The methodology used to obtain the values of the spin-orbit couplings from the spin expectation values from perturbation theory was incorrect. As a result Figs. 2 and 3 are incorrect.
The electronic band structure of graphene in the presence of spin-orbit coupling and transverse electric field is investigated from first principles using the linearized augmented plane-wave method. The spin-orbit coupling opens a gap at the $K(K)$-p
oint of the magnitude of 24 $mu$eV (0.28 K). This intrinsic splitting comes 96% from the usually neglected $d$ and higher orbitals. The electric field induces an additional (extrinsic) Bychkov-Rashba-type splitting of 10 $mu$eV (0.11 K) per V/nm, coming from the $sigma$-$pi$ mixing. A mini-ripple configuration with every other atom is shifted out of the sheet by less than 1% differs little from the intrinsic case.
Angular variation of giant magnetoresistance and spin-transfer torque in metallic spin-valve heterostructures is analyzed theoretically in the limit of diffusive transport. It is shown that the spin-transfer torque in asymmetric spin valves can vanis
h in non-collinear magnetic configurations, and such a non-standard behavior of the torque is generally associated with a non-monotonic angular dependence of the giant magnetoresistance, with a global minimum at a non-collinear magnetic configuration.
Spin-transfer torque in asymmetric spin valves can destabilize both parallel and antiparallel configurations and can lead to precessional modes also in the absence of an external magnetic field. We find a bistable precessional regime in such systems
and show that thermal fluctuations can excite transitions (telegraph noise) between the corresponding oscillatory regimes that are well separated by irreversible paths at low temperatures. Because of the thermally induced transitions, the frequency of the resulting current-driven oscillations is different from that obtained at very low temperatures. We also show that the power spectrum in the bistable region is dominated by the out-of-plane oscillatory mode.
