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arxiv: 1906.09089 · v2 · pith:AGALKFSTnew · submitted 2019-06-21 · ❄️ cond-mat.str-el · cond-mat.mtrl-sci

Anisotropic temperature-field phase diagram of single-crystalline β-Li₂IrO₃: magnetization, specific heat, and ⁷Li NMR study

M. Majumder , F. Freund , T. Dey , M. Prinz-Zwick , N. B\"uttgen , Y. Skourski , A. Jesche , A.A. Tsirlin
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P. Gegenwart
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Pith reviewed 2026-05-25 18:45 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.mtrl-sci
keywords β-Li₂IrO₃Kitaev magnetquantum paramagnet⁷Li NMRphase diagramanisotropic magnetismNéel temperature suppression
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The pith

Magnetic field along the b axis in β-Li₂IrO₃ suppresses Néel order at 2.8 T and produces a quantum paramagnetic state.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The measurements map how the temperature-field phase diagram of single-crystal β-Li₂IrO₃ depends on field direction. Fields along a or c lower the 38 K Néel temperature only modestly, while a field along b drives that temperature to zero at 2.8 T. In the resulting regime, ⁷Li NMR detects gradual line broadening, a continuously shifting resonance, a relaxation-rate peak near 40 K, and power-law relaxation at lower temperature, all interpreted as signs of developing local magnetic fields. High-temperature magnetization anisotropy matches a ferromagnetic Kitaev term combined with negative off-diagonal anisotropy.

Core claim

At high temperatures the magnetization anisotropy matches a ferromagnetic Kitaev interaction K combined with negative off-diagonal Γ. At low temperatures fields along a or c reduce T_N only slightly to 35.5 K at 14 T, while the b-directed field eliminates T_N at 2.8 T and produces a crossover to a quantum paramagnetic state in which ⁷Li NMR detects gradual line broadening, continuous shift evolution, a relaxation-rate peak near 40 K, and power-law behavior at lower temperatures.

What carries the argument

The b-axis field-induced crossover to a quantum paramagnetic state, marked by the vanishing of T_N together with NMR line broadening and a relaxation-rate peak.

If this is right

  • Fields along a or c leave the ordered state largely intact up to 14 T with no additional transitions seen to 58 T.
  • The b-axis field produces a quantum paramagnetic regime below approximately 2.8 T.
  • ⁷Li NMR line broadening indicates developing local magnetic fields in the quantum paramagnetic state.
  • The spin-lattice relaxation rate peaks near the 40 K crossover temperature and follows power-law decay below it.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The power-law relaxation may reflect critical fluctuations or fractionalized spin excitations that survive in the field-induced state.
  • Analogous field-induced paramagnetic regimes could appear in other Kitaev materials when the field is aligned with the dominant anisotropy axis.
  • Neutron scattering or muon spin rotation on the same crystals could test whether the local fields arise from true quantum paramagnetism or from undetected short-range correlations.

Load-bearing premise

The NMR line broadening and relaxation-rate peak are taken as evidence for developing local magnetic fields inside a field-induced quantum paramagnetic state rather than residual short-range order or impurity contributions.

What would settle it

A sharp NMR line that remains narrow down to the lowest temperatures, or a relaxation rate whose temperature dependence matches impurity or short-range-order models instead of power-law behavior, would falsify the quantum paramagnetic interpretation.

Figures

Figures reproduced from arXiv: 1906.09089 by A.A. Tsirlin, A. Jesche, F. Freund, M. Majumder, M. Prinz-Zwick, N. B\"uttgen, P. Gegenwart, T. Dey, Y. Skourski.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Temperature dependence of the magnetic suscep [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Inverse susceptibility measured on an individ [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Field-dependent magnetization measured on a pow [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a), (b) and (c) Temperature dependence of the magnetic susceptibility at different magnetic fields applied along the [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Field-dependent magnetic susceptibility measured [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Temperature-field phase diagram obtained from the [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Field-sweep [PITH_FULL_IMAGE:figures/full_fig_p006_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. (a): Temperature dependence of the line shift ( [PITH_FULL_IMAGE:figures/full_fig_p007_9.png] view at source ↗
read the original abstract

