# Injection locking at fractional frequencies of magnetic tunnel junction (MTJ)-based read sensors' ferromagnetic resonance modes

## TL;DR

This study investigates the nonlinear magnetization dynamics of MTJ-based read sensors, revealing fractional frequency resonances and their dependence on magnetic and spin-torque parameters through NVNA measurements and micromagnetic modeling.

## Contribution

The paper demonstrates the presence of fractional frequency resonances in MTJ sensors and links these to nonlinear spin-torque dynamics, enhancing understanding of sensor behavior.

## Key findings

- Distinct resonances at fractional frequencies of FMR mode identified
- DC response explained by low-order nonlinearity and magnetodipolar feedback
- Harmonic response is strongly influenced by mutual spin-torque effects

## Abstract

Being nonlinear dynamic systems, magnetic read sensors should respond to an excitation signal of a frequency considerably different from their natural ferromagnetic resonance (FMR) frequencies. Because of the magnetization dynamics' inherent nonlinear nature, the sensors' response should be measured at the DC, excitation frequency, and its multiples (harmonics). In this paper, we present results of such measurements, accomplished using a one-port nonlinear vector network analyzer (NVNA), which show distinct resonances at fractional frequencies of the free layer (FL) FMR mode. Identification of these resonances, resulting from the nonlinear nature of the spin-torque (ST)-induced magnetization dynamics, was performed using micromagnetic modeling. In particular, we show that the measured DC response at the above-mentioned fractional frequencies can be explained by a low-order nonlinearity and strong magnetodipolar feedback between magnetic layers adjacent to an MgO barrier. Additionally, we determined that the simulated harmonic response is strongly enhanced by the mutual ST effect between these layers. Finally, we demonstrate that the read sensors' nonlinear magnetization dynamics and, by extension, their harmonic response are highly sensitive to various magnetic and ST parameters. Thus, this study shows that using NVNA measurements in conjunction with micromagnetic modeling can clarify the uncertainty in the definition of these parameters.