Linear magnetoresistance due to sample thickness variations: Applications to aluminum

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Abstract
A model of transverse magnetoresistance (MR) in metals due to sample-thickness variations is presented. It predicts larger magnetoresistance then do previous models. The model is applied to magnetoresistance data on well annealed, polycrystalline aluminum plates which are wedge shaped, or which contain surface defects such as steps, grooves, or projections. For wedge-shaped samples or samples containing a surface step, the model predicts magnetically induced voltages which differ on opposite sides of the sample, and which are not strictly linear in magnetic field strength B. Both phenomena occur with the predicted magnitudes. For grooves or projections which extend completely across the width of the sample, the model predicts a MR which is linear in B (LMR) and directly proportional to both the groove (projection) depth (height) and the sample width. The data are found to be in quantitative agreement with prediction. The prediction and observation of a very large LMR for large surface defects provides at least a partial resolution of a disagreement in the literature concerning the magnitude of LMR in single-crystal Al samples when B is directed along the [110] crystallographic axis. Thermal magnetoresistance measurements are shown to be consistent with the electrical measurements. Measurements are also reported on (i) the angular variation of MR when B is rotated away from the perpendicular to the sample surface; (ii) MR for surface defects which extend only part way across the sample; and (iii) MR for surface defects in unannealed Al plates.