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Mathematical Model of the SOT-MRAM Cell based on the Spin Hall Effect
Authors
	Ostrovskaya N.V.
	Skidanov V.A.
	Iusipova Iu.A.
Date of publication
	2021
DOI
	10.31114/2078-7707-2021-2-2-8
Abstract
	We considered the model of the SOT-MRAM cell with the quadrat cross-section. The type of anisotropy of the ferromagnetic layers was proposed to be parallel to one of the sides of the quadrat. The model of the SOT-MRAM memory element was analyzed using the methods of the qualitative theory of dynamical systems. The basis for modelling is the fundamental Landau–Lifshits equation written for the case of the uniform approximation with the dissipative term in the Gilbert form. We performed the bifurcation analysis of the resulting dynamical system and revealed that at the external magnetic field parallel to the field of the anisotropy the system has no standard points of the equilibrium, but they appear when the external field is equal to zero. This fact is useful at impulse switching of the memory cell. However, the dynamical system describing the dynamics of magnetization, depending on the values of the control parameters, has two, four, or six additional equilibriums that dictates the modes of the magnetization dynamics. We constructed the bifurcation diagram in the terms of the external control parameters such as the magnetic field and charge current that allowed us to classify the types of the magnetization dynamics in the SOT-MRAM cell. All the types of the dynamics were illustrated by the direct solution of the dynamical systems with help of the Runge–Kutta method.
Keywords
	spin-orbit interaction, spin Hall effect, longitudinal anisotropy, magnetization, free layer, pinned layer, Landau–Lifshits equation, switching of magnetization
Library reference
	Ostrovskaya N.V., Skidanov V.A., Iusipova Iu.A. Mathematical Model of the SOT-MRAM Cell based on the Spin Hall Effect // Problems of Perspective Micro- and Nanoelectronic Systems Development - 2021. Issue 2. P. 2-8. doi:10.31114/2078-7707-2021-2-2-8
URL of paper
	http://www.mes-conference.ru/data/year2021/pdf/D009.pdf