Anisotropy and frequency dependence of the hopping magnetoresistance in the high-frequency limit in three-dimensional samples

摘要

The magnetic-field dependence of the magnetoconductivity due to quantum interferences of isotropic three-dimensional samples in the strongly localized regime is investigated at high frequencies. To this end the three-site model is used. The investigation shows that the magnetoconductivity at high frequencies is anisotropic, that is; it depends on the direction between the electric and the magnetic field. A simple relationship between the transverse part of the magnetoconductivity and the parallel part of the magnetoconductivity for all magnetic fields is obtained. The magnetoconductivity for crossed electric and magnetic fields is always larger than for parallel magnetic and electric fields. As a function of the magnetic held the magnetoconductivity is a quadratic function with respect to the magnetic held for small magnetic fields, a linear function for moderate fields and saturates at high fields. As a function of frequency the magnetoconductivity increases with decreasing frequency at frequencies which are low, but in the range of applicability of the three-site model. At very high frequencies the magnetoconductivity passes into a plateau. On the plateau the magnetoconductivity becomes independent of frequency. [References: 30]