In the 1920s Palmer H. Craig argued that thin bismuth behaves strangely in a magnetic field. Physicists have kept finding odd Hall behaviour in bismuth since then, and a 2024 preprint from McGill University in Montréal adds a recent example. "Observation of Temperature Independent Anomalous Hall Effect in Thin Bismuth from Near Absolute Zero to 300 K Temperature" is by Oulin Yu, F. Boivin, A. Silberztein and G. Gervais. It was posted to arXiv as 2406.12134v1 in June 2024. It reports an extra Hall signal in a very thin bismuth flake that stays the same from 15 mK up to room temperature.
The paper does not cite Craig or C. W. Heaps, and it works at magnetic fields roughly a million times stronger than the ones in Craig's dispute. It belongs in this dossier as part of bismuth's later scientific reputation. It is not evidence about Craig's measurements or his device.
What the paper claims
In the ordinary Hall Effect, the sideways voltage grows in proportion to the applied field. An anomalous Hall effect (AHE) is an additional contribution, usually associated with magnetic materials. In this paper it appears as a Hall resistance that jumps near zero field and then levels off. The authors report three main findings:
- An AHE in pure bismuth. Bismuth is diamagnetic, meaning it is weakly repelled by magnetic fields, so it is not expected to show this effect.
- No change with temperature. The anomalous signal was the same at every temperature measured. The authors say they know of no other material whose Hall transport is so insensitive to temperature over such a wide range.
- No magnetoresistance. The ordinary resistance of the device did not change with field anywhere between −30 T and +30 T. The paper calls this "particularly puzzling" because semi-metals like bismuth usually show resistance that grows with the square of the field.
How the device was made and measured
Bismuth's layers are strongly bonded to each other, so thin crystals can't easily be peeled off with tape the way graphite flakes can. The group used a method it had developed earlier. A bismuth crystal of 99.9% purity was mounted on a metal pen and scraped across a silicon dioxide surface patterned with micro-trenches, inside a nitrogen glovebox to prevent oxidation. A flake was given titanium/gold contacts and coated with PMMA, a protective plastic layer. The authors report that Raman spectroscopy showed no bismuth oxide and no ageing for more than two years after fabrication.
Atomic force microscopy gave the flake an average thickness of 68 ± 47 nm. The large uncertainty comes from the flake's wedge shape. The supplement says the AHE also appeared in two other devices, 29 ± 19 nm and 69 ± 20 nm thick, which were reported in an earlier paper by the same group.
The flake was too small for an ideal four-corner contact layout, so the Hall and ordinary resistances were mixed together in every reading. The authors separated them using Onsager reciprocity, a principle that lets a Hall component be extracted by swapping the current and voltage leads and comparing the two measurements. The main data were taken in a resistive magnet at the National High Magnetic Field Laboratory at 1.4, 40, 80, 160, 240 and 300 K, all in a single cooldown. A dilution refrigerator run down to 15 mK, at fields up to ±9 T, is cited from the earlier report as showing the same behaviour.
What was measured
At 1.4 K the authors fitted straight lines to the Hall data above 2 T and extrapolated them back to zero field. This gave an anomalous Hall resistance of 0.146(2) Ω and an ordinary Hall coefficient of 0.00106(13) Ω T⁻¹. At fields below 2 T, the Hall curves for all six temperatures lie on top of each other. The zero-field resistance did rise with temperature, which the paper says fits bismuth's semi-metallic character.
How the authors interpret it
The paper describes three standard sources of the AHE. Two of them, skew scattering and side jump, depend on impurities and should change with temperature. The third, the intrinsic contribution, comes from a property of the electron bands called Berry curvature and should not change with temperature. The authors tested two scaling relations against their data. They report that the relation for conductivity fits and the relation for resistivity does not, and they read this as further support for an intrinsic origin.
Berry curvature can only be non-zero where either time-reversal symmetry or inversion symmetry is broken. Bismuth's lack of magnetism means time-reversal symmetry is not broken. The paper notes that inversion symmetry, although present in the bulk, is broken at the crystal surface, and it cites calculations finding non-zero Berry curvature on bismuth surfaces. The authors present this surface Berry curvature only as a possible explanation. They speculate that bismuth might be a place to look for a quantised version of the effect.
What the evidence does and does not show
The authors are open about the gaps in their account:
- They say they know of no model that explains the Hall signal and the field-independent resistance together. A multi-carrier model would require an unreasonably small Hall coefficient or would predict magnetoresistance that was not seen.
- Because of the device's irregular shape, they could not confidently convert resistances into resistivities. The scaling test therefore used data normalised to the 300 K values.
- The error bars on the temperature comparison come mostly from an angle uncertainty of about 5° between the field and the sample.
- The detailed results come from a single flake measured by one group, in a preprint.
On the other hand, the paper points to other reports that agree with it. A 1988 study of MBE-grown films by Partin and colleagues showed, in the authors' reading, a similar Hall response with no field dependence in the resistance up to 17 T. The paper says those authors did not notice it. It also cites Conn and Donovan's bismuth-fibre work from the 1940s and the bulk-crystal result described in Camargo and Colleagues, 2021: A Ferromagnetic-Like Anomalous Hall Signal in Bismuth Crystals Below 30 mT. Its conclusion is that the AHE in elemental bismuth is genuine but that its mechanism remains unclear.
How it relates to Craig
The two cases do not overlap much. Craig's disputed rise in the Hall coefficient (see Anomalous Low-Field Hall Coefficient in Bismuth) occurred between 0.07 and 0.3 gauss in a sprayed film 0.012 cm thick (see Thin Bismuth Film Preparation). The McGill "low-field" region is below 2 T, or 20,000 gauss, and the sample is an exfoliated single-crystal flake about 68 nm thick. The paper therefore does not support Craig's numbers or Heaps's rebuttal. Nothing in it concerns rectification or power generation either. What it does show is that bismuth's Hall behaviour was still producing unexplained results nearly a century after Craig.
References
- O. Yu, F. Boivin, A. Silberztein, G. Gervais, "Observation of Temperature Independent Anomalous Hall Effect in Thin Bismuth from Near Absolute Zero to 300 K Temperature," arXiv:2406.12134v1 [cond-mat.mes-hall], June 2024. https://arxiv.org/pdf/2406.12134
- O. Yu et al., "Anomalous Hall effect in thin bismuth," Phys. Rev. B 109, L121406 (2024), as cited in the paper.
- D. L. Partin et al., "Growth and characterization of epitaxial bismuth films," Phys. Rev. B 38, 3818 (1988), as cited in the paper.
Source notes & attribution
- https://arxiv.org/pdf/2406.12134