Influence of spin-orbit coupling on the transport properties of magnetic tunnel junctions

Using a fully relativistic implementation of the Landauer-Büttiker formalism, the ballistic conductance and magnetoresistance in the $\mathrm{Fe}∕\mathrm{GaAs}∕\mathrm{Fe}$ tunnel junction has been calculated. The underlying electronic structure of the system was obtained using a spin-polarized relativistic version of the screened Korringa-Kohn-Rostoker Green-function method. To analyze the influence of spin-orbit coupling induced spin-flip processes on the spin-dependent transport, a scheme introduced recently by us which allows one to split the relativistic conductance in terms of individual spin-diagonal and spin off-diagonal (spin-flip) components has been applied. Our previous investigations showed that a strong spin-flip channel is present in the conductance, having the most important influence for an antiparallel alignment of the magnetization in the two Fe leads. Motivated by these findings and based on model calculations in which the strength of the spin-orbit interaction has been manipulated we present a detailed analysis of the various features induced by the spin-orbit coupling inside the barrier, and how these modify the tunneling. We found that even in the ideal case of a specular interface the magnetoresistance can significantly drop if the spacer is characterized by a strong spin-orbit coupling.

Figure 1

${\vec{k}}_{\Vert }$-resolved relativistic transmission probability $g\left({\vec{k}}_{\Vert }\right)$, as given by Eq. (9), in $\mathrm{Fe}∕n\left(\mathrm{GaAs}\right)∕\mathrm{Fe}$ along the (110) and (100) directions of the zinc-blende structure, for different numbers of layers $n$. Top: exact SOC calculations. Bottom: SOC switched off on the $2m-1$ Ga and As atoms inside the spacer (see text). Left and right side of each panel correspond, respectively, to a parallel (P) and antiparallel (AP) alignment of the magnetization in the two Fe leads.

Figure 2

Top: energy bands near the $\Gamma$ point obtained using the potentials of the bulklike GaAs middle layers in $\mathrm{Fe}∕\mathrm{GaAs}∕\mathrm{Fe}$ for the complex vector $q_z=k_z+\mathrm{i}{\kappa }_z$. The energy zero corresponds to the Fermi energy of the Fe leads. Bottom: dependence of the imaginary part ${\kappa }_z$ on ${\vec{k}}_{\Vert }$ as deduced from the complex energy bands at the Fermi energy $E_F$ for $k_z=0$. Solid lines: exact relativistic calculations; dashed lines: SOC switched off on As and Ga sites, without recalculating the Fermi energy.

Figure 3

Spin-decomposed terms ${\tilde{g}}^{m_s{m}_s^{\prime }}\left({\vec{k}}_{\Vert }\right)$ of the ${\vec{k}}_{\Vert }$-resolved transmission probability in $\mathrm{Fe}∕n\left(\mathrm{GaAs}\right)∕\mathrm{Fe}$ along the (110) and (100) directions of the zinc-blende structure, as obtained from Eq. (11), for several thicknesses $n$ in the AP alignment. Left and right panel show, respectively, the spin-diagonal, ${\tilde{g}}^{\downarrow \downarrow }\left({\vec{k}}_{\Vert }\right)$, and the spin-flip, ${\tilde{g}}^{\uparrow \downarrow }\left({\vec{k}}_{\Vert }\right)+{\tilde{g}}^{\downarrow \uparrow }\left({\vec{k}}_{\Vert }\right)$, contributions to the conductance. Thick lines: exact SOC calculations; dashed lines: SOC switched off within the $2m-1$ inner GaAs layers, without recalculating the Fermi energy.

Figure 4

Left: tunneling conductance for $\mathrm{Fe}∕n\left(\mathrm{GaAs}\right)∕\mathrm{Fe}$ trilayer system [for parallel (P) and antiparallel (AP) alignment] as a function of GaAs thickness $n$, calculated by means of the relativistic expression, Eq. (8), but with the SOC suppressed within the $2m-1$ inner GaAs layers. Right: The corresponding pessimistic TMR ratio $(g^{\mathrm{P}}-g^{\mathrm{AP}})∕g^{\mathrm{P}}$. The results for full SOC are also plotted (dashed lines) for comparison (see Ref. 14).

Figure 5

Left: tunneling conductance for $\mathrm{Fe}∕41\left(\mathrm{GaAs}\right)∕\mathrm{Fe}$ trilayer system [for parallel (P) and antiparallel (AP) alignment], calculated by means of the relativistic expression, Eq. (8), with the SOC manipulated within the $2m-1[m=(n-7)∕2=17]$ inner GaAs layers, as a function of spin-orbit interaction strength $x$. Right: The corresponding pessimistic TMR ratio $(g^{\mathrm{P}}-g^{\mathrm{AP}})∕g^{\mathrm{P}}$.

Figure 6

${\vec{k}}_{\Vert }$-resolved relativistic transmission probability $g\left({\vec{k}}_{\Vert }\right)$, Eq. (9), in $\mathrm{Fe}∕41\left(\mathrm{GaAs}\right)∕\mathrm{Fe}$ along the (110) and (100) directions of the zinc-blende structure, for several values of the spin-orbit interaction strength $x$, which has been modified on the $2m-1[m=(n-7)∕2=17]$ inner GaAs layers. Left and right side of each panel correspond, respectively, to a parallel (P) and antiparallel (AP) alignment of the magnetization in the two Fe leads.