Hyperbolic Spin Waves in 3D Magnetic Polar Metals

We demonstrate the emergence of particle-hole collective modes with hyperbolic dispersion in spin-orbit coupled polar metals in applied magnetic field. These novel collective modes are shown to exist for arbitrarily weak repulsive interactions due to the quasi two-dimensional nature of the low-energy particle-hole excitation spectrum; furrthermore these modes support localized solutions and carry a finite spin along the polar axis. We discuss these excitations for possible spintronic applications including optical spin current generation.