  CeMnNi$_4$ exhibits an unusually large spin polarization, but its origin has
baffled researchers for more than a decade. We use bulk sensitive hard x-ray
photoelectron spectroscopy (HAXPES) and density functional theory based on the
Green's function technique to demonstrate the importance of electron-electron
correlations of both the Ni 3$d$ ($U_{Ni}$) and Mn 3$d$ ($U_{Mn}$) electrons in
explaining the valence band of this multiply correlated material. We show that
Mn-Ni anti-site disorder as well as $U_{Ni}$ play crucial role in enhancing its
spin polarization: anti-site disorder broadens a Ni 3$d$ minority-spin peak
close to the Fermi level ($E_F$), while an increase in $U_{Ni}$ shifts it
towards $E_F$, both leading to a significant increase of minority-spin states
at $E_F$. Furthermore, rare occurrence of a valence state transition between
the bulk and the surface is demonstrated highlighting the importance of HAXPES
in resolving the electronic structure of materials unhindered by surface
effects.
