Dynamically stable negative-energy states induced by spin-transfer torques

We investigate instabilities of the magnetic ground state in ferromagnetic metals that are induced by uniform electrical currents, and, in particular, go beyond previous analyses by including dipolar interactions. These instabilities arise from spin-transfer torques that lead to Doppler-shifted spin waves. For sufficiently large electrical currents, spin-wave excitations have negative energy with respect to the uniform magnetic ground state while remaining dynamically stable due to dissipative spin-transfer torques. Hence, the uniform magnetic ground state is energetically unstable but is not able to dynamically reach the new ground state. We estimate this to happen for current densities $j\ensuremath{\gtrsim}(1\ensuremath{-}D/{D}_c){10}¹³\mathrm{A}/{\mathrm{m}}²$ in typical thin-film experiments, with $D$ the Dzyaloshinskii-Moriya interaction constant, and ${D}_c$ the Dzyaloshinskii-Moriya interaction that is required for spontaneous formation of spirals or skyrmions. The critical current density can be made arbitrarily small for ultrathin-film thicknesses at the order of nanometers due to surface and interlayer effects. From an analog gravity perspective, the stable negative-energy states are an essential ingredient to implement event horizons for magnons---the quanta of spin waves---giving rise to, e.g., Hawking radiation, and can be used to amplify spin waves in a so-called black-hole laser.