The change of resistance of gold crystals at very low temperatures in a magnetic field and supra-conductivity

In a paper published last year the author described a systematic research on the change of resistance which occurs in a number of metals in strong magnetic fields. As a result of these investigations the following formulæ expressing the relative change of resistance ∆R/Ro with the field H were found to hold :— ∆R/Ro = β' H2 /3Hk H ≼ Hk , (1) and ∆R/Ro = β' ( H-Hk +Hk 2 /3H) H ≽ Hk , (2) where β' and Hk are constant for a given sample of a metal and at a given temperature. These two expressions form a continuous curve, and it is evident that the formula (1) which holds for the weaker fields, shows that the resistance increases as the square of H, and formula (2) indicates that the change of resistance in strong fields approaches a linear law. These two formulæ have been obtained mathematically on the following assumption. It is known that in a metal which is not in a perfect crystalline state, and which contains even small traces of impurities, there exists a disturbance which increases its specific resistance. My hypothesis was that a magnetic field increases the specific resistance in a similar way to these imperfections, so that they are equivalent to an internal magnetic field Hk , orientated at random. Then, if the metal is brought under the influence of an outside magnetic field H, the increase of resistance is such as would be produced by a combination of the two fields. Further, I assumed that the increase of resistance is proportional to the magnetic field, and this led to formulæ (1) and (2) which appear to fit all my experimental results very well. Several important consequences follow from this hypothesis.