Internal and External Field Effects upon Crystal Field Excitations in REFeO${}_3$ (RE = Nd${}^{3+}$, Er${}^{3+}$, Yb${}^{3+}$, Pr${}^{3+}$, and Ho${}^{3+}$)

We systematically investigated crystal-field (CF) excitations of Kramers (Nd${}^{3+}$, Er${}^{3+}$, Yb${}^{3+}$) and non-Kramers (Pr${}^{3+}$, Ho${}^{3+}$) rare-earth ions in $REFe{O}_3$ using optimized CF simulations. Internal magnetic fields from the Fe${}^{3+}$ and RE${}^{3+}$ sublattices split the ground-state doublets of all Kramers ions (e.g. $NdFe{O}_3$, $ErFe{O}_3$, and $YbFe{O}_3$), generating low-energy excitations around 1 meV. In non-Kramers systems, low-energy excitations arise only when the ground state forms an accidental pseudo-doublet, as observed for Ho${}^{3+}$ in $HoFe{O}_3$; such pseudo-doublets exhibit field-induced splitting analogous to Kramers ions. In contrast, true singlet ground states, exemplified by Pr${}^{3+}$, show no zero-field splitting. Strong anisotropies are found in both internal- and external-field responses of the CF excitations in these $REFe{O}_3$. These results provide a unified explanation for the anomalous Zeeman splitting of CF ground states in $REFe{O}_3$.