# Band filling control of the Dzyaloshinskii-Moriya interaction in weakly ferromagnetic insulators

## TL;DR

This study investigates how the Dzyaloshinskii-Moriya interaction varies across a series of weak ferromagnetic insulators, revealing its dependence on 3d shell filling and confirming findings with first-principles calculations.

## Contribution

The paper provides the first comprehensive analysis of the Dzyaloshinskii-Moriya interaction evolution in related insulators, combining experimental observations with theoretical modeling.

## Key findings

- Sign of DMI is determined by x-ray magnetic diffraction phase.
- Quantitative agreement between experiments and first-principles calculations.
- A simplified model explains the sign change with 3d shell filling.

## Abstract

We observe and explain theoretically a dramatic evolution of the Dzyaloshinskii-Moriya interaction in the series of isostructural weak ferromagnets, MnCO$_3$, FeBO$_3$, CoCO$_3$ and NiCO$_3$. The sign of the interaction is encoded in the phase of x-ray magnetic diffraction amplitude, observed through interference with resonant quadrupole scattering. We find very good quantitative agreement with first-principles electronic structure calculations, reproducing both sign and magnitude through the series, and propose a simplified `toy model' to explain the change in sign with 3 d shell filling. The model gives a clue for qualitative understanding of the evolution of the DMI in Mott and charge transfer insulators.