Magnonic crystals—Prospective structures for shaping spin waves in nanoscale

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.

Driving Magnetization Dynamics in an On-Demand Magnonic Crystal via the Magnetoelastic Interactions

“…The MS are performed by solving numerically LL equation in real space and time domain 49 . For excitation of the SW precession, we used a microwave external magnetic field in the form of the sinc function in the time domain and spatially homogeneous in the whole sample.…”

Spin waves in planar quasicrystal of Penrose tiling

“…where H 0 means external field, H dm (r, t) is demagnetizing field and H ex (r, t) is exchange field. We have solved (LLE) using plane wave method (PWM) [39]. The PWM requires periodic structures.…”

Graded Magnonic Index and Spin Wave Fano Resonances in Magnetic Structures: Excite, Direct, Capture

“…53,54 The non-uniformity breaks the translational invariance, limiting the use of the wave vector and therefore the notion of wave dispersion. The notable exceptions are given by the periodic and slowly varying (spatially) non-uniformities, the former giving rise to magnonic crystals 1,2, [5][6][7][8][9] and the latter allowing the use of the geometrical optics (quasi-classical) approximation. 26,28…”

“…Thus, we have recently seen a number of excellent review papers with emphasis on different aspects of spin wave research and technology, e.g. magnonic crystals and metamaterials, [5][6][7][8][9] photo-magnonics, 10,11 spin caloritronics, 12 magnon spintronics, [13][14][15] nanoscience, [16][17][18][19] and applications of spin waves in microwave signal processing and data manipulation. [20][21][22] There is however an aspect of magnonics that has been both ubiquitous and somewhat underrated so far: magnonics is the study not only of spin but also (and most importantly) of waves, which have an extremely rich and peculiar dispersion that is nonlinear, anisotropic and non-reciprocal.…”