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.

时空的曲率和手性的概念是理解宇宙中有机生命和物质形成的基础。默认情况下，手性相互作用以及曲率效应被认为是局部的。一个典型的凝聚物例子是局部自旋轨道或曲率引起的Rashba或Dzyaloshinskii-Moriya相互作用。在这里，我们介绍一种手性效应，该效应本质上是非局部的，甚至在存在于曲线磁性纳米壳中的静态自旋纹理中也类似。它的物理起源是非局部静磁相互作用。为了确定这种相互作用，我们提出了曲线磁的自洽微磁框架。对弯曲的磁壳的非局部物理学的理解需要曲率引起的几何电荷，这将磁性子系统与曲线几何体耦合在一起。手性相互作用带来了非局部的手性对称性破坏作用：它在固有的非手性材料中引入了惯性，并可以设计磁电和铁磁响应。