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Studies of the Anomalous Hall Effect and Magnetic Structure of Nd2Mo2O7 -Test of the Chirality Mechanism-

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Yukio Yasui, Taketomo Kageyama, Taketo Moyoshi, Minoru Soda, Masatoshi Sato, Kazuhisa Kakurai

Strongly Correlated Electrons · Submitted 2 Mar 2006 · 33 references

Pith's verdict: A credible experimental test of the chirality mechanism for the anomalous Hall effect in Nd2Mo2O7, with a real gap in parameter sensitivity analysis.

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arXiv IDcond-mat/0603045 (version 2)
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CitationKazuhisa Kakurai, Masatoshi Sato, Minoru Soda, Taketomo Kageyama, Taketo Moyoshi, Yukio Yasui. "Studies of the Anomalous Hall Effect and Magnetic Structure of Nd2Mo2O7 -Test of the Chirality Mechanism-." arXiv:cond-mat/0603045 (2006). https://pith.science/paper/SXGKVQMQ
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The paper

The paper claims

Spin chirality cannot explain the anomalous Hall effect in Nd2Mo2O7.

The reading

The paper tests the spin-chirality mechanism for the anomalous Hall effect of the metallic pyrochlore molybdate Nd2Mo2O7. From neutron scattering in fields up to 5.7 T, the authors determine exchange constants and anisotropies that reproduce the neutron intensities, magnetization, and magnetic specific heat with one set of parameters. Using those parameters, they compute the fictitious magnetic flux generated by the local spin chirality of Mo moments through $\chi=\langle \mathbf{S}_1\cdot(\mathbf{S}_2\times\mathbf{S}_3)\rangle$, averaged over all local configurations, and compare its field and temperature dependence with the measured Hall resistivity. The calculated flux does not match the Hall data either quantitatively or qualitatively, so the paper concludes that the chirality mechanism is not the main source of the anomalous Hall effect. If correct, this redirects the search for the mechanism to other Berry-phase or scattering processes involving the Nd moments.

What carries the argument

The load-bearing object is the local spin chirality $\chi = \mathbf{S}_1\cdot(\mathbf{S}_2\times\mathbf{S}_3)$ of three Mo moments at the corners of a tetrahedron, whose statistical average defines a fictitious magnetic flux $\Phi \propto \langle \mathbf{S}_1\cdot(\mathbf{S}_2\times\mathbf{S}_3)\rangle$. The authors compute this flux by enumerating all local magnetic configurations of 16 Mo and 16 Nd moments in an fcc unit cell with a canonical distribution, using a Hamiltonian with fitted parameters: $J_{\mathrm{Mo-Mo}}=9.8$ K, $J_{\mathrm{Mo-Nd}}=-0.25$ K, $J_{\mathrm{Nd-Nd}}^{\mathrm{NN}}=0.29$ K, $J_{\mathrm{Nd-Nd}}^{\mathrm{2nd}}=-0.048$ K, $S_{\mathrm{Nd}}=2.65$, and Ising-like Nd anisotropy. The crucial feature is that they use the local, statistically averaged chirality rather than the chirality of the average magnetic structure, because the local nature of $\chi$ matters. This machinery yields the $H$ and $T$ dependence of $\Phi$ that is compared with the measured Hall resistivity.

Extended reading notes

Core claim

The central claim is that the unusual field- and temperature-dependence of the Hall resistivity of Nd2Mo2O7 cannot be explained by the spin-chirality mechanism once the actual magnetic structure is known. Neutron diffraction and inelastic scattering determine a model in which Mo moments are nearly collinear along crystal axes, tilted by only about 1 degree by a weak Mo-Nd exchange $J_{\mathrm{Mo-Nd}} = -0.25$ K, while Nd moments form spin-ice-like 'two-in two-out' configurations with $S_{\mathrm{Nd}}=2.65$ and net moment antiparallel to Mo below about 30 K. The fictitious flux $\Phi$ from local chirality $\chi=\langle \mathbf{S}_1\cdot(\mathbf{S}_2\times\mathbf{S}_3)\rangle$, averaged over all $2^{16}$ Nd configurations in the fcc unit cell, shows a minimum around $H=3$ T for $H\parallel[001]$ and a convex $H$-dependence for $H\parallel[111]$, whereas the observed Hall resistivity decreases monotonically in the first case and is concave in the second. The paper therefore concludes that spin chirality is at most a minor contributor, and that the Hall signal carries a separate Nd-related component that conventional mechanisms also do not explain.

Load-bearing premise

The load-bearing premise is that the fitted classical spin Hamiltonian—particularly the weak Mo-Nd exchange of $-0.25$ K that tilts Mo moments by only about a degree—faithfully describes the real magnetic structure and its statistical distribution in field and temperature.

