the 63/ 65Cu-NMR measurements. 63Cu and 65Cu nu- clei with spin I = 3/ 2 have nuclear gyromagnetic...

work page

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2 MHz on the powdered sample

Results and Discussion Figures 2(b) shows the H-swept 63/ 65Cu-NMR spectrum measured at the frequency of ν= 64. 2 MHz on the powdered sample. In general, the total e ﬀective NMR Hamiltonian of a /s51/s68/s32/s112/s111/s119/s100/s101/s114/s32/s112/s97/s116/s116/s101/s114/s110 /s54/s51 /s110 /s122/s122 /s32/s61/s32/s57/s46/s49/s52/s32/s77/s72/s122 /s54/s53 ...

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5 T, T = 4

2 K, (b) µ0H = 3. 5 T, T = 4. 2 K, (c) µ0H = 1. 7 T, T = 4. 2 K, and (d) µ0H = 0. 1 T, T = 1. 5 K. The dashed line represents the ﬁtting with the single component of T1. region µ0H < 0. 5 T, we used the theoretical relaxation curves obtained by the matrix diagonalization 29) on the assumption that H ‖Vyy, K = 1%, 63νzz = 9.14 MHz, and η= 0. 32. For exampl...

work page

[5] [5]

000 −0. 035 0 . 000 −0. 011 0 . 000 0 . 041           (T/µB) (6) is obtained. The experimental value of Ahf = 0. 14 T /µB is larger than all components of Ad. Thus, contributions except for the classical dipolar interactions may exist. This main ly originates from the transferred hyperﬁne ﬁeld from the mag- netic Yb site to the NMR atomic site. ...

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W. Liu, Z. Zhang, J. Ji, Y . Liu, J. Li, X. Wang, H. Lei, G. Chen , and Q. Zhang, Chin. Phys. Lett. 35, 117501 (2018)

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The NMR spectra can be re- produced by the simulations of the 3D powder pattern and the additional 2D powder pattern corresponding to the par- 5 J

Conclusion In conclusion, we have performed the 63/ 65Cu-NMR mea- surements to investigate the paramagnetic properties of YbCuS2 under magnetic ﬁelds. The NMR spectra can be re- produced by the simulations of the 3D powder pattern and the additional 2D powder pattern corresponding to the par- 5 J. Phys. Soc. Jpn. tial sample orientation under magnetic ﬁel...

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J. G. Rau and M. J. P . Gingras, Phys. Rev. B 98, 054408 (2018)

work page 2018