# Covalency, correlations, and inter-layer interactions governing the magnetic and electronic structure of Mn$_3$Si$_2$Te$_6$

## TL;DR

This study combines experimental spectroscopies and first-principles calculations to elucidate how covalency, correlations, and inter-layer interactions influence the magnetic and electronic structure of the layered ferrimagnet Mn$_3$Si$_2$Te$_6$, revealing the importance of hybridization and extended exchange interactions.

## Contribution

It provides a detailed analysis of the electronic and magnetic structure of Mn$_3$Si$_2$Te$_6$ using combined experimental and theoretical methods, highlighting covalency's role in stabilizing ferrimagnetism.

## Key findings

- Mn-Te hybridization weakens electronic correlations.
- Hybridization enhances magnetic anisotropy.
- Extended exchange interactions influence ordering temperature.

## Abstract

Mn$_3$Si$_2$Te$_6$ is a rare example of a layered ferrimagnet. It has recently been shown to host a colossal angular magnetoresistance as the spin orientation is rotated from the in- to out-of-plane direction, proposed to be underpinned by a topological nodal-line degeneracy in its electronic structure. Nonetheless, the origins of its ferrimagnetic structure remain controversial, while its experimental electronic structure, and the role of correlations in shaping this, are little explored to date. Here, we combine x-ray and photoemission-based spectroscopies with first-principles calculations, to probe the elemental-selective electronic structure and magnetic order in Mn$_3$Si$_2$Te$_6$. Through these, we identify a marked Mn-Te hybridisation, which weakens the electronic correlations and enhances the magnetic anisotropy. We demonstrate how this strengthens the magnetic frustration in Mn$_3$Si$_2$Te$_6$, which is key to stabilising its ferrimagnetic order, and find a crucial role of both exchange interactions extending beyond nearest-neighbours and anti-symmetric exchange in dictating its ordering temperature. Together, our results demonstrate a powerful methodology of using experimental electronic structure probes to constrain the parameter space for first-principles calculations of magnetic materials, and through this approach, reveal a pivotal role played by covalency in stabilising the ferrimagnetic order in Mn$_3$Si$_2$Te$_6$.