  An imposed chemical potential gradient $A_\uparrow=d\mu_\uparrow/dx$ on a
single fermionic species ("spin up") directly produces a gradient in the
density $d\rho_\uparrow/dx$ across a lattice. We study here the induced density
inhomogeneity $d\rho_\downarrow/dx$ in the second fermionic species ("spin
down") which results from fermionic interactions $U$, even in the absence of a
chemical potential gradient $A_\downarrow=0$ on that species. The magnitude of
$d\rho_\downarrow/dx$ acquired by the second species grows with $U$, while the
magnitude of $d\rho_\uparrow/dx$ remains relatively constant, that is, set only
by $A_\uparrow$. For a given $A_\uparrow$, we find an interaction strength
$U_*$ above which the two density gradients are equal in magnitude. We also
evaluate the spin-spin correlations and show that, as expected,
antiferromagnetism is most dominant at locations where the local density is
half-filled. The spin polarization induced by sufficiently large gradients, in
combination with $U$, drives ferromagnetic behavior. In the case of repulsive
interactions, $d\rho_\downarrow/dx = -d\rho_\uparrow/dx$. A simple
particle-hole transformation determines the related effect in the case of
attractive interactions.
