Oscillatory Hall effect in tin due to magnetic breakdown

Abstract

The Hall effect in single crystals of tin shows oscillations at temperatures below 4.2 K when B lies along, or very near, the [001] axis. The amplitude of the oscillations has a sharp maximum 1° away from the axis and has vanished by 4°. The oscillations are explained in terms of the migration of electrons by magnetic breakdown between the e 5 1 and δ 1 1 orbits, as has already been invoked to account for oscillatory magneto-resistance. To account for the existence of off-axis Hall oscillations when, as is known, breakdown is confined to a fairly narrow central zone, it is found necessary to include collisions of the electrons with impurities even though these are rare enough for ω c т to be as large as 200. The theory is developed in terms of diffusion of electrons on a limited orbit-network, and an explicit expression derived for the angular variation of oscillatory amplitude, which is found to agree well when independent estimates of the relevant parameters are used.