Magnetic-field-induced valence change in Eu(Co1−xNix)2P2 up…

The solid solution 122 compounds, Eu(Co$_{1-x}$Ni$_{x}$)$_{2}$P$_{2}$, show valence transition between divalent state and intermediate valence states at Eu, which is firmly correlated to multiple degrees of freedom in the solid such as the isostructural transition between the collapsed tetragonal (cT) and uncollapsed tetragonal (ucT) structures, $3d$ magnetism, and the formation of P-P dimers. To gain insights into the correlated behavior, we investigate the effect of high magnetic fields on the samples of $x = 0.4$ and $0.5$ using magnetostriction and magnetization measurements up to 60 T. The samples are in the Eu valence fluctuating regime, where the possible structural transition from cT to ucT may be induced by the Eu valence change under the magnetic fields. For both samples, magnetostriction smoothly increases with increasing magnetic fields. The behavior is in good agreement with the calculated results using the interconfigurational fluctuation (ICF) model that describes the valence change. This indicates that $\Delta L$ represents the change of the Eu valence state in these compounds. Magnetization curves for both compounds show good agreement with the ICF model at high magnetic fields. In contrast, in the low magnetic field region, magnetization curves do not agree with the ICF model. These results indicate that the Eu valence changes manifest themselves in the magnetization curves at high magnetic fields and that the magnetism of the $3d$ electrons manifests itself in the magnetization at low magnetic fields. Hence, we conclude that the valence change occurs within the Eu valence fluctuation regime coupled with the cT structure. Thereby, we believe that the transition to ucT structure which is firmly coupled with the divalent Eu state does not occur within the magnetic field range of the present study. (Continued)