From the spin eigenmodes of isolated N\'eel skyrmions to the magnonic bands of a skyrmionic crystal: a micromagnetic study as a function of the strength of both the interfacial Dzyaloshinskii-Moriya and the exchange constants

The presence of interfacial Dzyaloshinskii-Moriya interaction (DMI) may lead to the appearance of N\'eel 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 GHz range, i.e. in the operation range of current communication devices. Here we exploited the software MuMax3 to calculate the dynamics of N\'eel 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 D and A. The magnonic bands can be interpreted as derived from the eigenmodes of isolated skyrmions, even if hybridization and anti-crossing phenomena occur for specific ranges of values of D and A. 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.
Comment: 5 pages , 4 figures