Strongly constrained and appropriately normed density functional theory exchange-correlation functional applied to rare earth oxides

Density functional theory (DFT) is one of the main tools for studying the electronic structure of solids and molecules. Nevertheless, one of the main drawbacks of the implementation of DFT is the so-called self-interaction error (SIE) that can yield undesired delocalization errors and ultimately results in the prediction of metals instead of experimentally observed insulators. These SIEs can be amended by using more evolved exchange-correlation functionals than standard local density approximation such as the recent meta-generalized gradient approximation strongly constrained and appropriately normalized (SCAN) functional that is successful in describing electronic properties of $3d$ transition metal oxides. Nevertheless, the ability of such a functional to describe electronic properties of materials involving more localized states such as $4f$ orbitals is rather elusive. Here, we show that, even though SCAN can sometimes predict the insulating character of some compounds, it often fails in predicting the correct band edge orbital character of insulators. By comparing our SCAN results with benchmark simulations obtained with more accurate hybrid DFT calculations, we ascribe this failure to insufficiently amended SIEs by SCAN that results in an underestimation of Hund's splitting associated with $4f$ states. Thus, although appropriate for $3d$ transition metal elements, the SCAN functional is not yet a sufficient platform for studying electronic properties of materials involving rare-earth elements where $4f$ states play a key role in the properties.

Figure 1

Projected density of states on Ti $d$ (red line), O $p$ (dashed blue line), and Eu $4f$ (orange area) in $\mathrm{EuTi}{\mathrm{O}}_3$ using the meta-generalized gradient approximation (GGA) strongly constrained and appropriately normalized (SCAN) and HSE06 functionals and involving or not the $4f$ states in the simulations.

Figure 2

Projected density of states on Ti $d$ (red line), O $p$ (dashed blue line), and Gd $4f$ (orange area) in $\mathrm{GdTi}{\mathrm{O}}_3$ using the meta-generalized gradient approximation (GGA) strongly constrained and appropriately normalized (SCAN) and HSE06 functionals and involving or not the $4f$ states in the simulations.

Figure 3

Projected density of states on Ti and Fe $d$ (red line), O $p$ (dashed blue line), and Pr and Dy $4f$ (orange area) in $\mathrm{PrCr}{\mathrm{O}}_3$ (left panels) and $\mathrm{DyFe}{\mathrm{O}}_3$ (right panels) using the meta-generalized gradient approximation (GGA) strongly constrained and appropriately normalized (SCAN) and HSE06 functionals and involving or not the $4f$ states in the simulations.

Figure 4

Unfolded band structure to the high-symmetry primitive $P_4/mmm$ cell of $\mathrm{PrNi}{\mathrm{O}}_2$ (top panels) and $\mathrm{LaNi}{\mathrm{O}}_2$ (lower panels) using the meta-generalized gradient approximation (GGA) strongly constrained and appropriately normalized (SCAN) (left panels) and hybrid HSE06 (right panels) functionals. Calculations are performed with C-type antiferromagnetic (AFMC) order. Coordinates of the high-symmetry points are $\mathrm{\Gamma }$(0,0,0), $X$($\frac{1}{2}$,0,0), $M$($\frac{1}{2}, \frac{1}{2}$,0), $Z$(0,0,$\frac{1}{2}$), $A$($\frac{1}{2}, \frac{1}{2}, \frac{1}{2}$), and $R$($\frac{1}{2}$,0,$\frac{1}{2}$).