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

The magnetic-field dependence of the magnetoconductivity due to quantum int erferences of isotropic three-dimensional samples in the strongly localized regime is investigated at high frequencies. To this end the three-site mod el is used. The investigation shows that the magnetoconductivity at high fr equencies is anisotropic, that is; it depends on the direction between the electric and the magnetic field. A simple relationship between the transver se part of the magnetoconductivity and the parallel part of the magnetocond uctivity for all magnetic fields is obtained. The magnetoconductivity for c rossed electric and magnetic fields is always larger than for parallel magn etic and electric fields. As a function of the magnetic held the magnetocon ductivity is a quadratic function with respect to the magnetic held for sma ll magnetic fields, a linear function for moderate fields and saturates at high fields. As a function of frequency the magnetoconductivity increases w ith decreasing frequency at frequencies which are low, but in the range of applicability of the three-site model. At very high frequencies the magneto conductivity passes into a plateau. On the plateau the magnetoconductivity becomes independent of frequency.