Giant shifts of crystal-field excitations in ErFeO3 driven by internal magnetic fields

Crystal-field excitations in transition-metal oxides where -rare-earth elements locate in the space between the transition-metal-oxide tetrahedra and octahedra, are assumed to be robust with respect to external perturbations such as temperature. Using inelastic neutron-scattering experiments, a giant shift of the energy of the lowest crystal-field excitation of Er$^{3+}$ ($^{4}$I$_{15/2}$) in ErFeO$_3$ from 0.35 meV to 0.75 meV was observed on cooling from 10K to 1.5K through the magnetic ordering temperature of Er$^{3+}$ at 4.1 K. A crystal-field model was proposed to explain the observed crystal field excitations in this work. The model indicates the lowest-energy crystal-field excitation in ErFeO$_3$ is the first Kramers doublet above the ground state. Its energy substantially shifts by the internal field induced by the ordered Er$^{3+}$ magnetic moments. Further magnetic-field-dependent measurements provide strong supportive evidence for this scenario. By fitting the external magnetic-field dependency of the crystal-field excitation energy, the internal field generated by Er$^{3+}$ magnetic moments was derived to be ~0.33meV. The result indicates that the internal field of Er$^{3+}$ magnetic moments contribute to the energy shift of the crystal-field excitations. The giant energy shift under fields could be attributed to the anisotropy of the large effective g-factor.