# The chiral biquadratic pair interaction

## TL;DR

This paper introduces and analyzes a new chiral biquadratic pair interaction in magnetic systems, derived from microscopic models and studied through first-principles calculations, with implications for complex magnetic structures.

## Contribution

The paper derives the chiral biquadratic interaction from microscopic principles and explores its properties in magnetic dimers and extended systems.

## Key findings

- Identified a new chiral biquadratic pair interaction.
- Demonstrated its significance in magnetic dimers and spin structures.
- Discussed potential impact on magnetic skyrmion lattices.

## Abstract

Magnetic interactions underpin a plethora of magnetic states of matter, hence playing a central role both in fundamental physics and for future spintronic and quantum computation devices. The Dzyaloshinskii-Moriya interaction, being chiral and driven by relativistic effects, leads to the stabilization of highly-noncollinear spin textures such as skyrmions, which thanks to their topological nature are promising building blocks for magnetic data storage and processing elements. Here, we reveal and study a new chiral pair interaction, which is the biquadratic equivalent of the Dzyaloshinskii-Moriya interaction. First, we derive this interaction and its guiding principles from a microscopic model. Second, we study its properties in the simplest prototypical systems, magnetic dimers deposited on various substrates, resorting to systematic first-principles calculations. Lastly, we discuss its importance and implications not only for magnetic dimers but also for extended systems, namely one-dimensional spin spirals and complex two-dimensional magnetic structures, such as a nanoskyrmion lattice.