Spin fluctuations, absence of magnetic order, and crystal electric field studies in the Yb$^{3+}$-based triangular lattice antiferromagnet Rb$_3$Yb(VO$_4$)$_2$

Abhidev. B; Q.-P. Ding; R. Kolay; R. Nath; Sebin J. Sebastian; Y. Furukawa

REVIEW 3 major objections 4 minor 66 references

Spin fluctuations, absence of magnetic order, and crystal electric field studies in the Yb$^{3+}$-based triangular lattice antiferromagnet Rb$_3$Yb(VO$_4$)$_2$

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read A triangular-lattice Yb magnet shows no magnetic order down to 1.6 K and behaves as a clean $J_{\rm eff}=1/2$ antiferromagnet with $J/k_{\rm B}\simeq 0.18$ K, a disorder-free candidate for quantum spin liquid physics.

desk verdict A careful, honest multi-technique study that adds useful NMR and CEF analysis to a known candidate; the impurity attribution for the 2.23 K anomaly is the one place the no-LRO argument could use more support. read the letter →

arxiv 2506.07005 v1 pith:I5FQMQZ4 submitted 2025-06-08 cond-mat.mtrl-sci

Sebin J. Sebastian , R. Kolay , Abhidev. B , Q.-P. Ding , Y. Furukawa , R. Nath This is my paper

classification cond-mat.mtrl-sci

keywords triangularlatticeantiferromagnetquantumspinliquidcandidateKramersdoubleteffectivespin-1/2crystalelectricfieldytterbiumoxidemagnet51VNMRfrustratedmagnetism

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 argues that Rb$_3$Yb(VO$_4$)$_2$ realizes a clean effective spin-$1/2$ triangular lattice antiferromagnet with remarkably weak interactions and no sign of magnetic ordering down to 0.4 K in bulk measurements and 1.6 K in NMR. The authors establish, through susceptibility, magnetization, specific heat, and crystal electric field calculations, that the ground state is a Kramers' doublet with effective spin $J_{\rm eff}=1/2$, separated from the next doublet by about 18.61 meV (about 210 K). They extract a tiny antiferromagnetic exchange coupling $J/k_{\rm B}\simeq 0.18$ K and a low-temperature Curie-Weiss temperature of only $-0.26$ K, meaning the spins remain paramagnetic-like down to very low temperatures. Because the material is structurally ordered with no detectable site disorder, the authors propose it as an ideal platform to explore intrinsic quantum spin liquid physics in a Yb$^{3+}$-based triangular lattice antiferromagnet.

What carries the argument

The load-bearing object is the effective $J_{\rm eff}=1/2$ Kramers' doublet ground state, whose two Zeeman-split levels dominate all low-energy physics and whose $g$-tensor anisotropy ($g_{\perp}\simeq 3.19$, $g_z\simeq 0.74$ from CEF calculation) encodes the magnetic anisotropy. Three quantitative tools carry the argument: a modified two-level susceptibility model that combines Curie and Van-Vleck contributions and reproduces $\chi T$ over the entire 0.4–380 K range with $T_0=-0.26$ K; a high-temperature series expansion (Pad\'e approximants) for the $S=1/2$ triangular lattice Heisenberg antiferromagnet that fits the low-temperature susceptibility with $J/k_{\rm B}\simeq 0.19$ K; and a paramagnetic spin-fluctuation relation $1/T_1 \propto dB_{1/2}(x)/dx$ that collapses the NMR relaxation data onto a universal curve at low temperatures. The point-charge CEF calculation yields doublet levels at 0, 18.61, 38.32, and 72.10 meV and reproduces the measured magnetization and specific heat.

What would settle it

Perform $^{171}$Yb or $^{51}$V NMR, muon spin rotation, or neutron diffraction on a single-crystal sample verified free of Yb$_2$O$_3$ and cool below 1 K; observing a sharp resonance broadening, static internal fields, or a magnetic Bragg peak would disprove the no-order claim. Alternatively, showing that the 2.23 K $\lambda$ anomaly persists unchanged in Yb$_2$O$_3$-free material would falsify the impurity interpretation.

