Spin-Orbit Effects in Crossed Electric and Magnetic Fields;Γ7Band of Wurtzite-Type Crystals

Abstract

The ${\ensuremath{\Gamma}}_{7}$ conduction band of the wurtzite-type II-VI compounds has a spin-orbit term linear in k. Effects of this spin-orbit term in crossed electric and magnetic fields are investigated on the basis of a one-band formalism. The effective Hamiltonian is solved for four different cases, according to the strength of the crossed electric and magnetic fields: (A) Strong magnetic field and weak electric field---this is essentially the simple band case; (B) weak magnetic field and weak electric field (the coupling between cyclotron motion and spin states via the spin-orbit term plays a dominant role in determining the energy spectrum); (C) strong magnetic field and strong electric field. (The major contribution to the spin-orbit interaction comes from a term representing the influence of transverse drift motion upon spin states. As a result, the spin splitting exhibits a nearly linear dependence on the electric field, and the direction of the spin axis tends toward that of the electric field with increasing electric field); (D) weak magnetic field and strong electric field [both of the spin-orbit effects, which are predominant either in the case (B) or in the case (C), are equally important, and perturbation theory is not applicable. Variational solutions have amplitudes distributed over many Landau and spin states, so that the selection rule for the intraband transitions is relaxed.] The conditions for observing these spin-orbit effects by means of intraband transitions are discussed for the actual II-VI compounds. It is found that spin-orbit effects may possibly be observed in magnetic dipole transitions under the condition of case C for CdS and ZnS, as well as in electric and magnetic dipole transitions under the condition of case A or C for CdSe. In the strong electric field of case C, the transverse drift velocity is one or two orders of magnitude larger than the velocity of sound in the crystal. Hence, phonon clouds build up around an electron to cause broadening of the resonance line. This can be avoided by carrying out the resonance experiment before the phonon clouds build up, i.e., by employing a pulsed transverse electric field.