Crystal field with Wannier functions: Application to rare-earth aluminates

TL;DR

This paper introduces an ab initio method using Wannier functions to calculate crystal field parameters, applied to rare-earth impurities in yttrium aluminate, revealing trends and hybridization effects with experimental validation.

Contribution

The paper presents a novel approach to compute crystal field parameters ab initio using Wannier functions, applicable to rare-earth doped materials.

Findings

Crystal field decreases with more 4f electrons.

Hybridization with oxygen ligands is significant.

Theoretical results agree with experimental data.

Abstract

A method to calculate the crystal field parameters {\it ab initio} is proposed and applied to trivalent rare earth impurities in yttrium aluminate and to Tb$^{3+}$ ion in TbAlO$_3$. To determine crystal field parameters local Hamiltonian expressed in basis of Wannier functions is expanded in a series of spherical tensor operators. Wannier functions are obtained by transforming the Bloch functions calculated using the density functional theory based program. The results show that the crystal field is continuously decreasing as the number of $4f$ electrons increases and that the hybridization of $4f$ states with the states of oxygen ligands is important. Theory is confronted with experiment for Nd$^{3+}$ and Er$^{3+}$ ions in YAlO$_3$ and for Tb$^{3+}$ ion in TbAlO$_3$ and a fair agreement is found.