Table 2 Angular part of the integration of ϵx, denoted as \(\Omega ({\varepsilon }_{m}^{{\rm{x}}})\), for the f1 configuration, along with the exchange-correlation energy \({E}_{m}^{\,\text{xc}\,}\) and total energy \({E}_{m}^{\,\text{Tot}\,}\) of free Tb atoms calculated using DFT+U

From: Importance of enforcing Hund’s rules in density functional theory calculations of rare earth magnetocrystalline anisotropy

m

0

± 1

± 2

± 3

\(\Omega ({\epsilon }_{m}^{{\rm{x}}})\)

−0.5314

−0.4903

−0.4801

−0.4963

\(\Delta \Omega ({\epsilon }_{m}^{{\rm{x}}})\)

0

0.0411

0.0513

0.0351

\({E}_{m}^{\,\text{xc}\,}\) (meV)

0

406.1

757.3

689.0

\({E}_{m}^{\,\text{Tot}\,}\) (meV)

0

32.9

73.2

497.4

  1. \(\Delta \Omega ({\epsilon }_{m}^{{\rm{x}}})\) represents the \(\Omega ({\epsilon }_{m}^{{\rm{x}}})\) values relative to the \(\left\vert m=0\right\rangle\) state. Similarly, Tb \({E}_{m}^{\,\text{xc}\,}\) and \({E}_{m}^{\,\text{Tot}\,}\) are calculated relative to the \(\left\vert m=0,\downarrow \right\rangle\) state. SOC is not included in the DFT+U calculations.
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