# Comparative study of DFT+$U$ functionals for non-collinear magnetism

## TL;DR

This study compares different DFT+$U$ functionals to understand their effectiveness in modeling non-collinear magnetism, revealing how parameters like Hund J influence magnetic ground states in specific materials.

## Contribution

It provides a systematic comparison of DFT+$U$ formalisms and analyzes parameter effects, offering guidance for first-principles calculations of non-collinear magnetic materials.

## Key findings

- Ground state spin order depends strongly on Hund J.
- Opposite canting angle behavior observed in LiNiPO4.
- Parameter dependencies on U and F4/F2 are characterized.

## Abstract

We performed comparative analysis for DFT+$U$ functionals to better understand their applicability to non-collinear magnetism. Taking LiNiPO$_4$ and Sr$_2$IrO$_4$ as examples, we investigated the results out of two formalisms based on charge-only density and spin density functional plus $U$ calculations. Our results show that the ground state spin order in terms of tilting angle is strongly dependent on Hund $J$. In particular, the opposite behavior of canting angles as a function of $J$ is found for LiNiPO$_4$. The dependence on the other physical parameters such as Hubbard $U$ and Slater parameterization $F^4/F^2$ is investigated. We also discuss the formal aspects of these functional dependences as well as parameter dependences. The current study provides useful information and important intuition for the first-principles calculation of non-collinear magnetic materials.