one of these bands is dispersionless, a feature which is intimately tied to the appearance of ferromagnetism. (Random) site depletion of tight-binding Hamiltonians has also been used to understand the effects of the substitution of nonmagnetic atoms for magnetic ones, for example the replacement of Cu by Zn in cuprate materials.[@Xiao88; @Keimer92; @Mahajan94; @Julien00] In cases where the underlying geometry contains triangular lattice coordination, depletion can aid AF behavior by reducing frustration,[@coles87] eg in CeAl$_3$. More complex cases, such as depletion in the PAM seems relevant to understand the formation of magnetism in heavy fermion materials. In this case, mean-field and perturbation theory[@Potthoff14; @Potthoff15_2; @Seki16] have provided evidence of a ferromagnetic ground state.

In view of this, we investigate the combination of these two avenues, a PAM which [*begins*]{} already with two bands, but is then subject to site depletion. Our main conclusion is that depletion can drive the PAM into a magnetically ordered state, even for parameter choices which are deep in the singlet phase for the undepleted lattice. In addition to obtaining its magnetic phase diagram quantitatively, we will show that an unusual property develops in which the ordered regime is also compressible.

The organization of this paper 