Modeling High-Frequency Electromagnetics in Tunneling Magnetoresistive Sensors*

As operating frequencies of modern magnetic devices increase, effects of high-frequency (HF) electromagnetic fields on device behavior must be analyzed. Common micromagnetic (μM) software solve the Landau-Lifshitz-Gilbert (LLG) equation for the material magnetization under a magnetostatic approximation and can miss effects such as excited eddy currents which increasingly contribute to magnetization dynamics at HF [1]. To demonstrate the necessity of coupling the full dynamic Maxwell (M) and LLG equations, we radiate a sequence of waves up to 3 GHz from stripline antennas onto a tunneling magnetoresistive sensor and show the sensor resistance diverges from predictions of a LLG equation solver as wave frequency increases. We then formulate a hybrid M-LLG system of equations, modeling LLG terms using finite-differences (FD) and the M contribution to the demagnetization field using the FD time-domain method. We use the μM standard problems [2] to validate the proposed M-LLG solver and test its accuracy and computational costs. Finally, we discuss parallel performance of the solver on a supercomputing cluster.

[1] S. Couture, et al. IEEE Trans. Magn. 53, 12 (2017).

[2] https://www.ctcms.nist.gov/~rdm/mumag.org.html