| Summary: | Abstract Quasicrystals (QCs) possess a unique lattice structure without translational invariance, which is characterized by the rotational symmetry forbidden in periodic crystals such as the 5-fold rotation. Recent discovery of the ferromagnetic (FM) long-range order in the terbium-based QC has brought about breakthrough but the magnetic structure and dynamics remain unresolved. Here, we reveal the dynamical as well as static structure of the FM hedgehog state in the icosahedral QC. The FM hedgehog is shown to be characterized by the triple-Q state in the reciprocal-lattice $${{\varvec{q}}}$$ q space. Dynamical structure factor is shown to exhibit highly structured $${{\varvec{q}}}$$ q and energy dependences. We find a unique magnetic excitation mode along the 5-fold direction exhibiting the streak fine structure in the $${{\varvec{q}}}$$ q -energy plane, which is characteristic of the hedgehog in the icosahedral QC. Non-reciprocal magnetic excitations are shown to arise from the FM hedgehog order, which emerge in the vast extent of the $${{\varvec{q}}}$$ q -energy plane.
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