Fractional corner magnetization of collinear antiferromagnets

TL;DR

This paper demonstrates that collinear antiferromagnets on cubic lattices exhibit fractional corner magnetization quantized as S/2^d, robust against gapless excitations and slight symmetry breaking, revealing a magnetic analog of electric multipole phenomena.

Contribution

It introduces the concept of fractional corner magnetization in antiferromagnets and shows its robustness and quantization properties through theoretical analysis and numerical simulations.

Findings

Corner magnetization is quantized as S/2^d in d-dimensional cubic lattices.

Quantization remains robust despite gapless excitations from Néel order.

Deviations are negligible even when rotational symmetry is broken.

Abstract

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 $M_{\text{c}}^z=S/2^d$ at the corners. We find that the quantization is robust even in the presence of gapless excitations originating from the spontaneous formation of the N\'eel 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.