Spin-torque ac impedance in magnetic tunnel junctions

Subjecting a magnetic tunnel junction (MTJ) to a spin-transfer torque and/or electric voltage-induced magnetic anisotropy induces magnetic precession, which can reciprocally pump current through the circuit. This results in an ac impedance, which is sensitive to the magnetic field applied to the MTJ. Measurement of this impedance can be used to characterize the nature of the coupling between the magnetic free layer and the electric input as well as a readout of the magnetic configuration of the MTJ.

Figure 1

Schematics of a magnetic tunnel junction subjected to a magnetic field, as part of an ac circuit that drives magnetic precession by (a) VCMA or (b) Slonczewski torque, and the equivalent circuit diagrams (below) showing the additional impedance due to pumping by magnetic dynamics.

Figure 2

Relative change in impedance as a result of VCMA (black solid) or Slonczewski torque (red dashed) as a function of MgO spacer thickness, evaluated at ${\overline{m}}_x=0.73$ and ${\overline{m}}_x=0$, respectively. The kinks near $d\approx 2$ nm correspond to the crossover at $\sigma \sim {\omega }_{0}C$.

Figure 3

Relative change in impedance as a result of VCMA [solid (black) line] or Slonczewski torque [dashed (red) line] as a function of ${\overline{m}}_x$ at the MgO spacer thicknesses $d=2$ nm and $d=0.5$ nm, respectively. The voltage is assumed to be applied at the frequency of ferromagnetic resonance, ${\omega }_0$, which depends on ${\overline{m}}_x$.