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We investigate the intrinsic spin relaxation of conduction electrons ingermanium due to electron-phonon scattering. We derive intravalley andintervalley spin-flip matrix elements for a general spin orientation andquantify the resulting anisotropy in spin relaxation. The form of theintravalley spin-flip matrix element is derived from the eigenstates of acompact spin-dependent $\mathbf{k}$$\cdot$$\mathbf{p}$ Hamiltonian in thevicinity of the $L$ point (where thermal electrons are populated in Ge). Spinlifetimes from analytical integrations of the intravalley and intervalleymatrix elements show excellent agreement with independent results fromelaborate numerical methods.

Intrinsic Spin Lifetime of Conduction Electrons in Germanium