The article presents the results of a qualitative study of the model of a modern magnetic memory cell, in which the spin Hall effect is used for recording. Cells of square cross-section with longitudinal anisotropy of the active layer are considered. Based on the Landau-Lifshitz-Gilbert vector equation, a mathematical model for controlling the process of writing zero and one into a cell is constructed. In the approximation of a uniform distribution of magnetization, a system of equations is derived that describes the dynamics of magnetization under the action of a magnetic field and spin current. The parameters of the qualitatively equivalent dynamics of the model are determined. It has been established that at zero currents and fields in both cases there are two main stable equilibrium positions. These equilibria, depending on the mutual orientation of the magnetization vector of the active and reference layers, correspond to zero and one, written in the cell. The transition from one cell state to another is described by solving a system of differential equations. A bifurcation diagram of a dynamical system in the variables "field-current" is constructed. It is shown that with a given configuration of the memory element, external influences transfer the magnetization to an intermediate state in the plane of the free layer, which, when the current and field are turned off, leads to writing zero or one to the memory cell. The critical switching current is estimated as a function of the applied external magnetic field. Keywords: spintronics, orbitronics, magnetization, Landau-Lifshitz-Gilbert equation, spin Hall effect, spin current, charge current, spin torque, longitudinal anisotropy, planar anisotropy.

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