Magnetic dynamics of ferromagnetic long range order in icosahedral quasicrystal

Quasicrystals lack translational symmetry and have unique lattice structures with rotational symmetry forbidden in periodic crystals. The electric state and physical property are far from complete understanding, which are the frontiers of modern matter physics. Recent discovery of the ferromagnetic long-range order in the rare-earth based icosahedral quasicrystal has made the breakthrough. Here, we first reveal the dynamical as well as static magnetic structure in the ferromagnetic long-range order in the terbium-based quasicrystal. The dynamical structure factor exhibits highly structured energy and wavenumber dependences beyond the crystalline-electric-field excitation. We find the presence of the magnetic excitation mode analog to magnon with unique hierarchical structure as well as the localized magnetic excitation with high degeneracy in the quasicrystal. Non-collinear and non-coplanar magnetic structure on the icosahedron is discovered to give rise to non-reciprocal magnetic excitation in the quasicrystal as well as non-reciprocal magnon in the periodic cubic 1/1 approximant. These findings afford illuminating insight into the magnetic dynamics in the broad range of the rare-earth-based quasicrystals and approximants.