#### Date of Award

8-1973

#### Degree Type

Thesis

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Physics

#### Supervisor

Dr. W. R. Datars

#### Abstract

The components of the electrical magnetoconductivity and magnetoresistivity tensors of aluminum and indium were calculated by the path-integral method using closed nearly-free electron Fermi surfaces and a uniform relaxation time. The anisotropy of the components is shown to depend primarily on the symmetry of the Fermi surface in relation to the magnetic field axis. The high-field longitudinal magnetoresistance is found to be a minimum for fields along high-symmetry directions, where the mean orbitally averaged longitudinal component of carrier velocity is a minimum. The anisotropy of the transverse magnetoresistance is larger in indium, which is face centered tetragonal, than in face-centered-cubic aluminum. The calculated Hall coefficients of both metals are isotropic in the high-field regime, but show considerable anisotropy for intermediate fields. The longitudinal-transverse components of magnetoresistivity can saturate at values as high as 0.26 of the zero-field resistivity, but the effects of the longitudinal-transverse magnetoconductivity components on the Hall coefficients and magnetoresistance are small. The calculated results are compared with experiment where possible, and are used to fit the induced torque data for aluminum. The theory reproduces the field dependence and anisotropy of the induced torque data. Induced torque experiments in the high-purity aluminum showed no linear magnetoresistance (slope < 10‾³) except for fields within ±3º of <100>. This anomaly was tentatively identified as due to open orbits resulting from magnetic breakdown. Calculations were done which show that the anisotropy of the transverse linear magnetoresistance observed in four-probe experiments cannot be due to an orbital enhancement of the semi-classical transverse conductivity.

The uniform relaxation time path-integral magneto-conductivity was also calculated for Ashcroft's (1963) Fermi surface model of aluminum for a <100> direction. The transverse magnetoresistivity and Hall coefficient were the same as for the nearly-free-electron Fermi surface, but the low-field resistivity and the high-field longitudinal magnetoresistivity were some 50% larger than the nearly-free-electron calculations, and the absolute value of the low-field Hall coefficient was some 20% smaller.

The effects of an anisotropic relaxation time on the calculations were also illustrated. Assuming a different relaxation time for the electron and hole bands was found to explain, qualitatively, the low-field Hall coefficients of indium and aluminum, and their temperature dependences. The effects of neglecting the nearly free electron α arms of indium were also calculated, and it was found that these effects should be separable from the effects of relaxation time anisotropy if the anisotropy as well as the field dependence of the Hall coefficients of a single sample could be measured.

The path-integral method was found to be a powerful, flexible and economical computational method which was capable of generating physically useful insight. When used with a complete Fermi surface (even a nearly-free electron one), and not just some subset of "representative" orbits, the calculations agreed quite well with experiments. The anisotropy of the magnetoresistivity components was found to be of much greater use in testing transport theories than was the field dependence or the values of the galvano-magnetic coefficients.

#### Recommended Citation

Douglas, Robert James, "Anisotropy of Magnetoconductivity of Metals" (1973). *Open Access Dissertations and Theses.* Paper 69.

http://digitalcommons.mcmaster.ca/opendissertations/69