The vortex state is characterized by in-plane curling magnetization and a nanosize vortex core AZD2014 order with out-of-plane

magnetization. Since the vortex state of magnetization was discovered as the ground state of patterned magnetic dots, the dynamics of vortices have attracted considerable attention. Being displaced from its equilibrium position in the dot center, the vortex core reveals sub-GHz frequency oscillations with a narrow linewidth [2, 7, 12]. The oscillations of the vortex core are governed by a competition of the gyroforce, Gilbert damping force, spin transfer torque, and restoring force. The restoring force is determined by the vortex confinement in a nanodot. Vortex core oscillations with small amplitude can be well described in the linear regime, but for increasing find more of the STNO output power, a large-amplitude motion has to be excited. In the regime of large-amplitude spin transfer-induced vortex gyration, it is important to take into account nonlinear contributions to all the forces acting on the moving vortex. The analytical description and micromagnetic simulations of the magnetic field and spin transfer-induced vortex dynamics in the nonlinear regime have been proposed by several groups [12–22], but the results are still contradictory. It is unclear to what extent a standard nonlinear oscillator model [13] is applicable to the vortex STNO, how to calculate

the nonlinear parameters, and how the PF-6463922 nmr parameters depend on the nanodot sizes. Figure 1 Magnetic vortex dynamics in a thin circular FeNi nanodot. Vortex core steady-state orbit radius u 0(J) in the circular FeNi nanodot of thickness L = 7 nm and radius R = 100 nm vs. current J perpendicular to the dot plane. Solid black lines are

calculations by Equation 7; red circles mark the simulated points. Inset: sketch of the cylindrical vortex state dot with the core position X and used system of coordinates. In this paper, we show that a generalized Thiele approach [23] is adequate to describe the magnetic vortex motion in the nonlinear regime and calculate the nanosize vortex core transient and steady orbit dynamics in circular nanodots excited by spin-polarized current via spin angular momentum transfer effect. Metformin datasheet Methods Analytical method We apply the Landau-Lifshitz-Gilbert (LLG) equation of motion of the free layer magnetization , where m = M/M s, M s is the saturation magnetization, γ > 0 is the gyromagnetic ratio, H eff is the effective field, and α G is the Gilbert damping. We use a spin angular momentum transfer torque in the form suggested by Slonczewski [24], τ s  = σJ m × (m × P), where σ = ℏη/(2|e|LM s ), η is the current spin polarization (η ≅ 0.2 for FeNi), e is the electron charge, P is direction of the reference layer magnetization, and J is the dc current density. The current is flowing perpendicularly to the layers of nanopillar and we assume . The free layer (dot) radius is R and thickness is L.