Fig. 1: Dynamical stability of the spintronic Kapitza pendulum.
From: Dynamical stability by spin transfer in nearly isotropic magnets
a, Schematics of the mechanical Kapitza pendulum with and without an external drive. mg represents the gravitational force on the bob. b–d, Schematics of different magnetization switching and stability processes illustrated within the angular dependence of magnetic energy (U): field-induced switching (b), STT switching (c) and dynamical stability (d). θ is defined by the relative angle between the external magnetic field (Hext) and magnetic moment (M). See below for the mechanism of each process. e, Analogy between the Kapitza pendulum and dynamical stabilization by spin transfer in an isotropic magnet. The magnetic field provides a minimum and maximum of potential energy as the gravitational field does, and the STT plays the role of dynamical driving that controls their stability. Note that the arrows piercing through the conduction electrons (solid spheres) represent their spin pointing opposite to their magnetic moment. f, A typical solution of the stochastic LLG equation for a macrospin in an isotropic magnet. The initial condition is set at the south pole (red dot) and due to the anti-damping STT exceeding the Gilbert damping torque, the state precesses away from the field direction and settles around the inverted state (yellow dot). The coloured dots on the sphere have the corresponding potential energy values indicated in d.
