Stacked spin-vortex pairs in magnetic multilayered nanopillars, with vertical separation between the vortices small compared to the vortex core size, exhibit spin dynamics absent in individual vortices. This dynamics is nonlinear and is due to the strong direct core-core coupling in the system, dominating energetically for small- signal excitation. We observe and explain the appearance of spin resonance modes, forbidden within linear dynamics, and discuss how they depend on the magnetic and morphological asymmetries in the samples.
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