Watch

Extended reading notes

Core claim

Rb$_3$Yb(VO$_4$)$_2$ crystallizes in the hexagonal space group $P\bar{3}m1$ with Yb$^{3+}$ ions forming perfect triangular layers. The central discovery is that these Yb moments form a $J_{\rm eff}=1/2$ Kramers' doublet ground state with very weak antiferromagnetic coupling: the low-temperature Curie-Weiss temperature is $\theta_{\rm CW}^{\rm LT}\simeq -0.26$ K, the exchange coupling from the high-temperature series expansion and NMR is $J/k_{\rm B}\simeq 0.18$–0.27 K, and the point-charge CEF calculation places the first excited doublet at 18.61 meV, well above the temperature range of interest. $^{51}$V NMR spectra show no abrupt line broadening down to 1.6 K, excluding magnetic long-range order, and the spin-lattice relaxation rate $1/T_1$ exhibits pronounced frequency dependence that scales with the field derivative of the $S=1/2$ Brillouin function, the signature of paramagnetic fluctuations. Specific heat in applied fields shows a Schottky anomaly from the Zeeman-split doublet, while the zero-field $\lambda$ anomaly at 2.23 K is attributed to a trace of Yb$_2$O$_3$ impurity. Together these results position Rb$_3$Yb(VO$_4$)$_2$ as a disorder-free candidate for exploring quantum spin liquid physics on a triangular lattice.

Load-bearing premise

The argument assumes that the specific-heat anomaly at 2.23 K comes from a trace of Yb$_2$O$_3$ impurity in the sample rather than from an intrinsic magnetic transition of Rb$_3$Yb(VO$_4$)$_2$; if that anomaly were intrinsic, the claim of no magnetic long-range order would not hold.

Editorial extensions

If this is right

If the compound is an isotropic Heisenberg $S=1/2$ triangular antiferromagnet with $J/k_{\rm B}\sim 0.18$ K, it sits in the highly frustrated regime where quantum spin liquid behavior is theoretically expected at cryogenic temperatures.
The very small exchange scale means fields of order 1 T strongly polarize the spins, so field-tuned phases and a tunable spin Hamiltonian should be observable in this material.
The successful two-level susceptibility fit with $T_0\simeq -0.26$ K provides a template for extracting weak exchange couplings in other Yb-based frustrated magnets where CEF effects contaminate the high-temperature Curie-Weiss analysis.
The $g$-tensor anisotropy with $g_\perp \gg g_z$ implies predominantly in-plane moments, making the spin dynamics quasi-two-dimensional and motivating future anisotropic-exchange modeling.

Reading between the lines

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

The near-cancellation of the high-temperature Curie-Weiss region by CEF depopulation means published $\theta_{\rm CW}$ values for Yb vanadates should be reinterpreted with a two-level model before being quoted as exchange strengths; here the high-temperature scale ($-109.7$ K) is about 400 times the low-temperature scale.
With exchange of only $\sim 0.18$ K and a CEF gap of $\sim 210$ K, Rb$_3$Yb(VO$_4$)$_2$ is an unusually clean realization of the spin-only $J_{\rm eff}=1/2$ limit; an XXZ-type easy-plane Hamiltonian tied to the measured $g$-anisotropy would be a natural next model to test with neutron scattering or magnetocaloric measurement.
The paramagnetic relaxation observed down to 1.6 K, together with a concurrent report of no order to 100 mK, suggests the intrinsic magnetic scale may be even smaller than 0.18 K; measuring $1/T_1$ below 100 mK could reveal whether fluctuation slowing starts at a finite temperature or continues toward zero.
Because the lattice contribution is removed using a non-magnetic analog and the 2.23 K anomaly is assigned to about 1% Yb$_2$O$_3$, the cleanest test of the entropy accounting would be a specific-heat measurement to well below 1 K on a sample verified free of the impurity.

