Spin-transfer dynamics in MgO-based magnetic tunnel junctions with an out-of-plane magnetized free layer and an in-plane polarizer

TL;DR

This paper develops an analytical and numerical model for magnetization dynamics in MgO-based spin-torque nano-oscillators with specific magnetic layer orientations, highlighting the impact of bias-dependent tunnel magnetoresistance on oscillator behavior.

Contribution

It introduces a comprehensive model incorporating spin-transfer torque asymmetry and bias-dependent tunnel magnetoresistance, advancing understanding of out-of-plane free layer dynamics in MgO-based junctions.

Findings

Bias dependence significantly affects phase diagram and critical current.

Oscillations are quenched at high currents due to bias effects.

Model aligns well with experimental data.

Abstract

Here, we present an analytical and numerical model describing the magnetization dynamics in MgO-based spin-torque nano-oscillators with an in-plane magnetized polarizer and an out-of-plane free layer. We introduce the spin-transfer torque asymmetry by considering the cosine angular dependence of the resistance between the two magnetic layers in the stack. For the analytical solution, dynamics are determined by assuming a circular precession trajectory around the direction perpendicular to the plane, as set by the effective field, and calculating the energy integral over a single precession period. In a more realistic approach, we include the bias dependence of the tunnel magnetoresistance, which is assumed empirically to be a piecewise linear function of the applied voltage. The dynamical states are found by solving the stability condition for the Jacobian matrix for out-of-plane static states. We find that the bias dependence of the tunnel magnetoresistance, which is an inseparable effect in every tunnel junction, exhibits drastic impact on the spin-torque nano-oscillator phase diagram, mainly by increasing the critical current for dynamics and quenching the oscillations at high currents. The results are in good agreement with our experimental data published elsewhere.