This work bridges two gaps in the magnetic separation of rare-earth ions. (1) A material property database is provided for the solutal expansion coefficient and the magnetic susceptibility of 11 out of 17 trivalent rare-earths. (2) A novel protocol is developed to enhance and resolve the magnetic term of the Kelvin force. For that purpose, an assembly of partition magnets is created where the individual magnets function in the first quadrant of their magnetic hysteresis loop. The mutual reinforcement is quantified in a particle magnetic levitation system. Thus, compared to exisiting magnetic assemblies, an enhancement in â B/(2μ0â »â z) as high as 2 orders of magnitude is realized that covers 90% of the normalized spatial scale and requires 1 order of magnitude less magnet mass. Modeling the energy density field makes it possible to quantify the equilibrium position of the particle cloud at rest, which is attained via magnetophoresis of the particles regardless of their initial position. This enables the magnetic trapping and manipulation of particles with small hydrodynamic diameters. Optically tracking the transient magnetophoresis enables a high-fidelity, sub-mm resolution of â B2/(2μ0â »â z) which is further used to quantify the magnetic susceptibility of Ho(III), Tb(III), Er(III), and Gd(III).