Nonlinear spin to charge conversion in mesoscopic structures

Motivated by recent experiments [I. J. Vera-Marun, V. Ranjan, and B. J. van Wees, Nat. Phys. 8, 313 (2012)], we formulate a nonlinear theory of spin transport in quantum coherent conductors. We show how a mesoscopic constriction with energy-dependent transmission can convert a spin current injected by a spin accumulation into an electric signal, relying neither on magnetic nor exchange fields. When the transmission through the constriction is spin independent, the spin-charge coupling is nonlinear, with an electric signal that is quadratic in the accumulation. We estimate that gated mesoscopic constrictions have a sensitivity that allows to detect accumulations much smaller than a percent of the Fermi energy.

Figure 1

Measurement scheme: A mesoscopic constriction separates two nonmagnetic terminals with spin accumulations $\delta {\mu }_{s1,2}$. The transmission coefficient through the constriction is gate tunable (voltage $V_g$), and when it is energy dependent, an electric signal that is nonlinear in $\delta {\mu }_{s1,2}$ arises.

Figure 2

(a) Nonlinear conductance $G_2$ given in Eq. (8b). (b)–(d) Current, Eq. (7) for zero bias, $\delta V=0$, as a function of (b) gate voltage determining the QPC transmission [see Eq. (9)], (c) temperature, and (d) QPC energy resolution in units of the magnetic field.

Figure 3

(a) Linear conductance $G_1$, Eq. (8a). (b) Voltage, calculated according to Eq. (11) (dashed line) and adding a constant 0.1 $e^2/h$ to $G_1$ (solid line). (c) Current in external magnetic field antiparallel (solid line) and parallel (dashed line) to the spin polarization direction. The arrow denotes the zero current position, and the thin line is a guide to the eye. (d) Second derivative of the current with respect to $V$ and $B$.