Magnonic crystals - prospective structures for shaping spin waves in nanoscale

TL;DR

This paper theoretically investigates the band structure of spin waves in 1D, 2D, and 3D magnonic crystals using various computational methods, revealing complex behaviors and potential for tailored spin wave control.

Contribution

It demonstrates the application of multiple computational techniques to analyze spin wave spectra in magnonic crystals across different dimensions, highlighting surface modes and material distribution effects.

Findings

Surface character of Damon-Eshbach spin waves in 1D crystals

Complex band structures in 2D due to demagnetizing fields

Wide magnonic band gap in 3D crystals with small lattice constants

Abstract

We have investigated theoretically band structure of spin waves in magnonic crystals with periodicity in one-(1D), two- (2D) and three-dimensions (3D). We have solved Landau-Lifshitz equation with the use of plane wave method, finite element method in frequency domain and micromagnetic simulations in time domain to find the dynamics of spin waves and spectrum of their eigenmodes. The spin wave spectra were calculated in linear approximation. In this paper we show usefulness of these methods in calculations of various types of spin waves. We demonstrate the surface character of the Damon-Eshbach spin wave in 1D magnonic crystals and change of its surface localization with the band number and wavenumber in the first Brillouin zone. The surface property of the spin wave excitation is further exploited by covering plate of the magnonic crystal with conductor. The band structure in 2D magnonic crystals is complex due to additional spatial inhomogeneity introduced by the demagnetizing field. This modifies spin wave dispersion, makes the band structure of magnonic crystals strongly dependent on shape of the inclusions and type of the lattice. The inhomogeneity of the internal magnetic field becomes unimportant for magnonic crystals with small lattice constant, where exchange interactions dominate. For 3D magnonic crystals, characterized by small lattice constant, wide magnonic band gap is found. We show that the spatial distribution of different materials in magnonic crystals can be explored for tailored effective damping of spin waves.