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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

Here's my take. This is a solid, honest paper from a group that knows this materials family. The central claim – J_eff=1/2 ground state, weak AFM exchange (J/k_B ~ 0.18 K), and no order down to 1.6 K – is consistent across susceptibility, magnetization, specific heat, and 51V NMR, and it agrees with the concurrent work by Ma et al. (ref 55) that saw no order down to 100 mK. The genuinely new bits are the 51V NMR spin-lattice relaxation data and the point-charge CEF level scheme; the 1/T1 scaling onto the derivative of the Brillouin function is a nice way to show that the low-temperature dynamics are paramagnetic.

Where I push back: the specific-heat analysis has two soft spots that are related. The 2.23 K lambda anomaly in zero field is assigned to ~1% Yb2O3 on the basis of a presumption, not evidence. The paper itself says the phase fraction is 'presumed' because powder XRD can't see it. No entropy check, no control experiment. That is exactly where the no-LRO claim would break if the anomaly were intrinsic. I don't think it is intrinsic – the NMR and the Ma et al. result both point away from order – but the paper should tighten this. Second, the zero-field Schottky gap Δ/k_B(0)=1.66 K extracted from the linear fit in Fig 6(b) is unphysical for a Kramers doublet; at zero field there is no gap. The nonzero intercept suggests the fit is contaminated by the impurity anomaly or by short-range correlations. These are fixable, but they are real holes in the thermodynamic analysis.

The CEF calculations are parameter-free (derived from the point-charge model), which is reproducible, but point-charge is crude; the level scheme should be treated as indicative. The internal spread in the CEF gap (201–262 K from different susceptibility fits, 216 K from point-charge) is understandable but should be discussed. The g-values from different analyses (2.3 to 2.67) are in the same ballpark but not tightly consistent; that could be better addressed.

Bottom line: the main physical picture holds. The paper is most useful to people working on Yb-based triangular lattices and to experimentalists comparing local-probe and bulk techniques. It deserves serious peer review. My recommendation would be to send it out, and require the authors to address the impurity attribution – either with an entropy estimate for the anomaly or an explicit dilution control – and to comment on the zero-field Schottky gap.

Referee Report

3 major / 4 minor

Summary. The manuscript reports a comprehensive experimental and computational study of the triangular lattice antiferromagnet Rb3Yb(VO4)2. The authors measure powder XRD, magnetic susceptibility, isothermal magnetization, specific heat, and 51V NMR, and perform point-charge CEF calculations. They conclude that the Yb3+ ions form an effective J_eff=1/2 Kramers doublet ground state with weak antiferromagnetic exchange (theta_LT_CW ~ -0.26 K, J/kB ~ 0.18 K), no magnetic long-range order down to 1.6 K, and dominant paramagnetic fluctuations, positioning the compound as a disorder-free candidate for quantum spin liquid physics. The central claim of no magnetic order relies critically on attributing a 2.23 K lambda anomaly in the zero-field specific heat to a presumed trace Yb2O3 impurity, and on a Schottky analysis that yields a nonzero zero-field gap for the Kramers doublet.

Significance. If the central claim holds, the paper is a useful addition to the family of Yb3+-based triangular lattice antiferromagnets, providing a multi-technique characterization that cross-checks susceptibility, magnetization, specific heat, NMR shift, and relaxation data. The CEF calculations are carried out from structural parameters via the point charge approximation and are compared with the measured thermodynamic data, giving an internally consistent picture of a J_eff=1/2 ground state with a large CEF gap. The paper's strengths include the use of a nonmagnetic analog for phonon subtraction, the field-dependent Schottky analysis that recovers most of R ln2 entropy at high fields, the NMR spectra and relaxation scaling that support paramagnetic-like fluctuations, and the consistency of the derived exchange scales from multiple independent analyses. However, the attribution of the 2.23 K anomaly to Yb2O3 is not quantitatively supported, and the zero-field Schottky gap is physically problematic for a Kramers doublet; these issues are load-bearing for the 'no magnetic order' conclusion and the suitability of the compound as a QSL candidate.

major comments (3)

