# Charge density functional plus $U$ calculation of lacunar spinel GaM$_4$Se$_8$ (M = Nb, Mo, Ta, and W)

## TL;DR

This study uses charge density functional plus U calculations to validate the molecular J_eff=1/2 and 3/2 states in lacunar spinel GaM4Se8 compounds, supporting the existence of these states with implications for future research.

## Contribution

It demonstrates that LDA+U calculations confirm the molecular J_eff states in GaM4Se8, providing a theoretical basis for their validity beyond previous spin-polarized approaches.

## Key findings

- J_eff=1/2 and 3/2 states remain valid in LDA+U calculations
- Charge-only density causes minor differences in band structure
- Supports the existence of molecular J_eff states in these materials

## Abstract

Charge density functional plus $U$ calculations are carried out to examine the validity of molecular $J_\text{eff}$=1/2 and 3/2 state in lacunar spinel GaM$_4$X$_8$ (M = Nb, Mo, Ta, and W). With LDA (spin-unpolarized local density approximation)$+U$, which has recently been suggested as the more desirable choice than LSDA (local spin density approximation)$+U$, we examine the band structure in comparison with the previous prediction based on the spin-polarized version of functional and with the prototypical $J_\text{eff}$=1/2 material Sr$_2$IrO$_4$. It is found that the previously suggested $J_\text{eff}$=1/2 and 3/2 band characters remain valid still in LDA$+U$ calculations while the use of charge-only density causes some minor differences. Our result provides the further support for the novel molecular $J_\text{eff}$ state in this series of materials, which can hopefully motivate the future exploration toward its verification and the further search for new functionalities.