Editorial extensions

If this is right

  • The anomalous Hall resistivity of Nd2Mo2O7 requires a source other than Mo-spin chirality; the paper leaves this mechanism open.
  • The Nd-moment contribution to the Hall signal, $4\pi R_s' M_{\mathrm{Nd}}$, is unexplained by the chirality mechanism and by conventional skew-scattering or side-jump mechanisms.
  • Earlier chirality-based claims for this compound rested on an overestimated Mo-Nd exchange ($-2.7$ K versus $-0.25$ K) and an overestimated Mo tilting angle (about $4^\circ$ versus $1^\circ$).
  • The fitted parameter set, including a second-neighbor Nd-Nd exchange, simultaneously reproduces neutron intensities, magnetization, and magnetic specific heat, so it provides a benchmark for future Hall-effect theories.
  • The sign change of $\rho_H$ along [111] claimed as evidence for chirality is not reproduced by the computed flux, so that evidence no longer stands.

Reading between the lines

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

  • Beyond the paper: if the Mo-Nd exchange were actually closer to $-2.7$ K, the computed flux would track the Hall data; measuring this exchange directly, for instance through the field dependence of the Nd magnetic excitation energy, would settle the disagreement.
  • Beyond the paper: the same local-configuration-averaged chirality calculation could be applied to other pyrochlore Hall systems to test whether the chirality mechanism is similarly weak there.
  • Beyond the paper: the two-component Hall decomposition suggests that doping on the Nd site would change the Nd-related Hall term in a predictable way if that term is tied to Nd-moment configurations.
  • Beyond the paper: a field sweep that stabilizes the 'one-in three-out' or 'three-in one-out' Nd configurations should produce a sign change in any chirality contribution, which could be isolated by comparing $\rho_H$ with magnetization data.
Original abstract

Neutron scattering studies have been carried out under the magnetic fields H//[0_11] and H//[001] on a single crystal of Nd2Mo2O7, whose Hall resistivity(rhoH) exhibits quite unusual H- and temperature(T)-dependences. Material parameters such as the single ion anisotropies of the Mo- and Nd- moments and exchange coupling constants among the Mo-Mo, Mo-Nd and Nd-Nd moments, have been determined to reproduce various kinds of experimental data taken as a function of H and T. For example, the neutron Bragg intensities, magnetization curves and the magnetic specific heats have been reproduced by the common parameters. By using the magnetic structure reproduced by these parameters, the spin chirality (chi) of Mo spins or the fictitious magnetic flux Phi proportional to chi has been calculated as a function of H and T by using equation chi=<S1.S2x S3>, where the bracket means the statistical average. (Note that we do not use the equation chi=<S1><S2>x<S3>, because the local nature of the chirality should be correctly considered.) Comparing the calculated results with the observed rhoH, we can conclude that the unusual behavior of rH cannot be understood consistently only by the chirality mechanism.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,642 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.86 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.50 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Neutron scattering studies have been carried out under the magnetic fields H//[0_11] and H//[001] on a single crystal of Nd2Mo2O7, whose Hall resistivity(rhoH) exhibits quite unusual H- and temperature(T)-dependences. Material parameters such as the single ion anisotropies of the Mo- and Nd- moments and exchange coupling constants among the Mo-Mo, Mo-Nd and Nd-Nd moments, have been determined to reproduce various kinds of experimental data taken as a function of H and T. For example, the neutron Bragg intensities, magnetization curves and the magnetic specific heats have been reproduced by the common parameters. By using the magnetic structure reproduced by these parameters, the spin chirality (chi) of Mo spins or the fictitious magnetic flux Phi proportional to chi has been calculated as a function of H and T by using equation chi=<S1.S2x S3>, where the bracket means the statistical average. (Note that we do not use the equation chi=<S1><S2>x<S3>, because the local nature of the chirality should be correctly considered.) Comparing the calculated results with the observed rhoH, we can conclude that the unusual behavior of rH cannot be understood consistently only by the chirality mechanism.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Neutron scattering studies have been carried out under the magnetic fields H//[0_11] and H//[001] on a single crystal of Nd2Mo2O7, whose Hall resistivity(rhoH) exhibits quite unusual H- and temperature(T)-dependences. contribution 0.62 0.94 0.02 asserted 1.00
s1 Material parameters such as the single ion anisotropies of the Mo- and Nd- moments and exchange coupling constants among the Mo-Mo, Mo-Nd and Nd-Nd moments, have been determined to reproduce various kinds of experimental data taken as a function of H and T. method 0.64 0.90 0.03 asserted 1.00
s2 For example, the neutron Bragg intensities, magnetization curves and the magnetic specific heats have been reproduced by the common parameters. result 0.72 0.86 0.02 asserted 1.00
s3 By using the magnetic structure reproduced by these parameters, the spin chirality (chi) of Mo spins or the fictitious magnetic flux Phi proportional to chi has been calculated as a function of H and T by using equation chi=<S1.S2x S3>, where the bracket means the statistical average. method 0.95 0.93 0.03 asserted 0.99
s4 (Note that we do not use the equation chi=<S1><S2>x<S3>, because the local nature of the chirality should be correctly considered.) Comparing the calculated results with the observed rhoH, we can conclude that the unusual behavior of rH cannot be understood consistently only by the chirality mechanism. interpretation 0.91 0.94 0.94 asserted 0.97

