Anisotropy of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>4</mml:mn><mml:mi>f</mml:mi></mml:mrow></mml:math> states in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>3</mml:mn><mml:mi>d</mml:mi><mml:mo>?</mml:mo><mml:mn>4</mml:mn><mml:mi>f</mml:mi></mml:mrow></mml:math> 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 using crystal-field multiplet calculations reproduce experimentally observed spectra. The orientation molecules causes linear $4f$ absorption This natural shows anisotropic charge distribution rare-earth state in tetragonal crystal field despite small splitting. moment molecule is dominated by revealing a considerably large contribution orbital moment. From sum-rule analysis experimental simulated dichroism, we determined corrected spin Dy moments at low temperature (14 K) within 7 T. find significant angular dependence moments, indicating presence fourth-order anisotropy.