We note that the corresponding relaxation time is determined by only linear parameters, whereas the orbit radius (7) depends on ratio

of the nonlinear and linear model parameters. The solution of Equation 8 is plotted in Figure 3 as a function of time along with micromagnetic simulations for circular Py dot with thickness L = 7 nm and radius R = 100 nm. The vortex was excited by in-plane field pulse during approximately the first 5 ns, and then the vortex core approached the stationary orbit of radius u 0(J). We estimated u(0) after the pulse as u(0) = 0.1 and plotted the solid lines without see more any fitting except using the simulated value of the critical current J c1. Overall agreement of the calculations by Equation 8 and simulations is quite good, especially for large times t ≥ 3τ +, although the calculated relaxation time τ + is smaller than the simulated one due to overestimation of within TVA. The typical simulated ratio J c2/J c1 ≈ 1.5; therefore, minimal τ + ≈ 20 to 30 ns. But the transient time of saturation of u(t, J) is about of 100 ns and can reach several microseconds at J/J c1 < 1.1. The simulated value of λ = 0.83, whereas the

analytic theory based on TVA yields the close value of λ(J c1) = 0.81. Figure 3 Instant vortex core orbit radius selleck vs. time for different currents. The results are within the current range of the stable vortex steady-state orbit, J c1 < J < J c2 (5.0 MA/cm2). The nanodot thickness is L = 7 nm and the radius is R = 100 nm. Solid lines are calculations of the vortex transient dynamics

by Equation 8, and symbols (black squares, red circles, green triangles, and blue rhombi) mark the simulated points. Typical experiments on the vortex excitations during in https://www.selleckchem.com/products/sn-38.html nanopillars are conducted at room temperature T = 300 K without initial field pulse, i.e., a thermal level u(0) should be sufficient to start vortex core motion to a steady orbit. To find the thermal amplitude of u(0), we use the well-known relation between static susceptibility of the system and magnetization fluctuations . The in-plane components are , and M = ξM s s, where ξ = 2/3 within TVA [26]. This leads to the simple relation . It is reasonable to use for interpretation of the experiments. u T (0) ≈ 0.05 (5 nm in absolute units) for the dot made of permalloy with L = 7 nm and R = 100 nm. The nonlinear frequency coefficient N(β, R, J) = κ′(β, R, J)/κ(β, R, J) is positive (because of κ, κ′ >0 for typical dot parameters), and it is a strong function of the dot geometrical sizes L and R and a weak function of J. For the dot radii R > > L e , N(β, R, 0) ≈ 0.21 - 0.25 (the magnetostatic limit, see inset of Figure 2). If R > > L e and β → 0, then N(β, R, 0) ≈ 0.25 [14].