A method of thermomagnetically processing a material includes disposing a workpiece within a bore of a magnet; exposing the workpiece to a magnetic field of at least about 1 Tesla generated by the magnet; and, while exposing the workpiece to the magnetic field, applying heat energy to the workpiece at a plurality of frequencies to achieve spatially-controlled heating of the workpiece. An apparatus for thermomagnetically processing a material comprises: a high field strength magnet having a bore extending therethrough for insertion of a workpiece therein; and an energy source disposed adjacent to an entrance to the bore. The energy source is an emitter of variable frequency heat energy, and the bore comprises a waveguide for propagation of the variable frequency heat energy from the energy source to the workpiece.