[Section III.B, Fig. 6] The 2.23 K lambda anomaly in the zero-field specific heat is assigned to a 'presumed' ~1% Yb2O3 impurity with no direct quantitative evidence. Since the central claim of no magnetic long-range order depends on this attribution, the manuscript must provide a supporting entropy or phase-fraction analysis (e.g., comparing the anomaly's entropy with x R ln2 for the assumed impurity fraction), a control experiment (e.g., deliberate Yb2O3 doping), or independent phase-sensitive data (e.g., synchrotron XRD). As written, the anomaly could equally be an intrinsic transition, which would invalidate the no-LRO headline and contaminate the subsequent Schottky subtraction.
[Section III.B, Eq. (6) and Fig. 6(b)] The Schottky fit yields a zero-field extrapolated gap Delta/kB(0) ≈ 1.66 K for a Kramers doublet ground state. A Kramers doublet is degenerate at zero field in the absence of static magnetic order or a strong internal field; a nonzero intercept is therefore unphysical unless the doublet is split by an ordering field or the fit includes impurity contributions. This inconsistency suggests the two-level Schottky model is contaminated by the 2.23 K anomaly or by the assumed Yb2O3 phase. The authors should re-analyze the data excluding the anomalous region, model the impurity contribution, or otherwise explain the physical origin of the finite zero-field gap.
[Section IV, Table III and Fig. 11] The CEF calculation is performed only with nearest-neighbor O2- ligands within the point charge approximation and is not fitted to the susceptibility or specific heat data. While the comparison shows reasonable agreement, the calculated g-tensor (g_perp ≈ 3.19, g_z ≈ 0.74) is strongly anisotropic, whereas the HTSE fit to susceptibility and the NMR shift analysis use an isotropic g ≈ 2.59–2.67. The paper should acknowledge this discrepancy and discuss whether the CEF-derived anisotropy affects the extracted exchange coupling J/kB, which is otherwise presented as a single isotropic value.

minor comments (4)

[Section III.A, two-level CEF fits] The text states that the two-level CEF fit (Eq. (3)) gives theta_CEF_CW ≈ -12.6 K, drastically different from theta_LT_CW ≈ -0.26 K, and explains this by the neglect of Van-Vleck contributions; this discussion is somewhat confusing because the same fit also yields mu_eff values that are not obviously consistent with a ground Kramers doublet. Please clarify the physical meaning of the intermediate-temperature theta_CEF_CW and why the low-temperature CW limit is the relevant scale for exchange.
[Section III.B, Fig. 6(b) left inset] The scaling collapse of Cmag versus kBT/(Msat μ0H) is mentioned as a hallmark of weak interactions, but the text does not specify the universal function expected for a noninteracting Kramers doublet. Adding the functional form (or a reference) would strengthen the scaling argument.
[Section V, Note added] The note added mentions that Ref. [55] reports no magnetic order down to 100 mK, which strongly supports the impurity interpretation for the 2.23 K anomaly; however, this important corroborating evidence appears only as a note and is not integrated into the main analysis or discussion of the anomaly. I recommend incorporating it explicitly in Section III.B.
[General] The phrase 'disorder-free' in the abstract and summary is too strong given that powder XRD cannot exclude small amounts of site disorder or stacking faults; I suggest rewording to 'no detectable disorder' or 'structurally pristine within diffraction limits.'

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the CEF level scheme is an independent point-charge prediction, and the chi, M, Cmag, and NMR analyses cross-check each other; only minor self-citations and a non-load-bearing g input in the 1/T1 scaling keep this from a full zero.

