Hippopede curves for modelling radial spin waves in an azimuthal graded magnonic landscape

TL;DR

This paper introduces a mathematical model using hippopede curves to describe azimuthal spin wave propagation in magnetic patches, linking geometric curves with physical dispersion relations, validated by simulations.

Contribution

It presents a novel analytical approach connecting hippopede curves with spin wave dispersion, enabling accurate modeling of complex magnonic landscapes.

Findings

Model accurately predicts spin wave wavelengths for various geometries.

Good agreement between analytical results and micromagnetic simulations.

Method applicable to any n-corner magnetic patch geometry.

Abstract

We propose a mathematical model for describing radially propagating spin waves emitted from the core region in a magnetic patch with n vertices in a magnetic vortex state. The azimuthal anisotropic propagation of surface spin waves (SSW) into the domain, and confined spin waves (or Winter's Magnons, WM) in domain walls increases the complexity of the magnonic landscape. In order to understand the spin wave propagation in these systems, we first use an approach based on geometrical curves called 'hippopedes', however it provides no insight into the underlying physics. Analytical models rely on generalized expressions from the dispersion relation of SSW with an arbitrary angle between magnetization M and wavenumber k. The derived algebraic expression for the azimuthal dispersion is found to be equivalent to that of the 'hippopede' curves. The fitting curves from the model yield a spin wave wavelength for any given azimuthal direction, number of patch vertices and excitation frequency, showing a connection with fundamental physics of exchange dominated surface spin waves. Analytical results show good agreement with micromagnetic simulations and can be easily extrapolated to any n-corner patch geometry.