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

Abstract

A general theory of collective spin wave edge modes in semi-infinite and finite periodic arrays of magnetic nanodots having uniform dynamic magnetization (macrospin approximation) is developed. The theory is formulated using a formalism of multi-vectors of magnetization dynamics, which allows one to study edge modes in arrays having arbitrarily complex primitive cells and lattice structure. The developed formalism can describe spin wave edge modes localized both at the physical edges of the array and at the internal "domain walls" separating the array regions existing in different static magnetization states. Using a perturbation theory, in the framework of the developed formalism it is possible to calculate damping of the edge modes and to describe their excitation by external variable magnetic fields. The theory is illustrated on the following practically important examples: (i) calculation of the FMR absorption in a finite nanodot array having the shape of a right triangle; (ii) calculation of the spectra of nonreciprocal spin wave edge modes, including the modes at the physical edges of an array and modes at the domain walls inside the array; (iii) study of the influence of the domain wall modes on the FMR spectrum of an array existing in a non-ideal chessboard antiferromagnetic ground state.

Magnonic crystals for data processing

“…In particular, considerable attention has attracted investigations of magnonic crystals with defects [31][32][33][34][35], topological and nonreciprocal phenomena in magnonic crystals [36][37][38][39][40][41][42][43][44], linear and nonlinear spin-wave dynamics in coupled magnonic crystals [45][46][47], and the formation and propagation of solitons [48][49][50][51]. Besides one-dimensional magnonic crystals [81][82][83][84][85][86][87][88][89][90][91][92][93][94][95][96][97][98], two-dimensional magnonic crystals have been intensively studied experimentally while three-dimensional magnonic crystals [78][79][80] are investigated theor etically.…”

Broadband conversion of microwaves into propagating spin waves in patterned magnetic structures

“…The increase in fFMR(r) near the edges of patterned magnetic structures makes the demonstrated scheme of spin-wave generation truly general and relevant to the excitation of spin waves not only in stripes but also in any magnetic samples possessing non-uniformity, either geometrical and/or compositional. Our results will find application in interpretation of the magnetization dynamics observed in a variety of experimental schemes, 10,[12][13]14,[21][22]23,24,25 as well as being a crucial step towards development of miniaturized all-magnonic technology.…”

Interaction of Microwave Photons with Nanostructured Magnetic Metasurfaces

“…Thus, we have shown, that the developed theoretical formalism of photon scattering matrices allows one to solve analytically the problem of electromagnetic wave propagation in a parallel-plate waveguide containing a magnetic metasurface and having plates of a finite conductivity. The magnetic metasurface could have an arbitrary susceptibility tensorχ, meaning an arbitrary complex magnetic ground state and an arbitrary direction of the static magnetization 12,13,18 . We provided a method to compute the dispersion relation for the waveguide modes (24) and the field distribution of each of these modes (25).…”

“…However, it is highly desirable to have a reconfigurable metamaterial with ultra-short switching times, capable of working without mechanical changes in structure and without a bias magnetic field. To address this problem a new concept of nano-structured magnetic metamaterials based on the dipolarly coupled arrays of single-domain magnetic nanoelements has been introduced 12,13 . The elements in these arrays are sufficiently small to be monodomain and have sufficient shape or crystallographic anisotropy to keep a definite direction of their static magnetization in the absence of an external bias magnetic field.…”