Pico- and nanosecond synchronized nonlinear magnetization dynamics of an isotropic nanomagnet under sinusoidal linear excitation

Nanometric magnetic materials are of technological interest for applications in devices of smaller sizes and with ultrafast responses to electromagnetic excitation, for example, microwaves. In spintronics and communication technology, nano- and picosecond responses are searched for. We calculate numerically and analyze in detail the nonlinear dynamics that emerge from the Landau–Lifshitz equation with nano- and picosecond resolution. The magnetization of an isotropic (spherical) ferromagnetic nanoparticle is treated with unrestricted degrees of freedom θ and ϕ and with no anisotropies. The nanoparticle is immersed in a constant field and an oscillating, orthogonal microwave field H1(ωt). We report numerical calculations of nano- and picosecond dynamics. We use the Landau–Lifshitz equation with damping term α, static magnetic field H0, and microwave magnetic field H1 for vector magnetization M → (θ,φ,t). We observe pico- and nanoseconds oscillations of θ and φ. We find ultrafast oscillations with ±0.1° and 0.2° amplitude and picosecond periods immersed in the angular motions of θ (t) and ϕ ( t ) . Moreover, from the very start, these oscillations, θ (t) and ϕ ( t ) , are part of the nonlinear dynamics. We also find the existence of an asymptotic precession state that is reached after some 18 nanoseconds independent of the initial conditions. Our results show ultrafast nonlinear dynamics and magnetization reversal before the stationary state sets in. The angular velocities θ ′ and ϕ ′ are composed of picosecond oscillation within a slowly decreasing envelope. At every instant, they are synchronized. At the same time, ϕ ′ is synchronized with the microwave field. These fast and synchronized dynamics of the spherical degrees of freedom also show accelerated and decelerated features. In particular, we obtain the following two new results for these isotropic (spherical) nanomagnets. (1) The picosecond oscillations maintain a ∼π/2 phase difference between θ and φ and their velocities, (2) and magnetization reverses the direction just about a few tens of picoseconds after the motions starts. From the minimum reached, it moves steadily towards the stationary state. Mx, My, and Mz inherit these features from the very beginning of the dynamics. These findings are significantly more detailed than those previously found. Therefore, our results are useful for microwave and terahertz spectroscopy measurements on isotropic nano ferromagnetic particles. These novel picosecond dynamic characteristics could also be useful in the design of ultrafast magnetization reversal responses useful in spintronic and microwave devices. They are also relevant to fast data recording technology.