Crucial role of d−d Coulomb correlations in the magnetocaloric ferrimagnets Gd6(Mn1−x

It is well-known that in elemental metals, the onsite Coulomb energy of transition-metal (TM) $d$-electrons, ${U}_{dd}$, is significantly smaller than ${U}_{ff}$ of $f$-electron rare-earth (RE) metals. Consequently, ${U}_{dd}$ is often neglected in RE-TM intermetallic alloys. In spite of the low value of ${U}_{dd}$ compared to ${U}_{ff}$, we quantify and clarify the important role of ${U}_{dd}$ in partially filled $d$-bands of RE-TM alloys. We investigate the electronic structure of a typical RE-TM ferrimagnetic series ${\mathrm{Gd}}_{6}{({\mathrm{Mn}}_{1\ensuremath{-}x}{\mathrm{M}}_{x})}_{23}$ (M = Fe, Co; $x=0.0,0.3$), which shows promising magnetocaloric properties. Resonant photoemission and constant initial state spectroscopy is used to identify the Mn $3d$, Fe $3d$, and Co $3d$ partial density of states (PDOS) in the valence band. The photon energy-dependent spectral evolution allows us to separate out the lower Hubbard band and the two-hole correlation satellites in the Mn, Fe, and Co $3d$ PDOS. Using the Cini-Sawatzky method, we determine an average ${U}_{dd}=2.1\ifmmode\pm\else\textpm\fi{}0.4\phantom{\rule{0.16em}{0ex}}\mathrm{eV}, 2.2\ifmmode\pm\else\textpm\fi{}0.4\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$, and $2.9\ifmmode\pm\else\textpm\fi{}0.4\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ for the Mn $3d$, Fe $3d$, and Co $3d$ states, respectively. The relatively larger ${U}_{dd}$ for Co compared to Fe $3d$ states results in lower DOS for the coherent feature at the Fermi level (${E}_{F}$) and higher DOS in the lower Hubbard band away from ${E}_{F}$ in ${\mathrm{Gd}}_{6}{({\mathrm{Mn}}_{0.7}{\mathrm{Co}}_{0.3})}_{23}$ compared to ${\mathrm{Gd}}_{6}{({\mathrm{Mn}}_{0.7}{\mathrm{Fe}}_{0.3})}_{23}$. To understand the role of Coulomb correlations on the electronic structure and magnetic properties, ab initio electronic structure calculations using density functional theory with onsite Coulomb correlations ($\mathrm{DFT}+U$) were carried out for the parent ${\mathrm{Gd}}_{6}{\mathrm{Mn}}_{23}$. The results show that the calculated Mn magnetic moments are consistent with experiments when ${U}_{\text{Mn}}^{\text{DFT}}=0.75\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$, corresponding to ${U}_{dd}=1.65\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ and ${J}_{dd}=0.9\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$. Further, using the calculated Gd and Mn PDOS and known photoionization cross-sections, the simulated ${\mathrm{Gd}}_{6}{\mathrm{Mn}}_{23}$ spectrum is fairly consistent with the experimental valence band spectrum. The results indicate the crucial role of d-d correlations in the presence of large f-f correlations for tuning the electronic structure and magnetic properties of RE-TM intermetallics.