Detailed magnetization, specific heat, and $^7$Li nuclear magnetic resonance (NMR) measurements on single crystals of the hyperhoneycomb Kitaev magnet $\beta$-Li$_2$IrO$_3$ are reported. At high temperatures, {\cred anisotropy of the magnetization is reflected by the different Curie-Weiss temperatures for different field directions}, in agreement with the combination of a ferromagnetic Kitaev interaction ($K$) and a negative off-diagonal anisotropy ($\Gamma$) as two leading terms in the spin Hamiltonian. At low temperatures, magnetic fields applied along $a$ or $c$ have only a weak effect on the system and reduce the N\'eel temperature from 38 K at 0 T to about 35.5 K at 14 T, with no field-induced transitions observed up to 58 T on a powder sample. In contrast, the field applied along $b$ causes a drastic reduction in the $T_N$ that vanishes around $H_c=2.8$ T giving way to a crossover toward a quantum paramagnetic state. $^7$Li NMR measurements in this field-induced state reveal a gradual line broadening and a continuous evolution of the line shift with temperature, suggesting the development of local magnetic fields. The spin-lattice relaxation rate shows a peak around the crossover temperature 40 K and follows power-law behavior below this temperature.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript reports magnetization, specific heat, and ⁷Li NMR measurements on single crystals of the hyperhoneycomb Kitaev magnet β-Li₂IrO₃. It maps an anisotropic temperature-field phase diagram in which fields along a or c weakly suppress T_N from 38 K to ~35.5 K at 14 T with no transitions up to 58 T, while fields along b drive T_N to zero at H_c ≈ 2.8 T, crossing over to a quantum paramagnetic state in which NMR exhibits gradual line broadening, continuous shift evolution, a 1/T1 peak near 40 K, and power-law relaxation below that temperature.

Significance. If the central interpretation holds, the work supplies a well-documented experimental phase diagram for a Kitaev candidate, with internally consistent data from three complementary techniques on single crystals. The high-field NMR observables provide the microscopic evidence that distinguishes the quantum paramagnetic regime from simple T_N suppression.

major comments (1)
  1. [Abstract] Abstract (final paragraph) and the corresponding discussion of the high-field regime: the interpretation that gradual ⁷Li line broadening, continuous shift evolution, the 1/T1 peak near 40 K, and power-law relaxation directly evidence developing local magnetic fields in a field-induced quantum paramagnet is load-bearing for the microscopic claim, yet the reported observables do not quantitatively exclude dilute impurity moments or residual short-range order persisting above nominal H_c; magnetization and specific-heat data establish only the crossover in T_N.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and positive assessment of the significance of our multi-technique study on the anisotropic phase diagram of β-Li₂IrO₃. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract (final paragraph) and the corresponding discussion of the high-field regime: the interpretation that gradual ⁷Li line broadening, continuous shift evolution, the 1/T1 peak near 40 K, and power-law relaxation directly evidence developing local magnetic fields in a field-induced quantum paramagnet is load-bearing for the microscopic claim, yet the reported observables do not quantitatively exclude dilute impurity moments or residual short-range order persisting above nominal H_c; magnetization and specific-heat data establish only the crossover in T_N.

    Authors: We agree that the NMR observables are consistent with developing local fields but do not furnish a quantitative exclusion of dilute impurities or residual short-range order. The strongest elements supporting our interpretation are the directional anisotropy (only b-axis fields induce the crossover at 2.8 T), the absence of a low-T Curie tail in the single-crystal magnetization, the specific-heat confirmation of T_N suppression, and the NMR phenomenology itself: gradual rather than static broadening, continuous shift evolution, a 1/T1 peak near 40 K (well above the zero-field T_N), and power-law relaxation below that temperature, all of which differ from typical impurity-dominated signatures. Nevertheless, to address the concern we will revise the abstract and discussion to replace stronger phrasing with “consistent with the development of local magnetic fields in a field-induced quantum paramagnetic regime, while alternative contributions cannot be fully excluded on the basis of the present data alone.” This is a partial revision; the core multi-technique phase diagram remains unchanged. revision: partial

Circularity Check

0 steps flagged

No circularity: purely experimental report with no derivations or self-referential reductions

full rationale

The paper presents magnetization, specific heat, and ⁷Li NMR measurements on β-Li₂IrO₃ single crystals, reporting field-dependent suppression of T_N along b and NMR features (line broadening, shift evolution, 1/T1 peak, power-law) in the high-field regime. No equations, fitted parameters renamed as predictions, or derivation chains exist; interpretations rest on direct observables without reducing to inputs by construction. Self-citations are absent from load-bearing steps, and the work is self-contained as raw data plus standard analysis against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard high-T Curie-Weiss fitting to extract anisotropy and on conventional interpretation of NMR line shape and relaxation in a paramagnetic regime; no new entities or ad-hoc postulates are introduced.

free parameters (1)
  • Curie-Weiss temperatures
    Fitted separately for each field direction from high-T magnetization to quantify anisotropy.
axioms (2)
  • domain assumption Curie-Weiss law applies in the high-temperature paramagnetic regime
    Invoked to extract directional anisotropy from susceptibility data.
  • domain assumption NMR line broadening and relaxation-rate peak indicate local static fields rather than dynamics or impurities
    Used to interpret the field-induced state as quantum paramagnetic.

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