Numerical Model Of Harmonic Hall Voltage Detection For Spintronic Devices

We present a numerical macrospin model for harmonic voltage detection in multilayer spintronic devices. The core of the computational backend is based on the Landau-Lifshitz-Gilbert-Slonczewski equation, which combines high performance with satisfactory, for large-scale applications, agreement with the experimental results. We compare the simulations with the experimental findings in Ta/CoFeB bilayer system for angular- and magnetic field-dependent resistance measurements, electrically detected magnetisation dynamics, and harmonic Hall voltage detection. Using simulated scans of the selected system parameters such as the polar angle $\theta$, magnetisation saturation ($\mu_\textrm{0}M_\textrm{s}$) or uniaxial magnetic anisotropy ($K_\textrm{u}$) we show the resultant changes in the harmonic Hall voltage, demonstrating the dominating influence of the $\mu_\textrm{0}M_\textrm{s}$ on the first and second harmonics. In the spin-diode ferromagnetic resonance (SD-FMR) technique resonance method the ($\mu_\textrm{0}M_\textrm{s}$, $K_\textrm{u}$) parameter space may be optimised numerically to obtain a set of viable curves that fit the experimental data.