Magnetic dynamics and nonreciprocal excitation in uniform hedgehog order in icosahedral 1/1 approximant crystal

The hedgehog state in the icosahedral quasicrystal (QC) has attracted great interest as the theoretical discovery of topological magnetic texture in aperiodic systems. The revealed magnetic dynamics exhibits nonreciprocal excitation in the vast extent of the reciprocal lattice [Formula: see text] -energy [Formula: see text] space, whose emergence mechanism remains unresolved. Here, we analyze the dynamical as well as static structure of the hedgehog order in the 1/1 approximant crystal (AC) composed of the cubic lattice with spatial inversion symmetry. We find that the dispersion of the magnetic excitation energy exhibits nonreciprocal feature along the N-P-[Formula: see text] line in the [Formula: see text] space. The dynamical structure factor exhibits highly structured intensities where high intensities appear in the high-energy branches along the [Formula: see text] -H line and the P-[Formula: see text] -N line in the [Formula: see text] space. The nonreciprocity in the 1/1 AC and also in the QC is understood to be ascribed to inversion symmetry breaking by the hedgehog ordering. The sharp contrast on the emergence regime of nonreciprocal magnetic excitation between the QC and the 1/1 AC indicates that the emergence in the vast [Formula: see text] -[Formula: see text] regime in the QC is attributed to the QC lattice structure.