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In this work, we report the excitation of spin-waves modes in skyrmion clusters hosted in Co/Pt nanodots by applying an in-plane magnetic field pulse. The direction at which the magnetic field is applied enables the excitation of five main spin-waves modes that are understood in terms of only azimuthal-like modes, which are shown to be strongly dependent on the number of skyrmions stabilized in the system. This feature converts the present system in a mechanism to activate and suppress a set of given modes, which in turn we propose to be utilized as a magnonic key based skyrmion cluster. Our results could be useful in manufacturing potential magnonic logic devices based in skyrmionic textures.

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In this work we study the localization properties of diluted and nondiluted disordered direct transmission lines (TLs), when we distribute two values of inductances, L A and L B , according to an asymmetric dichotomous sequence. Using the scaling properties of the participation number D we study the localization properties in the thermodynamic limit. For certain and parameter speci¯c values, which characterize the dichotomous noise, we have found the following limit conditions: lim !1 mð!; ; Þ ! 1:0 or lim !1 mð!; ; Þ ! 1:0, for the appearing of the disorder-order transitions. Here mð!; ; Þ are the slopes of the linear relationships between lnðDÞ and lnðNÞ. In addition, in each ! c resonance frequency generated by the dilution process we demonstrate the existence of extended intermediate states in the thermodynamic limit.

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