Triakontadipole and high-order dysprosium multipoles in the   antiferromagnetic phase of DyB$_2$C$_2$
  Resonant soft x-ray Bragg diffraction at the Dy M$_{4,5}$ edges has been used to study Dy multipoles in the combined magnetic and orbitally ordered phase of DyB$_2$C$_2$. The analysis incorporates both the intra-atomic magnetic and quadrupolar interactions between the 3d core and 4f valence shells. Additionally, we introduce to the formalism the interference of magnetic and nonmagnetic oscillators. This allows a determination of the higher order multipole moments of rank 1 (dipole) to 6 (hexacontatetrapole). The strength of the Dy 4f multipole moments have been estimated at being between 7 and 78 % of the quadrupolar moment. 
A. J. Princep, A. M. Mulders, U. Staub, V. Scagnoli, T. Nakamura, A.   Kikkawa, S. W. Lovesey, E. Balcar
cond-mat.str-el