Anomalous Low-Field Hall Coefficient in Bismuth

The anomalous low-field Hall coefficient is Palmer H. Craig's 1926 claim that the Hall coefficient of thin bismuth films rises sharply as the magnetic field falls below about 0.3 gauss. It is the central physical claim of the dossier and the one directly contradicted by C. W. Heaps in 1927.

Craig's reported values

Craig measured the Hall effect in bismuth for fields between 0.07 and 1.00 gauss and reported -R ≈ 171 at 0.07 gauss, falling to about 12–13 by 0.3–1.0 gauss, about 11 at 15 gauss, and rising again to 29 at 4220 gauss. Each Table I value is reported as an average of about twelve readings, with reproducibility to roughly 0.1 µV. Craig's paper itself suggested that "certain modifications or explanations will have to be introduced into the theory of the Hall effect" to account for the low-field changes.

Heaps's null result

Heaps measured a bismuth plate of 0.011 × 0.9 × 2.0 cm over 0.07–2.40 gauss and obtained an average R of 11.5, with variations with field smaller than experimental error — against Craig's reported factor-of-ten rise. At larger fields Heaps found R falling from 13.5 at 650 gauss to 5.9 at 8600 gauss. He concluded Craig's data were erroneous, probably from insulation leakage or uncompensated thermomagnetic effects.

Error mechanisms proposed

• Insulation leakage. Craig grounded his potentiometer to increase stability; Heaps reads this as evidence of variable-resistance leaks.
• Uncompensated thermomagnetic effects. Craig did not report reversing the magnetic field to average out thermal effects, and measured Thomson and allied potentials only at the instant the longitudinal current was broken.

The recommended control is to reverse the magnetic field and average, since the Hall emf reverses with the field while thermal effects do not.

Later low-field work

A 2021 preprint by Camargo and colleagues reports a hysteretic, ferromagnetic-like anomalous Hall signal in bismuth crystals below 30 mT (300 gauss) at 2–10 K, which it attributes to surfaces and grain boundaries. The field range, temperatures and samples are all far from Craig's 0.07–0.3 gauss thin films, so the paper neither confirms nor refutes his values: Camargo and Colleagues, 2021: A Ferromagnetic-Like Anomalous Hall Signal in Bismuth Crystals Below 30 mT.

A 2024 McGill preprint reports an anomalous Hall signal in a 68 nm exfoliated bismuth flake that does not change between 15 mK and 300 K, measured in fields up to ±30 T. It also concerns a regime far from Craig's sub-gauss fields and does not cite him: Yu and Colleagues, 2024: A Temperature-Independent Anomalous Hall Signal in a 68 nm Bismuth Flake.

See also

Hall Effect, C. W. Heaps, comparisons/comparison-craig-hall-effect-claims-vs-evidence.