# Boundary-Driven Twist States in Systems with Broken Spatial Inversion Symmetry

## TL;DR

This paper derives comprehensive boundary conditions for ferromagnets with Dzyaloshinskii-Moriya interaction, revealing a boundary-driven twist state at edges that affects magnetoresistance, independent of internal DMI fields.

## Contribution

It provides the full tensorial form of boundary conditions for systems with DMI, highlighting the emergence of boundary-driven twist states in thin films.

## Key findings

- Boundary conditions require the full DMI tensor structure.
- A boundary-driven twist state exists at the edges of thin films.
- The twist state influences magnetoresistance similarly to domain walls.

## Abstract

A full description of a magnetic sample includes a correct treatment of the boundary conditions (BCs). This is in particular important in thin film systems, where even bulk properties might be modified by the properties of the boundary of the sample. We study generic ferromagnets with broken spatial inversion symmetry and derive the general micromagnetic BCs of a system with Dzyaloshinskii-Moriya interaction (DMI). We demonstrate that the BCs require the full tensorial structure of the third-rank DMI tensor and not just the antisymmetric part, which is usually taken into account. Specifically, we study systems with $C_{\infty v}$ symmetry and explore the consequences of the DMI. Interestingly, we find that the DMI already in the simplest case of a ferromagnetic thin-film leads to a purely boundary-driven magnetic twist state at the edges of the sample. The twist state represents a new type of DMI-induced spin structure, which is completely independent of the internal DMI field. We estimate the size of the texture-induced magnetoresistance effect being in the range of that of domain walls.