$V/t$ more than twice $V_c/t \sim 1$ where the system becomes a spin liquid in the undepleted case. Fig. \[Fig:phase\_diag1\](a) presents the behavior of $m_{tot}$ (squares; black solid line) as a function of $V/t$. Interestingly, the ferromagnetic order parameter is almost independent of hybridization $V/t$ over the range shown.

![(a) The order parameter $m_{tot}^{F}$ and its individual contributions $m_{d_{0}d_{0}}^{F}$ and $m_{ff}^{F}$ as well as (b) $m_{d_{0}d_{1}}^{AF}$, $m_{d_{1}f}^{AF}$ and $m_{d_{0}f}^{F}$ as functions of $V/t$. $m_{d_{1}d_{1}}^{F}$ is zero for all values of $V/t$. The curves are guides to the eye.[]{data-label="Fig:phase_diag1"}](phase_diagram.pdf)

The analysis of the short range spin correlations for different orbitals in Figs.\[Fig:local\_mom\] and \[Fig:Corr\_NN\] already provided some insight into where the magnetism “lives". Then, we proceed by investigating the individual contributions to magnetism, by means of Eq.. However, as discussed above, the correlation functions of $d_{0}$-$d_{1}$ and $d_{1}$-$f$ sites are always negative, thus we define $S^{AF}_{\alpha \gamma} = -S_{\alpha \gamma}$ for these pairs of sites; This corresponds to taking their antiferromagnetic contribution. By the same token, we define $S^{F}_{\alpha \gamma} = S_{\alpha \gamma}$ for those pairs of sites in which their correlation funtions are always ferromagnetic. As with the global structure factor, we perform a linear scaling for each channel [^1], 