# Understanding the ferromagnetic insulating state in Cr doped VO$_2$

## TL;DR

This study investigates how Cr doping stabilizes a ferromagnetic insulating state in VO$_2$, revealing the role of charge ordering and exchange interactions through combined ab-initio and microscopic modeling.

## Contribution

It provides a detailed microscopic understanding of the charge ordering and exchange mechanisms stabilizing the ferromagnetic insulating state in Cr-doped VO$_2$.

## Key findings

- Reproduces ferromagnetic insulating state with charge ordering at V and Cr sites.
- Quantifies energy gain from exchange pathways for the first time.
- Highlights the role of charge ordering in stabilizing the magnetic state.

## Abstract

Experimentally Cr doping in the rutile phase of VO$_2$ is found to stabilize a charge ordered ferromagnetic insulating state in the doping range of 10\% to 20\%. In this work, we investigated its origin at 12.5\% Cr doping using a combination of ab-initio electronic structure calculations as well as microscopic modeling. Our calculations are found to reproduce the ferromagnetic insulating state as well as a charge ordering at the V and Cr sites. The mapping of the ab-initio band structure onto a tight-binding Hamiltonian allows one to calculate the energy gain from different exchange pathways. This gain is quantified in this work for the first time and the role of charge ordering in stabilizing a ferromagnetic insulating state is understood.