Tunable eigenmodes of coupled magnetic vortex oscillators

Abstract

We study the magnetization dynamics of coupled vortices in arrays of Permalloy disks via analytical calculations and scanning transmission x-ray microscopy. The Thiele approach is used to derive linear equations of motion of the vortices. Thereby, vortex motions following a nanosecond field pulse are described by a superposition of eigenmodes that depend on the vortex polarizations. Eigenmodes are calculated for a specific polarization pattern of a 3 × 3 vortex array. With magnetic field pulses distinct oscillations are excited and imaged in space and time. The calculated eigenmodes precisely describe the measured oscillations.

Gyrational modes of benzenelike magnetic vortex molecules

“…A convenient and powerful model to describe the motions of coupled vortices is the Thiele model [2, [13][14][15]. It describes the magnetic vortex as a quasiparticle that is exposed to a force F = − ∇E that acts in the plane of the disk.…”

“…A linear energy term is commonly used to describe the influence of external magnetic fields. Recent approaches for systems of vortices in coupled arrays employ surface charges that emerge when the vortex is deflected from the center of the disk to approximate the coupling mediated by the stray field [11,[14][15][16]. Even when neglecting the damping, for a number of N coupled vortices, the Thiele equation becomes a 2N -dimensional system of differential A stripline is fabricated on one disk in order to excite the gyrotropic mode with the unidirectional high-frequency magnetic field generated by an alternating current sent through the stripline.…”

Two-body problem of core-region coupled magnetic vortex stacks

“…Since neighboring vortices couple due to stray fields emerging at the surfaces of the ferromagnetic elements [10], the motions of closely packed vortices are strongly influenced by their surrounding ferromagnetic structures [11,12]. The interaction between laterally arranged elements has been studied for pairs [13,14], chains [15], and two-dimensional arrangements [16][17][18] of vortices. In laterally coupled arrangements it has been shown recently that memorylike writing processes are possible based on the excitation of the gyrotropic mode [19], where bits are stored as polarization patterns.…”

Burst-mode manipulation of magnonic vortex crystals

“…They have been imaged * mhaenze@physnet.uni-hamburg.de using time-resolved scanning transmission x-ray microscopy at the MAXYMUS beamline of the synchrotron BESSY II in Berlin, Germany. Different polarization states lead to different resonance frequencies of the excited eigenmodes in the crystal [21]. These polarization states can be identified using ferromagnetic-resonance (FMR) measurements.…”