Simulation of spin wave amplification using the method of characteristics to the transport equation

Mitrofanova A.Y., Temnaya O.S., Safin A.R., Kravchenko O.V., Nikitov S.A.
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The paper presents an analysis of the nonlinear equation of spin wave transport by the method of characteristics. The conclusion of a new mathematical model of spin wave propagation is presented for the solution of which the characteristic is applied. The behavior analysis of the behavior of the real and imaginary parts of the wave and its amplitude is performed. The phase portraits demonstrate the dependence of the desired function on the nonlinearity coefficient. It is established that the real and imaginary parts of the wave oscillate by studying the nature of the evolution of the initial wave profile by the phase plane method. The transition of trajectories from an unstable focus to a limiting cycle, which corresponds to the oscillation of the real and imaginary parts, is shown. For the amplitude of the wave, such a transition is characterized by its amplification or attenuation (depending on the nonlinearity coefficient and the chosen initial conditions) up to a certain threshold value. It is shown that the time of the transition process from amplification (attenuation) to stabilization of the amplitude also depends on the nonlinearity parameter. It was found out that at the interval of amplification of the amplitude of the spin wave, the time of the transition process decreases, and lower amplitude values correspond to higher parameters of nonlinearity.

Keywords: spin wave, spintronics, ferromagnetic materials, method of characteristics, transport equation, hyperbolic system of equations
Citation in English: Mitrofanova A.Y., Temnaya O.S., Safin A.R., Kravchenko O.V., Nikitov S.A. Simulation of spin wave amplification using the method of characteristics to the transport equation // Computer Research and Modeling, 2022, vol. 14, no. 4, pp. 795-803
Citation in English: Mitrofanova A.Y., Temnaya O.S., Safin A.R., Kravchenko O.V., Nikitov S.A. Simulation of spin wave amplification using the method of characteristics to the transport equation // Computer Research and Modeling, 2022, vol. 14, no. 4, pp. 795-803
DOI: 10.20537/2076-7633-2022-14-4-795-803
URL: http://crm-en.ics.org.ru/journal/article/3225/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

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