Rare-Earth Tetraborides RB$_4$: Analysis of Trends in the Electronic Structure

TL;DR

This study investigates the electronic structure of rare-earth tetraborides using advanced band theory methods, revealing bonding characteristics, the role of boron orbitals, and trends in 4f electron levels across the lanthanide series.

Contribution

It provides a detailed analysis of the electronic structure and bonding trends in RB4 compounds, highlighting the effects of lanthanide variation and cation valency on stability and electronic properties.

Findings

Identification of well-separated boron bonding and antibonding bands

Non-bonding 'dimer B' orbitals strongly hybridize with metal d states

Trends in 4f levels across the lanthanide series are characterized

Abstract

Both the basic electronic structure of tetraborides, and the changes across the lanthanide series in $R$B$_4$ ($R$ = rare earth) compounds, are studied using the correlated band theory LDA+U method in the all-electron Full Potential Local Orbital (FPLO) code. A set of boron bonding bands can be identified that are well separated from the antibonding bands. Separately, the ``dimer B'' $2p_z$ orbital is non-bonding ({\it viz.} graphite and MgB$_2$), and mixes strongly with the metal 4d or $5d$ states that form the conduction states. The bonding bands are not entirely filled even for the trivalent compounds (thus the cation $d$ bands have some filling), which accounts for the lack of stability of this structure when the cations are divalent (with more bonding states unfilled). The trends in the mean $4f$ level for both majority and minority, and occupied and unoccupied, states are presented and interpreted.