Anisotropy of 4f states in 3d−4f single-molecule magnets

We have measured angular-dependent fluorescence-yield x-ray magnetic circular dichroism spectra on single crystals of the heterometallic $3d\ensuremath{-}4f$ 12-metallacrown-4 ${\mathrm{TbMn}}₄$ and ${\mathrm{DyMn}}₄$ complexes. Simulated spectra using crystal-field multiplet calculations reproduce the experimentally observed spectra. The orientation of the molecules causes linear dichroism spectra of the $4f$ absorption spectra. This natural linear dichroism shows the anisotropic charge distribution of the rare-earth $4f$ state in the tetragonal crystal field despite the small $4f$ crystal-field splitting. The magnetic moment of the molecule is dominated by the rare-earth moment revealing a considerably large contribution of orbital moment. From a sum-rule analysis of experimental and simulated x-ray magnetic circular dichroism, we determined corrected spin and orbital Dy moments at low temperature (14 K) within a magnetic field of 7 T. We find a significant angular dependence of the Dy magnetic moments, indicating the presence of fourth-order magnetic anisotropy.