Magnetic hyperbolic metamaterial of high-index nanowires

We show that the axial component of the magnetic permeability tensor is resonant for a wire medium consisting of high-index epsilon-positive nanowires, and its real part changes the sign at a certain frequency. At this frequency the medium experiences the topological phase transition between the elliptic and hyperbolic type of dispersion. We show that the transition regime is characterized by an extremely strong dependence of the permeability on the wave vector. This implies very high density of electromagnetic states that results in the filamentary pattern and noticeable Purcell factor for a transversely oriented magnetic dipole.