Collective spin modes in magnetized spin-orbit coupled 3D polar metals

We study collective spin modes emerging in spin-orbit coupled 3D polar metals due to electron-electron and electron-phonon interactions in the presence of Zeeman field. Zeeman splitting (generated by applied magnetic field or magnetic doping) leads to the emergence of collective electronic modes already at weak coupling. These modes possess unusual dispersion characteristics that can be controlled by magnetic field orientation. We discuss their experimental signatures and behavior in polar metals close to a quantum critical point.