The influence of magnetic breakdown on the high field magnetoresistance of aluminium

Abstract

The transverse magnetoresistance, pxx, of an aluminium single crystal has been measured at 4·2°K in fields in the [001] direction up to 60 koe. Above 20 koe it is observed to undergo large oscillations, periodic in reciprocal field, with a frequency of 4·59 × 10⁵ oe. The oscillations are superimposed on a background whose slope increases with field. The Hall component of resistance, pyx, is found to be proportional to field and not to oscillate, and the longitudinal magnetoresistance, pzz, does not saturate and undergoes small oscillations. The cause of the behaviour of pxx and pyx is shown to be magnetic breakdown, which allows holes to change from one orbit to another in an adjacent Brillouin zone using a third zone part of the Fermi surface as a bridge. This mechanism alters the effective paths of the electrons and leads to a higher resistance than would obtain if only simply closed orbits were possible. The resistance oscillations are a consequence of the field dependence of the probability of breakdown between hole orbits, which itself oscillates with the de Haas–van Alphen frequency appropriate to the connecting orbit. From a simple model, based on the band structure of aluminium, values are calculated for pxx and pyx which agree tolerably well with the experimental results.