Alfvén-wave oscillations in a sphere, with applications to electron-hole drops in Ge

The problem of Alfven-wave oscillations in an anisotropic sphere is studied, and two solutions are presented. One solution is exact, involving an expansion of the current inside the sphere in a series of orthonormal modes. The second is approximate, based on a perturbation expansion of the induced fields and currents in powers of the sphere radius. The approximate solution can be applied to a material having a completely general conductivity tensor, while the exact solution is restricted to situations of high symmetry. As an illustration of these solutions, the resonant power absorption by electron-hole droplets in Ge is calculated explicitly. Size-dependent resonances, for which the resonant field increases with the drop radius, have been observed experimentally. The present calculation shows that such resonances occur both in the magnetic- and electric-dipole absorption, with the magnetic-dipole absorption being most intense for the drop sizes and frequencies under consideration, particularly for small drops. From the approximate solution, it is found that certain of the resonances can have a very strong dependence on the orientation of the magnetic field with respect to the crystal axes, similar to cyclotron resonance of an electron in Ge. As a second application of these results, the transition from Alfven waves (in a material having equal numbers of electrons and holes) to helicon waves (only one-carrier type) is studied, using the approximate solution only. The 'elimination' of one-carrier type can be accomplished by increasing its mass, decreasing its concentration, or increasing its collision rate. The Alfven-to-helicon transitions are quite different in each of these three cases, and examples of intermediate states are presented