Spin accumulation created electrically in an n-type germanium channel using Schottky tunnel contacts

Using high-quality Fe$_{3}$Si/$n^{+}$-Ge Schottky-tunnel-barrier contacts, we study spin accumulation in an $n$-type germanium ($n$-Ge) channel. In the three- or two-terminal voltage measurements with low bias current conditions at 50 K, Hanle-effect signals are clearly detected only at a forward-biased contact. These are reliable evidence for electrical detection of the spin accumulation created in the $n$-Ge channel. The estimated spin lifetime in $n$-Ge at 50 K is one order of magnitude shorter than those in $n$-Si reported recently. The magnitude of the spin signals cannot be explained by the commonly used spin diffusion model. We discuss a possible origin of the difference between experimental data and theoretical values.Comment: 4 pages, 3 figures, To appear in J. Appl. Phy

Scale Dependence of the Retarded van der Waals Potential

We study the ground state energy for a system of two hydrogen atoms coupled to the quantized Maxwell field in the limit $\alpha \to 0$ together with the relative distance between the atoms increasing as $\alpha^{-\gamma} R$, $\gamma > 0$. In particular we determine explicitly the crossover function from the $R^{-6}$ van der Waals potential to the $R^{-7}$ retarded van der Waals potential, which takes place at scale $\alpha^{-2} R$.Comment: 19 page