Physics, mathematics, and technology

2020 Issue №3

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A surprising tale of long-periodic spin oscillations in the synthetic antiferromagnets: some exact solutions



This article is devoted to construction of a mathematical theory capable of explaining those experimentally observable periodic magnetic oscillations in the synthetic antiferromagnet Pt/Co/Ir/Co/Pt that take place after a switch in the direction of an external magnetic field. In particular, we demonstrate that in order to understand the aforementioned phenomenon it is essential to first properly model the collisions between the magnetic domains of different spin orientations (  and ). The resulting model comprised of a system of nonlinear differential equations is closely examined, after which we propose a simple analytical method of construction of its exact solutions. This method is shown to generate an infinite family of solutions associated with the degener­ate hypergeometric functions, parameterized by a natural number N. One of those solutions with N = 2 produces the magnetization function which perfect­ly fits the experimental data.