Single crystals of mixed uranium-plutonium dioxides have been grown by means of a chemical vapor transport reaction and characterized by x-ray diffraction on bulk and powdered single crystals. Magnetization and susceptibility data were taken using a commercial superconducting quantum interference device. Characteristic ordering temperatures have been determined as well as paramagnetic Curie temperatures and effective magnetic moments. Departures of the reciprocal susceptibility as a function of temperature from linearity have been treated in detail based on a model of vibronic interactions introduced to explain the gross features of susceptibility measurements on thorium-diluted ${\mathrm{UO}}_{2}$ [Sasaki and Obata, J. Phys. Soc. Jpn. 28, 1157 (1970)]. The influence of spin-lattice interactions causes a certain shape of the observed $1/\ensuremath{\chi}$ vs T curves from which we are able to suggest different mechanisms for the interactions as a function of the constituent's concentrations. From our susceptibility measurements characteristic parameters have been calculated using a model of tetragonal vibrational modes of the oxygen cage surrounding each uranium ion. These include specific coupling parameters G, mode characteristic temperatures ${T}_{\ensuremath{\omega}},$ and molecular-field constants $\ensuremath{\lambda}.$
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