Intrinsic spin lifetime of conduction electrons in germanium

Abstract

We investigate the intrinsic spin relaxation of conduction electrons in germanium due to electronphonon scattering. We derive intravalley and intervalley spin-flip matrix elements for a general spin orientation and quantify the resulting anisotropy in spin relaxation. The form of the intravalley spinflip matrix element is derived from the eigenstates of a compact spin-dependent k·p Hamiltonian in the vicinity of the L point (where thermal electrons are populated in Ge). Spin lifetimes from analytical integrations of the intravalley and intervalley matrix elements show excellent agreement with independent results from elaborate numerical methods.

Experimental Demonstration of Room-Temperature Spin Transport inn-Type Germanium Epilayers

“…However, due to the spatial inversion and time reversal symmetries of the L point in Ge, the intravalley spin-flip matrix elements for both phononinduced scattering [62] and impurity-induced scattering [63] are very small. Thus, intravalley-induced spin scattering can only be dominant at low temperatures (T < 20 K [62]), rendering intervalley spin scattering as the main spin relaxation mechanism in this work (T < 130 K). Recently, a spin relaxation mechanism by intervalley scattering in the presence of a magnetic field originating from g-factor anisotropy was discovered in Ge [64].…”

“…Spin relaxation due to intervalley electron-phonon scattering is governed by X phonons, which connect the centers of two different L valleys [13]. These phonons have an energy of approximately 30 meV [13,62,65] and obey the Bose-Einstein temperature distribution. It results in a strong exponential behavior of this spin relaxation time around RT [62].…”

“…The spin relaxation time due to intravalley scattering between the lower conduction and upper valence bands follows a T −7=2 dependence [56]. However, due to the spatial inversion and time reversal symmetries of the L point in Ge, the intravalley spin-flip matrix elements for both phononinduced scattering [62] and impurity-induced scattering [63] are very small. Thus, intravalley-induced spin scattering can only be dominant at low temperatures (T < 20 K [62]), rendering intervalley spin scattering as the main spin relaxation mechanism in this work (T < 130 K).…”

“…However, in our case, due to the degenerate doping and ultrafast spinconserving momentum relaxation time at temperatures close to RT, this mechanism is suppressed. Using the amplitude of the external magnetic field B ∼ 0.1 T and an intervalley momentum relaxation time <1 ps [62] in Eq. (4) from Ref.…”

Spin and energy relaxation in germanium studied by spin-polarized direct-gap photoluminescence

“…15 Optical orientation via absorption of circularly polarized photons at the direct energy gap can then be exploited to readily investigate the spin properties of Ge. [16][17][18][19] Noticeably, spin-polarized electrons optically pumped in the Γ valley can conserve their spin during ultrafast scattering to the lower energy L valleys, 14 which are responsible for charge and spin transport. Such mechanism, which is absent in the widely studied III-V semiconductors, makes Ge spin dynamics very rich, but still poorly understood.…”