Quantitative moment study and coupling of 4 f rare earth and 3 d metal by transmitted electrons

We report a simultaneous investigation of $3d$ and $4f$ magnetic moments by exploring the $\mathrm{Fe}\ensuremath{-}{L}_{2,3}$ and $\mathrm{Dy}\ensuremath{-}{M}_{4,5}$ electron energy-loss edges of a $\mathrm{DyF}{\mathrm{e}}_{2}/\mathrm{YF}{\mathrm{e}}_{2}$ superlattice using the energy-loss magnetic chiral dichroism (EMCD) technique. Specific EMCD sum rules for ${M}_{4,5}$ edges were established and carefully applied to the dichroic signal at $\mathrm{Dy}\ensuremath{-}{M}_{4,5}$ edges, giving an orbital to the effective spin moment ratio of $5.1\ifmmode\pm\else\textpm\fi{}1.8$. With dynamic diffraction effects considered, the opposite signs of $\mathrm{Fe}\ensuremath{-}{L}_{3}$ and $\mathrm{Dy}\ensuremath{-}{M}_{5}$ dichroic peaks unambiguously indicate the antiparallel alignment of net Fe $3d$ and Dy $4f$ moments. The EMCD technique is shown to be an effective tool to locally characterize the $4f$ moment of rare earth elements and study $3d\ensuremath{-}4f$ moment coupling.