Tunnel-barrier-enhanced dc voltage signals induced by magnetization dynamics in magnetic tunnel junctions

We theoretically study the recently observed tunnel-barrier-enhanced dc voltage signals generated by magnetization precession in magnetic tunnel junctions. While the spin pumping is suppressed by the high tunneling impedance, two complementary processes are predicted to result in a sizable voltage generation in ferromagnet $\left(\text{F}\right)\left|\text{insulator}\left(\text{I}\right)\right|\text{normal}\text{metal}\left(\text{N}\right)$ and $\text{F}\left|\text{I}\right|\text{F}$ junctions with one ferromagnet being resonantly excited. Magnetic dynamics in $\text{F}\left|\text{I}\right|\text{F}$ systems induce a robust charge pumping, translating into voltage in open circuits. In addition, dynamics in a single ferromagnetic layer develop longitudinal spin accumulation inside the ferromagnet. A tunnel barrier then acts as a nonintrusive probe that converts the spin accumulation into a measurable voltage. Neither of the proposed mechanisms suffers from spin relaxation, which is typically fast on the scale of the exponentially slow tunneling rates. The longitudinal spin-accumulation buildup, however, is very sensitive to the phenomenological ingredients of the spin-relaxation picture.

Figure 1

(Color online) Voltage generated in an ${\text{F}}_L\left|\text{I}\right|{\text{F}}_R$ junction by magnetically induced charge pumping $I_c$. In the absence of spin relaxation, magnetic precession builds up a spin imbalance of $\hslash \omega$ in ${\text{F}}_R$ and $\hslash \omega \text{cos}\theta$ in ${\text{F}}_L$ along the respective magnetization directions. As shown in the text, this must necessarily be accompanied by a charge pumping for a finite $\theta$. In a realistic situation where the spin-relaxation rate is much faster than the tunneling injection rate, we can safely neglect the spin-pumping component and calculate the resulting voltage signal $V$ induced by the charge pumping $I_c$ alone.

Figure 2

(Color online) Voltage measured in an $\text{F}\left|\text{I}\right|\text{N}$ junction. In this case, charge pumping across the tunnel barrier vanishes, rendering the mechanism depicted in Fig. 1 ineffective. Depending on the model of spin relaxation in the ferromagnet, however, a tunnel barrier may detect a voltage signal due to the nonequilibrium spin buildup inside the precessing magnet. According to Eqs. (10, 11), the corresponding spin accumulation may, under the most favorable circumstances, be at most $\mu \sim \hslash \omega \text{cos}\theta$ in the case of magnetic impurities adiabatically following the magnetization precession. This spin accumulation is measurable (Ref. 13) by the tunnel barrier with the conductance polarization $P$ as a voltage $P\mu /2$. The normal metal on the left mimics an ohmic contact, which sets the reference potential at the spin-averaged electrochemical potential of the ferromagnet. Also schematically plotted on the left is the spin-diffusion profile of the spin-dependent electrochemical potential.