Abstract: A material can be locally etched with arbitrary changes in the direction of the etch. A ferromagnetic-material-including catalytic particle is employed to etch the material. A wet etch chemical or a plasma condition can be employed in conjunction with the ferromagnetic-material-including catalytic particle to etch a material through a catalytic reaction between the catalytic particle and the material. During a catalytic etch process, a magnetic field is applied to the ferromagnetic-material-including catalytic particle to direct the movement of the particle to any direction, which is chosen so as to form a contiguous cavity having at least two cavity portions having different directions. The direction of the magnetic field can be controlled so as to form the contiguous cavity in a preplanned pattern, and each segment of the contiguous cavity can extend along an arbitrary direction.