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Caption : figure s1. hysteresis curves for a hexagonal cell of nineteen circular nanodots (second-nearest neighbors) when the external magnetic field is applied along (a) z-axis and (b) x-axis. hysteresis curves for a hexagonal cell of nineteen square nanodots (second-nearest neighbors) when the external magnetic field is applied along (c) z-axis and (d) x-axis. for all the curves: dcc=1.25d (⎯⎯), 1.75d (⎯⎯), 2.5d (⎯⎯) and 3d (- - - -).

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Caption : figure s2. (a) hysteresis curves of an isolated circular nanodot when the external magnetic field is applied along the z-axis. circular nanodots with diameters of 20 nm (⎯⎯), 40 nm (− − − −), 60 nm (∙ − ∙ −), 80 nm (∙ ∙ ∙ ∙) and 100 nm (⎯⎯) are considered. (b) coercivity (◼) and reduced remanence (●) as a function of nanodot diameter. (c) hysteresis curve for a 40 nm diameter circular nanodot and snapshots of the magnetization at the point on the hysteresis curve that are highlighted. (d) hysteresis curve for a 100 nm diameter circular nanodot and snapshots of the magnetization at the point on the hysteresis curve that are highlighted.

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Caption : figure s3. (a) hysteresis curves of an isolated square nanodot when the external magnetic field is applied along the z-axis. square nanodots with lengths of 20 nm (⎯⎯), 40 nm (− − − −), 60 nm (∙ − ∙ −), 80 nm (∙ ∙ ∙ ∙) and 100 nm (⎯⎯) are considered. (b) coercivity (◼) and reduced remanence (●) as a function of nanodot length.

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Caption : figure s4. (a) hysteresis curves of an isolated circular nanodot when the external magnetic field is applied along the x-axis. circular nanodots with diameters of 20 nm (⎯⎯), 40 nm (− − − −), 60 nm (∙ − ∙ −), 80 nm (∙ ∙ ∙ ∙) and 100 nm (⎯⎯) are considered. (b) coercivity (◼) and reduced remanence (●) as a function of nanodot diameter. (c) vectorial representation of the magnetic vortex configuration with c = -1 and p = +1 obtained for a 100 nm diameter circular nanodot in the absence of an external magnetic field.

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Caption : figure s5. (a) hysteresis curves of an isolated square nanodot when the external magnetic field is applied along the x-axis. square nanodots with lengths of 20 nm (⎯⎯), 40 nm (− − − −), 60 nm (∙ − ∙ −), 80 nm (∙ ∙ ∙ ∙) and 100 nm (⎯⎯) are considered. (b) coercivity (◼) and reduced remanence (●) as a function of nanodot length. (c) vectorial representation of the magnetic vortex configuration with c = -1 and p = +1 obtained for a 100 nm length square nanodot in the absence of an external magnetic field.

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Caption : figure s6. profile of the 1s and 1c resonance modes for the (a) square and (b) circular nanodot arrays, when we apply a fixed external magnetic field of 1000 mt in the z-direction and a sinc wave excitation field in the y-direction.

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Caption : figure s7. spatial distribution of the phases corresponding to the spectra of the resonant modes for arrays of (a) square and (b) circular nanodots obtained when a fixed external magnetic field of 1000 mt is applied in the z-direction and a sinc wave excitation field in the y-direction. the rows correspond to different values of center-to-center distance between the nanodots. the color code establishes the phase of the fft used in the y-component of the magnetizing field.

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Caption : figure s8. profile of the 1s and 1c resonance modes for the (a) square and (b) circular nanodot arrays, respectively, when we apply a fixed external magnetic field of 1000 mt in the x-direction and a sinc wave excitation field in the y-direction.

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Caption : figure s9. spatial distribution of the phases corresponding to the spectra of the resonant modes for arrays of (a) square and (b) circular nanodots obtained when a fixed external magnetic field of 1000 mt is applied in the x-direction and a sinc wave excitation field in the y-direction. the rows correspond to different values of center-to-center distance between the nanodots. the color code establishes the phase of the fft used in the y-component of the magnetizing field.

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Caption : figure s10. profile of the 2s resonance mode for the square nanodot arrays when we apply a fixed external magnetic field of 1000 mt in the x-direction and a sinc wave excitation field in the y-direction. this profile shows a localized mode with two nodal line.

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Caption : figure s11. comparison between the dynamic susceptibility measured for an array of nanodots separated at a distance of 3.0d and an isolated nanodot in the presence of a fixed magnetic field of 1000 mt applied along the z-axis for (a) square and (b) circular nanodots.

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Caption : figure s12. comparison between the dynamic susceptibility measured for an array of nanodots separated at a distance of 3.0d and an isolated nanodot in the presence of a fixed magnetic field of 1000 mt applied along the x-axis for (a) square and (b) circular nanodots.