This disclosure describes microfluidic devices that include one or more magnets, each magnet being operable to emit a magnetic field; and a magnetizable layer adjacent to the one or more magnets, in which the magnetizable layer is configured to induce a gradient in the magnetic field of at least one of the magnets. For example, the gradient can be at least 103 T/m at a position that is at least 20 μm away from a surface of the magnetizable layer. The magnetizable layer includes a first high magnetic permeability material and a low magnetic permeability material arranged adjacent to the high magnetic permeability material. The devices also include a microfluidic channel arranged on a surface of the magnetizable layer, wherein a central longitudinal axis of the microfluidic channel is arranged at an angle to or laterally offset from an interface between the high magnetic permeability material and the low magnetic permeability material.