External magnetic field control of the magnetic breather parameters in a three-layer ferromagnetic structure

Abstract

The generation and autoresonant excitation of a magnetic breather in a three-layer ferromagnet by fields of variable frequency and small amplitude in the presence of dissipation in the system is considered. The ferromagnetic structure consists of two wide identical layers separated by a thin layer with modified values of the magnetic anisotropy parameter. The anisotropy parameters are considered functions of the coordinate directed perpendicular to the layer interface. In the one-dimensional case, the function of the anisotropy parameter is modeled in the form of a rectangle. The external magnetic field is variable in time with a small amplitude and frequency, which is a linear function of time. The obtained equation of motion for magnetization in the form of a sine-Gordon equation was solved numerically using an explicit integration scheme. The distribution of magnetization at the initial time was set in the form of a Bloch domain boundary, located far from a thin layer. At certain values of the parameters of a thin layer, when a domain wall passes at a constant speed through it, a magnetic inhomogeneity is formed in the form of a magnetic breather. In the absence of an external field, the breather amplitude decays with time. An analysis of the solutions of the equation of motion in an alternating field shows the possibility, under certain conditions, of increasing with time the amplitude of the magnetic breather. For each case of magnetic anisotropy parameter values, there is a threshold value of the magnetic field amplitude leading to resonance. The resonance effect is also affected by the geometric parameters of a thin layer: with a decrease in the width of the layer, the amplitude of the breather increases more slowly in time. With a large layer width, the translational mode of breather oscillations is also excited.

Возможность Управления Динамикой И Структурой Магнитного Солитона В Трехслойной Ферромагнитной Структуре

“…Рассмотрим трехслойную ферромагнитную структуру, состоящую из двух широких одинаковых слоев, разделенных тонким слоем с измененными значениями параметра магнитной анизотропии [14]. Параметры анизотропии будем считать функциями координаты x, направленной перпендикулярно границе раздела слоев.…”

“…Следует заметить, что другие виды функции (2), например гауссова типа, ведут к изменению набора параметров, приводящих к образованию магнитного солитона и его собственной частоты колебаний [9]. Уравнение (1) решалось численно с использованием явной схемы интегрирования [14]. Для этого выбиралась трехслойная схема решения с аппроксимацией производных на пятиточечном шаблоне типа "…”

“…Известно, что при определенных значениях параметров тонкого слоя при прохождении ДГ с постоянной скоростью через него образуется магнитная неоднородность в виде магнитного бризера или солитона. Случай магнитного бризера в переменном внешнем магнитном поле был нами рассмотрен ранее в [14]. Рассмотрим теперь магнитные неоднородности солитонного типа.…”

The Possibility of Controlling the Dynamics and Structure of a Magnetic Soliton in a Three-Layer Ferromagnetic Structure

“…Let us consider a three-layer ferromagnetic structure consisting of two wide identical layers separated by a thin layer with a changed magnetic anisotropy parameter [14]. The anisotropy parameters are assumed to be functions of coordinate x directed perpendicular to the layer interface.…”

“…It should be noted that other forms of function ( 2) (e.g., Gaussian) change the set of parameters, which induce the formation of an MS and its eigenfrequency [9]. Equation ( 1) was solved numerically using the explicit integration scheme [14]. For this purpose, a three-layer scheme of solution with approximation of derivatives using a five-point stencil of cross type was chosen [11].…”