Anisotropy of thegFactor of the Free Hole in Ge and Conduction-Band Spin-Orbit Splitting

We report a significant anisotropy of the $g$ factor of the free hole in uniaxially stressed Ge which represents the first observation in any band structure of the $q$ term postulated by Luttinger in the valence-band Hamiltonian. It is shown that this effect arises from the spin-orbit splitting $\Delta \left(\Gamma _{15}^{}{}_{}{}^{-}\right)$ of the nearby $\Gamma _{15}^{}{}_{}{}^{-}$ conduction band. The measurements yield the value $\Delta \left(\Gamma _{15}^{}{}_{}{}^{-}\right)=0.15\mathrm{}\pm 0.03$ eV.