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

Abstract

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 $REFeO_3$ 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. $NdFeO_3$, $ErFeO_3$, and $YbFeO_3$), 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 $HoFeO_3$; 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 $REFeO_3$. These results provide a unified explanation for the anomalous Zeeman splitting of CF ground states in $REFeO_3$.