Resonant X-ray Scattering Study of Magnetic and Electric-quadrupole Order in U$_{0.75}$Np$_{0.25}$O$_2$

We have used element specific X-ray resonant scattering to investigate the M edge resonances in a single crystal of \\unpo. Earlier neutron diffraction and M\\\"{o}ssbauer studies had shown the presence of long-range AF order below T$_{N}$ = 19 K, with sizeable magnetic moment both on the U and the Np ions. RXS results confirm the presence of an ordered dipole magnetic moment on the Np ions, but also reveal the presence of an anti-ferro arrangement of the electric quadrupole moments on both U and Np ions, with the same propagation vector that defines the magnetic structure. From the azimuthal dependence of the intensities we are able to determine the exact configuration of the quadrupolar ordering. The intensities of Bragg peaks associated with magnetic dipole and electric quadrupole order have different temperature dependences. On cooling below T$_{N}$, the magnetic dipole order develops faster on the uranium ions, with magnetic order on the Np ions increasing at a lower rate. At the same temperature, quadrupolar order on both the U and Np ions occurs along with an internal Jahn-Teller lattice distortion