Effects of magnetic fields on the Datta-Das spin field-effect transistor

A Datta-Das spin field-effect transistor is built of a heterostructure with a Rashba spin-orbit interaction (SOI) at the interface (or quantum well) separating two possibly magnetized reservoirs. The particle and spin currents between the two reservoirs are driven by chemical potentials that are (possibly) different for each spin direction. These currents are also tuned by varying the strength of the SOI, which changes the amount of the rotation of the spins of electrons crossing the heterostructure. Here we investigate the dependence of these currents on additional Zeeman fields on the heterostructure and on variations of the reservoir magnetizations. In contrast to the particle current, the spin currents are not necessarily conserved; an additional spin polarization is injected into the reservoirs. If a reservoir has a finite (equilibrium) magnetization, then we surprisingly find that the spin current into that reservoir can only have spins which are parallel to the reservoir magnetization, independent of all the other fields. This spin current can be enhanced by increasing the magnetization of the other reservoir, and can also be tuned by the SOI and the various magnetic fields. When only one reservoir is magnetized then the spin current into the other reservoir has arbitrary tunable size and direction. In particular, this spin current changes as the magnetization of the other reservoir is rotated. The optimal conditions for accumulating spin polarization on an unpolarized reservoir are to either apply a Zeeman field in addition to the SOI, or to polarize the other reservoir.

Figure 1

The model: Two spin-polarized reservoirs, denoted by $L$ and $R$, have spin polarizations along the unit vectors ${\widehat{\mathbf{n}}}_L^{}$ and ${\widehat{\mathbf{n}}}_R^{}$ (indicated by the thick arrows). The reservoirs are connected via a weak link, represented by a one-dimensional wire (grey line), which points along the unit vector $\widehat{\mathbf{s}}$. The unit vector ${\widehat{\mathbf{b}}}_{\mathrm{so}}$ denotes the direction of an effective magnetic field induced by the spin-orbit interaction on the wire. An external magnetic field $\mathbf{B}=B\widehat{\mathbf{b}}$ is also applied on the wire.

Figure 2

Conductance coefficients (in units of $\gamma =4\pi J^2{\mathcal{N}}_L^0{\mathcal{N}}_R^0$) versus the strength $q_{\mathrm{so}}^{}$ of the spin-orbit coupling (in units of $1/s)$, or the length of the link $s$ (in units of $1/q_{\mathrm{so}}^{}$) for unpolarized leads. The three lines are for $m^{*}aBs=0.1,0.5,1$ (blue, red, black, with increasing dashes). (a) $G_0^{}\left(B\right)$, Eq. (34); (b) ${\mathbf{G}}_L^{}·\widehat{\mathbf{b}}$ and (c) ${\mathbf{G}}_L^{}·\widehat{\mathbf{s}}$, Eq. (36).

Figure 3

The magnetization conductance ${\mathbf{G}}_L^{}$ (in units of $\gamma$) injected into the left unpolarized lead ($p_L^{}=0$) due to a full polarization of the right lead ($p_R^{}=1$), for different values of the SOI and the Zeeman energy on the link, with ${\widehat{\mathbf{n}}}_R^{}=\widehat{\mathbf{b}}$. The arrows are all in the $\widehat{\mathbf{b}}-\widehat{\mathbf{s}}$ plane.