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

A method to calculate the crystal field parameters is proposed and applied to trivalent rare-earth impurities in yttrium aluminate and to Tb3+ ion in TbAlO3. To determine crystal field parameters local Hamiltonian expressed in the 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. The method contains a single adjustable parameter characterizing the 4f-ligand charge transfer. Theory is confronted with experiment for Nd3+ and Er3+ ions in the YAlO3 matrix and for the Tb3+ ion in TbAlO3, and a good agreement within a few meV is found.