full rationale

The central derivation chain is not circular. The CEF calculation in Sec. IV takes only the XRD-refined structural parameters as inputs ('The required structural parameters, including lattice constants and atomic positions, were taken from the powder XRD refinement (Table I)') and evaluates the B_l^m coefficients with PyCrystalField; no CEF parameter is fitted to chi(T), M(H), or Cp(T). The four-doublet scheme (0, 18.61, 38.32, 72.10 meV) is therefore an independent structural prediction, and the reproduction of chi, M, and Cmag in Fig. 11 is a consistency check rather than the source of the level scheme. The exchange estimates are also cross-checks rather than constructions: theta_LT_CW is obtained from a low-T Curie-Weiss fit after subtracting chi_VV, J/kB ~ 2theta/3 is a mean-field conversion, the high-temperature series expansion fit to Eq. (2) uses independent Pade coefficients, and the NMR shift fit to Eq. (9) uses a hyperfine coupling separately obtained from the K versus chi plot. The 1/T1 scaling plot fixes g = 2.3 from magnetization and uses one proportionality constant, so the collapse onto the derivative of the Brillouin function is a nontrivial consistency test, not a prediction forced by the fit. The one passage that deserves explicit flagging is Section III.B's attribution of the 2.23 K lambda anomaly to a presumed ~1% Yb2O3 impurity ('In this case, as the extrinsic phase is untraceable in powder XRD, we presume that its phase fraction would be about 1 %'). That is an empirical assumption with missing internal quantitative support, so it is a correctness risk for the no-LRO claim if the anomaly were intrinsic; but it is not a self-referential reduction, and the Note added cites concurrent work (Ref. [55]) reporting no magnetic order down to 100 mK, independently supporting the no-LRO interpretation. The self-citations present (e.g., Refs. 14, 29, 37, 44) are decorative or standard and are not load-bearing. No circular step satisfies the required quote-and-reduction test, so the steps list is empty.

Assumptions & free parameters 13 free parameters · 6 assumptions · 0 invented entities

The central physics rests on standard condensed-matter models (Curie-Weiss, HTSE, Schottky, point-charge CEF) and one material-specific assumption: the weak 2.23 K lambda anomaly is extrinsic Yb2O3 rather than intrinsic order. The point-charge CEF approximation is a significant modeling assumption because it ignores covalency, more distant ligands, and lattice dynamics. No new entities are introduced.

free parameters (13)

chi0_HT = -2.56(1)e-4 cm3/mol
Temperature-independent susceptibility in high-T Curie-Weiss fit, Eq. (1).
theta_CW_HT = -109.7(2) K
High-temperature Curie-Weiss temperature from Eq. (1), dominated by CEF effects.
C_HT = 2.82(1) cm3 K/mol
High-temperature Curie constant giving mu_eff ~ 4.74 mu_B.
theta_CW_LT = -0.26(1) K
Low-temperature Curie-Weiss temperature after Van-Vleck subtraction, used to infer J/kB ~ 0.18 K.
J/kB (HTSE) = 0.19(2) K
Exchange coupling from high-temperature series expansion fit to chi(T), Eq. (2).
chi_VV = 6.6(1)e-3 cm3/mol
Van-Vleck susceptibility extracted from linear high-field slope of M(H) at 0.4 K.
g_avg (magnetization) = 2.3(1)
Landé g-factor from Brillouin function fits to isothermal magnetization, Eq. (5).
g_avg (low-T chi) = 2.67(1)
Average g-value from C_LT of the low-T Curie-Weiss fit.
g_avg (NMR shift) = 2.59(1)
g-value from fitting Kiso(T) to the spin-1/2 TLAF susceptibility, Eq. (9).
Delta/kB (two-level fit) = 201(3) K
CEF gap from the effective two-level model, Eq. (3), fitted for T >= 25 K.
Delta/kB (modified two-level) = 262.3(2) K
CEF gap from the modified two-level scheme with Curie and Van-Vleck terms, Eq. (4), fitted over the full temperature range.
Delta/kB(0) (Schottky) = 1.66(1) K
Zero-field effective gap from the two-level Schottky fit to Cmag; unphysical for a Kramers doublet and likely absorbing correlations or impurity contributions.
f (Schottky fraction) = field-dependent, approaching 1 at high fields
Molar fraction of free spins in the Schottky fit, Eq. (6).

