Spin-wave dynamics in permalloy/cobalt magnonic crystals in the presence of a nonmagnetic spacer

Abstract

In this paper, we theoretically study the influence of a non-magnetic spacer between ferromagnetic dots and ferromagnetic matrix on the frequency dispersion of the spin wave excitations in twodimensional bi-component magnonic crystals. By means of the dynamical matrix method we investigate structures inhomogeneous across the thickness represented by square arrays of Cobalt or Permalloy dots in a Permalloy matrix. We show that the introduction of a non-magnetic spacer significantly modifies the total internal magnetic field especially at the edges of the grooves and dots. This permits the manipulation of the magnonic band structure of spin waves localized either at the edges of the dots or in matrix material at the edges of grooves. According to the micromagnetic simulations two types of end modes were found. The corresponding frequencies are significantly influenced by the end modes localization region. We also show that, with the use of a single ferromagnetic material, it is possible to design a magnonic crystal preserving properties of bicomponent magnonic crystals and magnonic antidot lattices. Finally, the influence of the nonmagnetic spacers on the technologically relevant parameters like group velocity and magnonic band width are discussed.

Formation of the band spectrum of spin waves in 1D magnonic crystals with different types of interfacial boundary conditions

“…The strength of coupling between layers could be modified by introducing air gaps between layers. [128][129][130] Yet, any generalization to the case of dipole-exchange spin waves could be only approximate since the corresponding differential (or integro-differential equations) are of a higher order, so that a greater number of boundary conditions is required to stitch their solutions at interfaces. However, it is likely that even qualitative analysis based on the ideas presented here could prove useful in some cases.…”

Formation of Néel-type skyrmions in an antidot lattice with perpendicular magnetic anisotropy

“…Additionally, the magnetic properties of a film can be influenced via patterning. For example, magnonic crystals 14,15 , which are spatially modulated magnetic thin films, form well-defined spin wave band structures 16 due to their periodicity. One common example of magnonic crystals are ferromagnetic antidot lattices [17][18][19] consisting of periodically arranged holes in a ferromagnetic thin film.…”

Theoretical formalism for collective spin-wave edge excitations in arrays of dipolarly interacting magnetic nanodots

“…The bulk and edge modes are orthogonal to each other in the sense of equation (44). The norm defined by equation (44a) is not practical for the numerical computations, as it cannot be obtained directly from numerical solutions of equation (27).…”

“…Later, several theoretical approaches were developed to describe spin-wave excitations in systems where magnetic properties are spatially periodic. The developed approaches include the method of plane wave expansion (PWE) [37][38][39][40] , which was adopted from the theory of periodic dielectric 41 and acoustic 42 structures, the dynamic matrix method 12,[43][44][45] , the transfer matrix method 46,47 , the multiple scattering theory 32 , and several other. The above mentioned methods have proven their applicability and convenience for the analysis of infinite periodic magnetic systems.…”

“…To find the amplitudes of the excited modes, one should plug (47) into (45) and use the normalization conditions (44) to separate the equation of motion into a set of equations for individual spin wave amplitudes. In the first approximation we can neglect all the terms that are non-linear inm n , and for the non-degenerate modes the stationary amplitude of each of the edge modes is given by…”