Nonlinear interaction of spin and charge currents in graphene

We describe a nonlinear interaction between charge currents and spin currents which arises from the energy dependence of the conductivity. This allows nonmagnetic contacts to be used for measuring and controlling spin signals. We choose graphene as a model system to study these effects and predict its magnitudes in nonlocal spin valve devices. The ambipolar behavior of graphene is used to demonstrate amplification of spin accumulation in p-n junctions by applying a charge current through nonmagnetic contacts.

Figure 1

Generation of a nonlocal charge voltage $V_{\text{nl}}=-{\mu }_{\text{avg}}/e$ by spin injection in graphene. (a) Profiles of ${\mu }_{\text{avg}}$ and $\Delta \mu$ created by a spin current. The linear ohmic drop due to $I_1$ on the right-hand side of the circuit has been subtracted from ${\mu }_{\text{avg}}$ for the sake of clarity. (b) Charge carrier density dependence of the nonlocal potential 1 $\mu$m away from the injector. The inset shows $V_{\text{nl}}$ measured by a nonmagnetic contact vs $I_1$. Dashed curves correspond to injection of pure spin current $P{I}_1$ without a charge current, whereas solid curves are for considering the effect of a charge current $I_1$ in the right-hand side of the circuit.

Figure 2

Effect of charge current on spin accumulation $\Delta \mu$. (a) Profile of $\Delta \mu$ due to its interaction with $I_1$ on the right-hand side of the circuit. Inset: Nonlinearity of the nonlocal $\Delta \mu$, $1\mu$m away from the injector. (b) Redistribution of $\Delta \mu$ caused by a current $I_2$ via a nonmagnetic contact.

Figure 3

Change in spin accumulation $\Delta \mu$ profile in a graphene p-n junction due to a charge current $I_2$ (assuming pure spin current injection $P{I}_1$). Inset: Amplification of $\Delta \mu$ at the junction (under the magnetic contact) due to $I_2$.