We developed a method to experimentally quantify the fourth-order multipole moment of the rare-earth 4 f orbital. Linear dichroism (LD) in the Er 3d5=2 core-level photoemission spectra of cubic ErCo2 was measured using bulksensitive hard X-ray photoemission spectroscopy. Theoretical calculation reproduced the observed LD, and the result showed that the observed result does not contradict the suggested
3 8 ground state. Theoretical calculation further showed a linear relationship between the LD size and the size of the fourth-order multipole moment of the Er 3+ ion, which is proportional to the expectation value hO0 4 þ 5O4 4i, where Om n are the Stevens operators. These analyses indicate that the LD in 3d photoemission spectra can be used to quantify the average fourth-order multipole moment of rare-earth atoms in a cubic crystal electric field.