Autoresonance control model of nonlinear dynamics of magnetization in a three-layer antiferromagnetic structure in the presence of attenuation

Abstract

An autoresonance method for excitation of nonlinear breather-type oscillations of the magnetization in a three-layer antiferromagnet by applying an external alternating magnetic field is considered. The first constant of magnetic anisotropy is assumed to be a one-dimensional function of the coordinate with a local change in its value. Such dependence of the magnetic anisotropy constant on the coordinate mimics the presence of a three-layered magnetic structure in which the thick layers with the same value of anisotropy are separated by a thin layer with different value of anisotropy. The external magnetic field is represented as a resonance field and an alternating field with a small amplitude. At a constant pumping frequency, there is a small amplitude change, with solutions being constructed under the condition of parametric resonance, when the pumping frequency is equal to twice the frequency of linear ferromagnetic or antiferromagnetic resonance. Of special interest is the variable pump frequency, described by a slowly varying function of time. In such an alternating field, resonance effects may appear, leading to a significant increase in the amplitude of the breather. The main resonance equations are obtained, the analysis of which reveals the existence of solutions with elevating amplitudes. In an alternating field, the increase of amplitude of the magnetic breather is observed, whereas in the absence of the external influence, only localization of the nucleation center on the defect occurs at spatial inhomogeneity of the magnetic anisotropy. With an increase in the depth of the spatial inhomogeneity of the magnetic anisotropy, autoresonance breaks down. With a decrease in the width of the inhomogeneity region of the magnetic anisotropy or a decrease in the thickness of a thin layer in a three-layer antiferromagnet, a growing solution also exists in the alternating field, which cannot be obtained in a constant magnetic field. The effect of the initial phase of the magnetic breather on its evolution is also considered in the paper.

Changing the Dynamic Parameters of Localized Breather and Soliton Waves in the Sine-Gordon Model with Extended Impurity, External Force, and Decay in the Autoresonance Mode

“…Here ω 0 is the natural frequency of the breather localized in the impurity area, calculated earlier in [13], and μ is the small parameter. As was shown earlier analytically in [35], with this type of function, we can expect a sharp increase in the breather amplitude. The numerical simulation shows that the natural frequency of the breather weakly depends on the amplitude for the case of attracting impurity and becomes constant under the defined parameters.…”

“…Nevertheless, the solutions with the increasing amplitude may appear under an appropriate change in the frequency of external force. As in [35], the h(t) function will be considered in the following form:…”

“…Using the autoresonance phenomenon, it is possible to control the structure and dynamics of solitons by applying an external variable force [31,32] and accounting for the decay in the system. The autoresonant models of control allow one to substantially decrease the external influence on the system [31][32][33][34][35]. The phenomenon of autoresonance described by nonlinear partial differential equations (e. g., [36]) was also investigated for the case of SGE [32,35].…”

“…The autoresonant models of control allow one to substantially decrease the external influence on the system [31][32][33][34][35]. The phenomenon of autoresonance described by nonlinear partial differential equations (e. g., [36]) was also investigated for the case of SGE [32,35]. However, the presence of solitons and breathers in the system was accounted for in these articles from the beginning.…”