An imposed chemical potential gradient A ↑ = dµ ↑ /dx on a single fermionic species ("spin up") directly produces a gradient in the density dρ ↑ /dx across a lattice. We study here the induced density inhomogeneity dρ ↓ /dx in the second fermionic species ("spin down") which results from fermionic interactions U , even in the absence of a chemical potential gradient A ↓ = 0 on that species. The magnitude of dρ ↓ /dx acquired by the second species grows with U , while the magnitude of dρ ↑ /dx remains relatively constant, that is, set only by A ↑ . For a given A ↑ , 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, dρ ↓ /dx = −dρ ↑ /dx. A simple particle-hole transformation determines the related effect in the case of attractive interactions.