The ratio χ 1/χ 0 = O(c 2 u 2) < < 1, therefore, the nonlinear parameter χ 1 can be neglected. The
buy GSK126 statement about linearity of the ST-force agrees also with our simulations and the micromagnetic simulations performed in [12, 19]. The coefficient λ(J) describes nonlinearity of the system and decreases smoothly with the current J increasing. Numerical method We have simulated the vortex motion in a single permalloy (Fe20Ni80 alloy, Py) circular nanodot under the influence of a spin-polarized dc current flowing through it. Micromagnetic simulations of the spin-torque-induced magnetization dynamics in this system were carried out with the micromagnetic simulation package MicroMagus (General BYL719 Numerics Research Lab, Jena, Germany) . This package solves numerically the LLG equation of the magnetization motion using the optimized version of the adaptive (i.e., with the time step control) Runge-Kutta method. this website Thermal fluctuations have been neglected in our modeling, so that the simulated dynamics corresponds to T = 0. Material parameters for Py are as follows: exchange stiffness constant A = 10-6
erg/cm, saturation magnetization M s = 800 G, and the damping constant used in the LLG equation α G = 0.01. Permalloy dot with the radius R = 100 nm and thickness L = 5, 7, and 10 nm was discretized in-plane into 100 × 100 cells. No additional discretization was performed in the direction perpendicular TCL to the dot plane, so that the discretization cell size was 2 × 2 × L nm3. In order to obtain the vortex core with a desired polarity (spin polarization direction of dc current and vortex core polarity should have opposite directions in order to ensure the steady-state vortex precession) and to displace the vortex core from its equilibrium position in the nanodot
center, we have initially applied a short magnetic field pulse with the out-of-plane projection of 200 Oe, the in-plane projection H x = 10 Oe, and the duration Δt = 3 ns. Simulations were carried out for the physical time t = 200 to 3,000 ns depending on the applied dc current because for currents close to the threshold current J c1, the time for establishing the vortex steady-state precession regime was much larger than for higher currents (see Equation 8 below). Results and discussion Calculated analytically, the vortex core steady orbit radius in circular dot u 0(J) as a function of current J is compared with the simulations (see Figure 1). There is no fitting except only taking the critical current J c1 value from simulations.