Negative Refractive Index Ferromagnetic Materials with Negative Permeability at Zero Applied Magnetic Field

Negative magnetic permeability of ferromagnetic materials is studied in the microwave frequency region. The magnetic permeability is analyzed by employing the dynamic equation of motion of magnetization for different directions of the applied magnetic field with respect to crystalline axes. In the calculations, a very thin ferromagnetic layer with the cubic magneto-crystalline anisotropy energy is considered. It is found that there can be multiple regions of the field value in which the real component of the dynamic permeability becomes negative. In addition, the low-field region for negative permeability can be extended even to the zero external static magnetic field.