Spin waves in unsaturated single- and double-layered ferromagnetic nanorings

Abstract

A theoretical analysis is described for the spin waves in single- and double-layered nanorings using a microscopic, or Hamiltonian-based, formalism. The calculations, which yield the frequencies and spatially-dependent intensities of the quantized spin waves, are applied to the vortex and onion (bi-domain) states in a single nanoring, as well as to the field-induced switching. In the case of asymmetric double-layered nanorings (with a nonmagnetic spacer) there are coupled spin waves controlled by varying the spacer thickness to change the strength of the inter-ring dipolar interactions. The different possible magnetic states, depending on the applied magnetic field, may involve vortex states (with the same or opposite chirality) in both layers, a vortex state in one layer and onion state in the other, or onion states in both layers. Numerical applications are made to permalloy nanorings with realistic dimensions and magnetic parameter values.

Spin Waves in Ferromagnetic Nanorings with Interfacial Dzyaloshinskii–Moriya Interactions: II. Directional Effects

“…The in-plane applied magnetic field B 0 is taken to be along the z direction. As in some of our recent work on the spin dynamics of nanorings and nanotubes (our preceding paper I and [31]), we employed a spin Hamiltonian together with a finite-element method. The spin sites form an array of elements filling the volume of the nanoring and were chosen to lie on a simple cubic lattice (with lattice constant a).…”

“…In accordance with the established results from micromagnetic modelling, a must be chosen to be less than the so-called exchange correlation length a ex , which is about 5 to 7 nm in metallic ferromagnets like permalloy or cobalt, for example). We can express the total spin Hamiltonian as H = H ring + H DM , where H ring is the dipole-exchange part in the absence of DMIs [31] and H DM describes the additional DMI effects considered here. We write…”

“…We recently carried out studies of the spin waves (SWs) in the vortex and onion states of nanorings using a microscopic, or Hamiltonian-based, method. Initially, the SW modes were investigated without DMIs [31]. Subsequently, a separate calculation was reported for nanorings with interfacial DMIs (or i-DMIs) included [32].…”

Ultrastrong Magnon-Magnon Coupling and Chiral Symmetry Breaking in a 3D Magnonic Metamaterial

“…Artificial spin systems have made impressive forays into the third-dimension, led by the likes of Ladak et al [23][24][25][26][27][28] & Donnelly et al [29][30][31][32] amongst others [33][34][35] , though these remain exchange-coupled rather than dipolar. Three-dimensional magnonic crystals have also been explored, with excellent studies by Gubbiotti et al 36,37 and Barman et al 27,28 amongst others 38,39 . Three-dimensional systems are ideal for enriching the range of accessible magnetic states, and the increased freedom to design the 3D spatial positioning of dipolar charges offers an attractive route to engineering stronger dipolar coupling.…”

Engineering spin wave spectra in thick Ni80Fe20 rings by using competition between exchange and dipolar fields

“…The discovery of fascinating properties of ferromagnetic rings (vortex and onion magnetic states below saturation, specific features of the switching behavior, and peculiarities of magnetic dynamics) [16][17][18][19][20][21] as well as the possibility to control vortex chirality in rings [22,23] make them a promising candidate for usage in magnetoresistive random access memory (MRAM) devices [24,25] and logic circuits [26]. Very recently nanovolcanoes-nanodisks overlaid by nanoringswere proposed as purpose-engineered three-dimensional (3D) architectures for nanomagnonics [27].…”