assumptions (6)

domain assumption Point-charge approximation for the crystal electric field, including only the six nearest-neighbor O2- ligands around Yb3+
Used in Section IV to compute B_l^m parameters and the CEF level scheme. Known to be quantitatively limited but standard for rough estimates.
standard math Kramers theorem guarantees a doubly degenerate ground state for odd-electron Yb3+ at zero magnetic field
Invoked to justify the J_eff=1/2 Kramers doublet picture and the zero-field entropy.
domain assumption Mean-field relation J/kB = 2 theta_CW / 3 for a triangular lattice with coordination z=6
Used in Section III.A to convert theta_LT_CW into exchange coupling J/kB ~ 0.18 K.
standard math High-temperature series expansion (Padé approximant) for the S=1/2 isotropic triangular lattice antiferromagnet with coefficients from Elstner et al.
Used to fit chi(T) below 100 K, Eq. (2), assuming purely Heisenberg isotropic exchange.
domain assumption Phonon specific heat of Rb3Yb(VO4)2 is identical to that of the non-magnetic analog Rb3Y(VO4)2 after mass correction
Used in Section III.B to subtract the lattice contribution and extract Cmag.
domain assumption Two-level Schottky model describes the low-temperature magnetic specific heat of the Zeeman-split Kramers doublet
Used to fit Cmag in Eq. (6), implicitly assuming negligible contributions from excited CEF doublets and weak correlations.

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Cite this review

Pith. "Pith review of Spin fluctuations, absence of magnetic order, and crystal electric field studies in the Yb$^{3+}$-based triangular lattice antiferromagnet Rb$_3$Yb(VO$_4$)$_2$." pith.science (2026). https://pith.science/paper/I5FQMQZ4

@misc{pith2026250607005,
  author       = {Pith},
  title        = {Pith review of: Spin fluctuations, absence of magnetic order, and crystal electric field studies in the Yb$^3+$-based triangular lattice antiferromagnet Rb$_3$Yb(VO$_4$)$_2$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/I5FQMQZ4}},
  note         = {Machine review of arXiv:2506.07005}
}

abstract

We report a comprehensive experimental investigation of the structural, thermodynamic, static, and dynamic properties of a triangular lattice antiferromagnet Rb$_3$Yb(VO$_4$)$_2$. Through the analysis of magnetic susceptibility, magnetization, and specific heat, complemented by crystal electric field (CEF) calculations, we confirm the Kramers' doublet with effective spin $J_{\rm{eff}}=1/2$ ground state. Magnetic susceptibility and isothermal magnetization analysis reveal a weak antiferromagnetic interaction among the $J_{\rm{eff}}=1/2$ spins, characterized by a small Curie-Weiss temperature ($\theta_{\text{CW}}^{\text{LT}}\simeq-0.26$ K) or a reduced exchange coupling ($J/k_{\rm B} \simeq 0.18$ K). The $^{51}$V NMR spectra and spin-lattice relaxation rate ($1/T_1$) show no evidence of magnetic long-range-order down to 1.6 K but reflect strong influence of CEF excitations in the intermediate temperatures. At low temperatures, $1/T_1(T)$ shows pronounced frequency dependence and $1/T_1$ vs field in different temperatures follows the scaling behaviour, highlighting the role of paramagnetic fluctuations. The CEF calculations using the point charge approximation divulge a large energy gap ($\sim 18.61$ meV) between the lowest and second lowest energy doublets, further establishing Kramers' doublet as the ground state. Our calculations also reproduce the experimental magnetization and specific heat data and indicate an in-plane magnetic anisotropy. These findings position Rb$_3$Yb(VO$_4$)$_2$ as an ideal and disorder-free candidate to explore intrinsic quantum fluctuations and possible quantum spin-liquid physics in a Yb$^{3+}$-based triangular lattice antiferromagnet.

Figures

Figures reproduced from arXiv: 2506.07005 by the authors.

**Figure 3.** FIG. 3. (a) [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

Figures from the paper (7 more)

**Figure 5.** Figure 5: (a) presents the isothermal magnetization M(H) of Rb3Yb(VO4)2 measured at various temperatures. At T = 0.4 K, the M(H) curve exhibits saturation near µ0HS ≃ 1.1 T, followed by a slow and linear increase at higher fields. This linear increase reflects the characterist…

