Unusual magnetism of Gd$_{5}$Ge$_{4}$ with non magnetic rare earths substitutions*

We present first principles and experimental studies on the small substitutions of Gd atoms by Lu, La, Y, and Sc atoms in Gd$_{5}$Ge$_{4}$. While replacing the Gd atoms located inside the slabs with the Lu or Y atoms leads to a substantial loss of ferromagnetism, the identical substitutions of other Gd locations preferred by La atoms have essentially no effect on the magnetostructural transitions. On the other hand, the Sc atoms prefer the same locations as the Lu and Y atoms. This substitution, however, changes the crystal structure of Gd$_{5}$Ge$_{4}$ from Sm$_{5}$Ge$_{4}$ type to Pu$_{5}$Rh$_{4 }$type at 25{\%} of Sc which was not observed with the former substitutions. The Pu$_{5}$Rh$_{4}$-type has structural parameters that are intermediate between the Gd$_{5}$Si$_{4}$ and Sm$_{5}$Ge$_{4}$ types. The exchange interactions in this substitution are positive which indicates that the Sc substituted Gd$_{5}$Ge$_{4}$ has the ferromagnetic ground state.