What kind of paper the classifier reports this is: empirical study 1.00 · evidence from observation or experiment 0.98.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. Hall resistivity ρH of Nd2Mo2O7 is shown at various temperatures against the magnetic field H applied along [111]. Solid lines show the results of the fittings. Details of the fittings are described in the text. Inset shows the magnetization curves of Nd2Mo2O7 measured under the applied magnetic field along the [111] direction. The Hall resistivity and magnetization data were reported previously by the authors’ group.7,8)
Figure 2. Energy-scan profiles taken at 1.5 K at Q=(0.9,0.9,1.1) and (1.4,1.4,0.6) with the resolution of ∆E=0.052 meV. The solid lines show the results of the fittings. Inset shows the dispersion curve along (h, h, 2-h) in the reciprocal space
Figure 4. The integrated intensities of the magnetic scattering Nd2Mo2O7 at 1.6 K are shown against the magnetic field H (//[001]) for 200, 400, 600 and 240 reflections in (a)-(d), respectively. These data were taken after the zero field cooling (ZFC) by scanning H stepwise up to 5.7 T (H-increase) and then down to zero (H-decrease). Solid lines and arrows in (a)-(d) show the results of the calculation. Details of analysis are described in the text. The magnetic correlation patterns whose probabilities are dominant, are shown for the Mo4- and Nd4- tetrahedra at 1.6K under the magnetic field…
Figure 5. The integrated intensities of the magnetic scattering of Nd
Figure 6. Temperature dependence of the magnetic scattering intensities of the 200 reflection of Nd2Mo2O7 is shown at H=0. The solid line shows the calculated intensity
Figure 7. The Nd-components of the magnetizations (M
Figure 8. (a) Calculated specific heat of the magnetic contribution divided by the temperature, Cmag/T of Nd2Mo2O7 is shown as a function of T under the various magnetic field along H//[001]. Inset shows the observed Cmag/T data of Nd2Mo2O7 (lines) and the C/T data of Nd2Zr2O7 (open circles), respectively. The raw data of C/T shown by the solid circles were reported previously by authors’ group in refs. 23 and data shown by the lines were reported in ref. 24. (b) Calculated specific heat of the magnetic contribution divided by the temperature, Cmag/T of Nd2Mo2O7 is shown as a function of T…
Figure 9. Calculated fictitious magnetic flux components parallel to H contributed from the Mo-moments, // ΦΜο , are shown at 5 K against the magnetic fields H applied along (a) [001], (b) [110] and (c) [111], respectively. The observed data of ρH are shown by the solid circles. 0246 0 2 4 6 8 0 5 10 H (T) T=5K ρ H (10–6 Ωcm) ΦMo (calc.) ρH (exp.) (a) H//[001] // ΦMo (arb. unit) // Nd2Mo2O7 0246 0 2 4 6 0 2 4 6 8 H (T) T=5K ρ H (10–6 Ωcm) ΦMo (calc.) ρH (exp.) (b) H//[110] // ΦMo (arb. unit) // 0246 0 2 4 6 0 2 4 6 8 H (T) T=5K ρ H (10–6 Ωcm) ΦM
Figure 10. The magnetic correlation patterns whose probabilities are dominant, are shown for the Mo4- and Nd4- tetrahedra at 5 K under the magnetic fields along H//[111] for (a)H→0, (b)H~3 T and (c)H=6 T, respectively. The solid arrows indicate the directions of the magnetic moments. The open arrows show the net moment direction of the Nd3+ tetrahedra, which has the “two-in two-out” structure of the Nd-moments. The several different correlation patterns shown in the figures have the almost degenerate energies. Mo (a) H 0 (b) H～3T (c) H=6T Nd H//[111] Mo Mo Nd Nd Nd Nd Nd + ++ ΦMo>0 // ΦM
Figure 11. Calculated // ΦΜο at 1.0 K is plotted against the magnetic fields H applied along (a) [001] and (b) [111], respec tively, together with the observed ρH data11) taken at various temperatures with the magnetic fields up to 15 T
Figure 12. Calculated fictitious magnetic flux component parallel to the [001] direction contributed from the Mo-moments is shown at H=0 as a function T. The ρH data taken under the magnetic field H=0.5 T along the [001] direction are shown by the closed circles. 0 5 10 15 –2 0 2 4 6 –10 0 10 20 30 H (T) ΦMo (arb. unit) T=0.05K T=0.3K T=1.0K ρH (exp.) ΦMo (calc.) ρ H (10–6 Ωcm) Nd2Mo2O7 (H//[001]) // // T=1.0K 0 5 10 15 –10 –5 0 5 –20 –10 0 10 H (T) ΦMo (arb. unit) T=0.05K T=0.3K T=1.0K ρH (exp.) ΦMo (calc.) ρ H (10–6 Ωcm) Nd2Mo2O7 (H//[111]) // // T=1

Showing 11 of the paper's 12 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:cond-mat/0603045 by the authors.

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