Gyromagnetic ratios of electrons confined in quantum wells in $\mathrm{ZnSe}/{\mathrm{Zn}}_x{\mathrm{Mg}}_{1-x}{\mathrm{S}}_y{\mathrm{Se}}_{1-y}$ heterostructures

The gyromagnetic ratios $(g$ values) of electrons in ZnSe quantum wells with ${\mathrm{Zn}}_x{\mathrm{Mg}}_{1-x}{\mathrm{S}}_y{\mathrm{Se}}_{1-y}$ barriers have been determined by resonance spin-flip Raman scattering as functions of well width and of the direction of the applied magnetic field. These heterostructures provide an excellent test of $\mathbf{k}\cdot \mathbf{p}$ perturbation theories since there is both a large penetration of the electron wave function into the barrier and a considerable difference in the light-hole and heavy-hole confinement energies in the well. The former leads to exposure of the electron to a region in which the spin-orbit coupling is significantly reduced, while the latter introduces a marked anisotropy in the g tensor. The behavior of the g tensor as the well width is decreased is described very well by simple analytic expressions obtained from three-band $\mathbf{k}\cdot \mathbf{p}$ theory, excellent agreement with experiment being obtained with a 10% conduction band offset ratio.