From the Spin Eigenmodes of Isolated Néel Skyrmions to the Magnonic Bands of Skyrmionic Crystals: A Micromagnetic Study as a Function of the Interfacial Dzyaloshinskii-Moriya Interaction and the Exchange Constants

Abstract

The presence of interfacial Dzyaloshinskii-Moriya interaction (DMI) may lead to the appearance of Néel skyrmions in ferromagnetic films. These topologically protected structures, whose diameter is as small as a few nanometers, can be nowadays stabilized at room temperature and have been proposed for the realization of artificial magnonic crystals and new spintronic devices, such as racetrack memories. In this perspective, it is of utmost importance to analyze their dynamical properties in the gigahertz range, i.e., in the operation range of current communication devices. In this letter, we exploited the software MuMax3 to calculate the dynamics of Néel skyrmions in the range between 1 and 30 GHz, considering first the eigenmodes of an isolated skyrmion, then the case of two interacting skyrmions, and finally a linear chain, representing a one-dimensional magnonic crystal, whose magnonic band structure has been calculated as a function of the strength of both the DMI- and the exchange-constants, namely <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$D$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$A$</tex-math></inline-formula> . The magnonic bands can be interpreted as derived from the eigenmodes of isolated skyrmions, even if hybridization and anticrossing phenomena occur for specific ranges of values of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$D$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$A$</tex-math></inline-formula> . Therefore, varying the latter parameters, for instance, by a proper choice of the materials and thicknesses, may enable one to fine-tune the permitted and forbidden frequency interval of the corresponding magnonic crystal.