**Figure 6.** Figure 6: FIG. 6. Temperature dependence of [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

**Figure 7.** Figure 7: FIG. 7. Typical field-sweep [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

**Figure 8.** Figure 8: FIG. 8. Temperature dependence of [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]

**Figure 9.** Figure 9: FIG. 9. Temperature dependence of 1 [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]

**Figure 10.** Figure 10: FIG. 10. Schematic representation of the CEF energy levels [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]

**Figure 11.** Figure 11: FIG. 11. (a) Comparison of the experimental [PITH_FULL_IMAGE:figures/full_fig_p010_11.png]

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987(1) ˚ A, c = 7

61 ˚ A3 for Rb 3Yb(VO4)2 and a = b = 5. 987(1) ˚ A, c = 7. 888(1) ˚ A, β = 120(1) ◦, and Vcell ≃ 244. 86 ˚ A3 for Rb3Y(VO4)2. Similarly, the reﬁned atomic positions are summarized in Table I. No extra peaks associated with any foreign phases was detected in the powder XRD. Mag...
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This value of T0 agrees very well with θLT CW

3(2) K. This value of T0 agrees very well with θLT CW. In the low- T regime where T ≪ ∆ CEF/k B, the second term within the parentheses in Eq. ( 4) is almost negligi- ble. The terms C0/k B and C2/k B share similarity with the Curie constant from Eq. ( 1). We observed that the ...

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

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82(1) cm 3K/mol, and θHT CW ≃ − 109. 7(2) K. From the value ofCHT, the eﬀective magnetic moment is estimated as µ HT eﬀ = √ 8Cµ B ≃ 4. 74(1) µ B, which is in good agree- ment with the expected value µ eﬀ ≃ 4. 54 µ B for a free Yb3+ ion (J = 7/ 2, gJ = 1. 14) in a 4 f 13 conﬁguration. The large and negative θHT CW does not necessarily indicate strong AFM i...

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67(1), typically ex- pected for Yb 3+ based systems [ 24]

31(1) µ B, suggestive of an eﬀective spin Jeﬀ = 1 / 2 with an average g-value of gave ≃ 2. 67(1), typically ex- pected for Yb 3+ based systems [ 24]. A small value of θLT CW indicates very weak AFM interactions among the Jeﬀ = 1/ 2 moments. Using the mean-ﬁeld approxima- tion for a TLAF with coordination number z = 6, the exchange coupling is estimated to...

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18(1) K [ 29]. Since the Yb 3+ ions form an isotropic triangular lattice and the CEF stabilizes an eﬀective Jeﬀ = 1/ 2 Kramers’ doublet ground state, we employed the high-temperature series expansion for an S = 1/ 2 isotropic triangular lat- tice antiferromagnet to ﬁt the χ (T ) data at low temper- atures. This uses the Pad´ e approximation and has the fo...

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This further supports a Jeﬀ = 1/ 2 ground state at low temperatures for Rb 3Yb(VO4)2

76 Jmol −1K−1). This further supports a Jeﬀ = 1/ 2 ground state at low temperatures for Rb 3Yb(VO4)2. To quantitatively analyze this Schottky anomaly, Cmag(T ) was ﬁtted using a two-level Schottky model CSch(T,H ) = fR ( ∆ kBT ) 2 e ( ∆ kB T ) [ e ( ∆ kB T ) + 1 ] 2. (6) Here, f represents the molar fraction of free spins and ∆ /k B denotes the energy gap...

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012%, η = 0, and νQ ≈ 0

036%, Kax ≃ − 0. 012%, η = 0, and νQ ≈ 0. 105 MHz. The quadrupole frequency was found to remain constant down to 1.6 K, ruling out any possible structural distor- tion in the compound. Temperature-dependent NMR shift K(T ) at 12.72 MHz and 77.1 MHz is shown in Fig

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From the linear K vs χ plot (inset Fig

Since K(T ) directly reﬂects the spin susceptibility χ spin, the linear relation can be expressed as K(T ) = K0 + Ahf NAµ B χ spin, (9) where K0 is the temperature-independent orbital con- tribution and Ahf the hyperﬁne coupling constant be- tween 51V nuclear spin with the Yb 3+ electronic spins. From the linear K vs χ plot (inset Fig. 8), we obtained K0 ...

work page