Theoretical study of XAS and XMCD spectra for the field-induced valence transition in Eu compounds

It is known that some of Eu compounds, such as EuNi₂(Si _1-xGe_x)₂, show the valence mixing phenomenon between a nonmagnetic state Eu³⁺ (4f⁶) and a magnetic state Eu²⁺ (4f⁷). Recently, the field-induced valence transition of EuNi₂(Si_1-xGe_x)₂ (x = 0:82) has been observed, using X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) under high magnetic fields. Both spectra show two peaks corresponding to the two valence states, although the Eu²⁺ state is magnetic while the Eu³⁺ state is nonmagnetic. In order to understand the phenomenon, we calculate XAS and XMCD spectra based on an effective model, in which the two valence states of Eu and the matrix element between them due to the hybridization of a 4f electron with a conduction electron are taken into consideration. Reproducing XAS and XMCD spectra as a function of the field, we conclude that XAS and XMCD can give detailed information on the degree of the mixing states as well as the valence selective magnetization through the polarization of the 5d states due to that of the 4f states. Thus, the magnetization process of each valence state as a function of the field is discussed in detail in connection with the intensity of XMCD.