A method of forming a TAMR (Thermal Assisted Magnetic Recording) write head that uses the energy of optical-laser generated edge plasmons in a plasmon antenna to locally heat a magnetic recording medium and reduce its coercivity and magnetic anisotropy. The method incorporates forming a magnetic core within the plasmon antenna, so the antenna effectively becomes an extension of the magnetic pole and produces a magnetic field whose maximum gradient overlaps the region being heated by the edge plasmons generated in the conducting layer of the antenna surrounding the antenna's magnetic core.