Unified weak-field magnetoresistance phenomenology for (111)-oriented thin films and surface layers with cubic, trigonal, and hexagonal symmetries

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Abstract
The Seitz-Pearson-Suhl formalism for weak-field magnetoresistance (WFMR) in cubically symmetric crystals is generalized to apply to (111)-oriented thin films and surface layers having cubic, trigonal, or hexagonal symmetry, including the limiting case of two-dimensional conductivity in quantized systems. Compact, four-parameter WFMR expressions are presented which apply to any sample-current direction in the (111) plane, and to three mutually orthogonal planes of rotation of the magnetic field. The common notation used makes it easy to identify the similarities and differences in the WFMR behavior for the three kinds of symmetry. The results demonstrate that four distinct WFMR measurements may always be made on a single sample, so that it is possible to distinguish one symmetry from another in a convenient and reliable manner. These measurements can be used as a sensitive detector of crystalline anisotropy resulting from substrate strain. Their application to such position-dependent anisotropies as band-bending effects and surface scattering is also considered.