Abstract

The concept of curvature and chirality in space and time are foundational for the understanding of the organic life and formation of matter in the Universe. Chiral interactions but also curvature effects are tacitly accepted to be local. A prototypical condensed matter example is a local spin-orbit- or curvature-induced Rashba or Dzyaloshinskii-Moriya interactions. Here, we introduce a chiral effect, which is essentially nonlocal and resembles itself even in static spin textures living in curvilinear magnetic nanoshells. Its physical origin is the nonlocal magnetostatic interaction. To identify this interaction, we put forth a self-consistent micromagnetic framework of curvilinear magnetism. Understanding of the nonlocal physics of curved magnetic shells requires a curvature-induced geometrical charge, which couples the magnetic sub-system with the curvilinear geometry. The chiral interaction brings about a nonlocal chiral symmetry breaking effect: it introduces handedness in an intrinsically achiral material and enables the design of magnetolectric and ferrotoroidic responses.