Morphic effects — III. Effects of an external magnetic field on the long wavelength optical phonons

Abstract

The changes in the frequencies of the k ≈ 0 optical vibration modes on the application of a static, external magnetic field to a non-magnetic crystal are determined to first order in the field strength. Second order effects are equivalent to the effects of an electric field in second order and they are not considered here. It is shown that the frequency of a nondegenerate mode is not altered to first order in the magnetic field. In the case of the noncubic crystal structures it is found that the magnetic field must have a component along the axis of highest symmetry in order that the doubly degenerate modes at k ≈ 0 have their degeneracy lifted. In the case of the cubic structures a magnetic field applied in any direction can completely split the degeneracy of modes which are triply degenerate at k ≈ 0. Expressions are given for the field induced changes in the normal mode frequencies. The modes whose frequencies are shifted are found to be right or left circularly polarized. A brief discussion is given of spatial dispersion effects, that is, splitting of the mode degeneracy linear in the phonon wave-vector. Finally, a review of the symmetry aspects of acoustical activity and Faraday effects of acoustical phonons is presented.