Fractional corner magnetization of collinear antiferromagnets

Recent studies revealed that the electric multipole moments of insulators result in fractional electric charges localized to the hinges and corners of the sample. We here explore the magnetic analog of this relation. We show that a collinear antiferromagnet with spin S defined on a d-dimensional cubic lattice features fractionally quantized magnetization {M}_c^z=S/{2}^d at the corners. We find that the quantization is robust even in the presence of gapless excitations originating from the spontaneous formation of the Néel order, although the localization length diverges, suggesting a power-law localization of the corner magnetization. When the spin rotational symmetry about the z axis is explicitly broken, the corner magnetization is no longer sharply quantized. Even in this case, we numerically find that the deviation from the quantized value is negligibly small based on quantum Monte Carlo simulations.