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Modeling of Forced Oscillations of Magnetization in a System of Three Ferromagnetic Nanodisks R. V. Goreva, *, E. V. Skorokhodova, and V. L. Mironova a

Institute for Physics of Microstructures, Russian Academy of Sciences, Nizhny Novgorod, 603087 Russia *e-mail: [email protected] Received March 26, 2020; revised March 26, 2020; accepted April 2, 2020

Abstract—Micromagnetic modeling of ferromagnetic resonance (FMR) is carried out in a system comprising a cylindrical stack consisting of three ferromagnetic nanodisks, in which a helicoidal distribution of magnetic moments is realized due to magnetostatic interaction in the equilibrium state. Specificities of the rearrangement of the FMR spectrum and the spatial structure of the resonant oscillations of such a system in an external magnetic field are studied. Keywords: micromagnetic modeling, ferromagnetic resonance, submicron structures, helicoidal distribution DOI: 10.1134/S1063783420090085

1. INTRODUCTION Since recently, intensive studies of the magnetization dynamics of ferromagnetic nanostructures are carried out, which are of interest from the viewpoint of creating new microwave electronic devices, such as magnetic field sensors and storage devices [1–3]. Along with systems in a uniform magnetic state [4–9], much attention is paid to magnetic systems with a nonuniform equilibrium magnetization distribution such as a vortex, an antivortex [10–13], and a skyrmion [15–19]. The use of multilayer patterned structures makes it possible to create three-dimensional systems with a noncollinear magnetization distribution. In particular, we recently proposed and implemented a system consisting of three disks one above the other, in which a helicoidal distribution of the magnetic moment is realized [20, 21]. The nonuniform states are often studied using methods based on microstrip coplanar waveguides and magnetic resonance force microscopy [12, 22]. In this work, we use micromagnetic modeling to study the specific features of the ferromagnetic resonance in a system of three disks in an external magnetic field. We analyze the rearrangement of the FMR spectrum and the mode composition of resonance oscillations during the transition of this system between states with ferromagnetic and antiferromagnetic ordering of the moments of neighboring disks, as well as in a state with a helicoidal distribution of magnetic moments.

2. THE METHOD OF CALCULATION The system under consideration comprises a stack of coaxial circular ferromagnetic disks with a diameter of 100 nm and a thickness of 4 nm, separated by 4-nmthick nonmagnetic interlayers. Micromagnetic modeling of magnetic states and forced oscillations of the magnetization of this system was carried out using the Object Oriented MicroMagnetic Framework (OOMMF) package [21]. The disks were made from Permalloy Ni80Fe20 (saturation magnetization of 8 × 105 A/m, exchange interaction constant of 13 × 10–12 J/m, and dissipation parameter of 0.01). In the equilibrium state of this system, a helicoidal state is realized with the angle