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Mathematical model of a cylindrical SOT-MRAM cell
Authors
	Iusipova Iu.A.
	Ostrovskaya N.V.
	Skidanov V.A.
Date of publication
	2022
DOI
	10.31114/2078-7707-2022-4-142-148
Abstract
	In previous works, we considered in detail the model of a free-access magnetic memory cell (MRAM) of a square section, which is most convenient for analyzing and identifying the main patterns of its functioning [Ost-YuYu]. The consideration was carried out within the framework of the model of uniform distribution of magnetization over the cell cross section. However, near the boundaries and corner points of the element, even in the case of its small size, the assumption of a uniform distribution of magnetization over the cross section is not fulfilled. The question arises, how to minimize the influence of the inhomogeneity of the magnetization distribution on the operation of MRAM? In foreign works, an MRAM element was proposed, in which the influence of boundaries was weakened by a special choice of the shape of the active ferromagnetic layer of the element, namely, elliptical. The construction of a system of differential equations for describing the dynamics of the magnetization vector in such an element almost completely coincides with the construction of a system for an element with a square section, carried out in our works, but the difference lies in the expression for the effective magnetic demagnetization field. As reported in the work of J. Osborn [13], in the case of uniaxial anisotropy, the shape of the active layer can be considered as an ellipsoid of revolution around the anisotropy axis in the case of an elongated section, or as an oblate ellipsoid of revolution around the vertical axis for a section close to the shape of a circle. In this paper, we consider a mathematical model of a cylindrical magnetic random access memory cell based on the spin Hall effect with a free ferromagnetic layer in the form of an oblate ellipsoid. In the approximation of uniform magnetization, a system of differential equations is constructed that describes the dynamics of magnetization in the free ferromagnetic layer of the cell. Its analysis was carried out and the values of the “field–current” control parameters were revealed, at which the cell switches from the parallel state to the antiparallel state and vice versa, the corresponding entries in the cell “zero” or “one”.
Keywords
	three-layer structure, magnetic random-access memory, spin-orbit torque, spin Hall effect, free ferromagnetic layer, Landau–Lifshitz–Gilbert equation, dynamical system.
Library reference
	Iusipova Iu.A., Ostrovskaya N.V., Skidanov V.A. Mathematical model of a cylindrical SOT-MRAM cell // Problems of Perspective Micro- and Nanoelectronic Systems Development - 2022. Issue 4. P. 142-148. doi:10.31114/2078-7707-2022-4-142-148
URL of paper
	http://www.mes-conference.ru/data/year2022/pdf/D039.pdf