Spin-Torque Nano-Oscillator (STNO)

The Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation: dm/dt = −γm×H_eff + αm×(dm/dt) + (σI)m×(m×p̂). The spin-transfer torque (Slonczewski term) can overcome Gilbert damping, driving sustained magnetization precession — a spin-torque oscillator. Above a critical current I_c, self-oscillation begins; frequency is tunable via field and current. STNOs are nanoscale microwave generators (GHz). The sphere shows m(t) trajectory; time plot shows m_z oscillation.