Treatment of 4f states of the rare-earths: the case study of TbN

TL;DR

This study compares various computational methods for treating 4f electrons in TbN, assessing their accuracy in predicting structural, elastic, magnetic, and spectral properties, and highlights the importance of method choice.

Contribution

It systematically evaluates the effects of different DFT-based approaches on the properties of TbN, revealing new insights into the stability of cubic symmetry and the spectral characteristics.

Findings

LDA+U predicts cubic symmetry as energetically favored over Hund's rules state.

Hubbard-I approximation best reproduces experimental magnetic properties.

Method sensitivity significantly affects shear constant predictions.

Abstract

The lattice constant, bulk modulus and shear constant of TbN are calculated by means of density functional theory (DFT) in the local density approximation (LDA) and generalized gradient approximation (GGA), with 4f-states treated as valence electrons or core electrons. In addition, local Coulomb repulsions U are treated both statically as in the LDA+U approach and dynamically as in the dynamical mean-field theory (DMFT) in the Hubbard-I approximation. It is shown that all methods, except DFT-LDA with 4f electrons treated as either valence states, produce lattice constants and bulk moduli in good agreement with experiment. In the LDA+U approach multiple minima are found, and we focus on the competition between a state with cubic symmetry and a state obtained from atomic Hund's rules. We find the state with cubic symmetry to be 0.59 eV lower in energy than the Hund's rules state, while the opposite was obtained in previous literature. The shear constant is shown to be rather sensitive to the theoretical method used, and the Hund's rules state obtained in LDA+U is found to be unstable towards tetragonal shear. As to the magnetism, we find that the calculation based on the Hubbard-I approximation reproduces observations with the best accuracy. Finally, the spectral properties of TbN are discussed, together with the general applicability of the different methods in describing rare-earth elements and compounds.