Influence of spin-orbit interaction within the insulating barrier on the electron transport in magnetic tunnel junctions

We present a theory of the anisotropy of tunneling magnetoresistance (ATMR) phenomenon in magnetic tunnel junctions (MTJs) attributed to Rashba spin-orbit interaction in the insulating barrier. ATMR represents the difference of tunnel magnetoresistance (TMR) amplitude measured with in-plane and out-of-plane magnetic configurations. It is demonstrated that within the spin-polarized free-electron model the change of conductance associated with the ATMR is exactly twice the change of conductance measured at full saturation (i.e., in parallel configuration of magnetizations) between in-plane and out-of-plane configuration, i.e., the tunneling anisotropic magnetoresistance (TAMR). Both ATMR and TAMR are closely related to the TMR amplitude and spin-orbit constant. The predicted ATMR phenomenon is confirmed experimentally, showing a few percent value in the case of the widely studied CoFeB/MgO/CoFeB based MTJ.

Figure 1

Sandwich structure. 1 and 3, ferromagnetic layers; 2, insulator. Averaged spin ${\langle {\widehat{S}}_d\rangle }_1$ is collinear (P or AP) to the ${\langle {\widehat{S}}_d\rangle }_3$.

Figure 2

The dependence of the absolute TAMR $(J_{\theta =\pi /2}-J_{\theta =0})$ at a given voltage $V=0.5$ V on the value of Rashba constant $\alpha$. For $\theta =\pi /2$, the direction of magnetization is perpendicular to the current (in-plane magnetization) and for $\theta =0$ it is parallel to the current (out-of-plane magnetization). The upper half of the figure corresponds to the configuration with parallel directions of magnetizations of F electrodes (magnetic configurations shown in top inset) and the lower half corresponds to the antiparallel one (magnetic configurations shown in bottom inset). The curves are given for different values of $k_F^{\downarrow }$ (${\AA }^{-1}$) and fixed $k_F^{\uparrow }=1{\AA }^{-1}, q_0=1{\AA }^{-1}, d=7\AA$. The values of constant $\alpha$ are given in Table I of [4]. They vary in the interval $0.01–1$.

Figure 3

Normalized magnetization vs field. (a) Field applied in plane ($x$ direction). (b) Field applied out of plane ($z$ direction). The vertical lines indicate the corresponding maximum field available in the CIPTMR experimental setups.

Figure 4

$R_{\mathrm{CIPTMR}}$ vs field. (a) Field applied in plane ($x$ direction). (b) Field applied out of plane ($z$ direction). Inset: Conductance (inverse of $R_{\mathrm{CIPTMR}}$) vs the reduced component of the rotating magnetization along the applied field direction. The red line represents a linear fit of the experimental variation.

Figure 5

(a) Toy model as in Fig. 1 of Ref. [26] for the CIPTMR experiment. (b) Spatial variation of the voltage in the top electrode $V_T\left(\xi \right)$ and in the bottom electrode $V_B\left(\xi \right), \xi$ being the in-plane coordinate between the two electrical contacts. The voltage drop across the barrier to which the Rashba coefficient is proportional is represented by the vertical separation $V_T\left(\xi \right)-V_B\left(\xi \right)$.