Non-linearities in galvanomagnetic effects in bismuth at low temperatures

Abstract

The magnetoresistance and Hall coefficient of two single crystals of bismuth have been measured at liquid helium temperatures. The purpose of the work was to investigate the non-linearities which had previously been observed in the longitudinal and Hall voltages as a function of current. In addition to continuous current measurements, a pulsed DC technique was used in an attempt to discriminate between the non-linear effects due to heating and a possible intrinsic current dependence of the magnetoresistance and Hall coefficient. The time dependence of both of these galvanomagnetic effects indicates that the rate of heat dissipation from the crystal into the normal helium increases suddenly about 50 rns after the current is applied. For example, at 4.2 K, 15 kG, and 50 mA, the sample temperature first rises to a value 0.2 K above the bath temperature, and then falls to a steady state value 0.06 K above the bath temperature. The resistance using a continuous current correlates with the steady state value of the time dependent resistance. A possible indication of gravitational dependence of the lambda transition was seen. Both above and below the lambda point the results of the low duty cycle pulsed DC measurements indicate the existence of an intrinsic non-ohmic effect when heating is minimized. The change in the resistance is of the order of I part per thousand per mA. In the normal fluid, the total current dependence of the magnetoresistance and the Hall coefficient is expressible as the sum of the intrinsic current dependence and that due to heating.