Autoresonant switching of the magnetization in single-domain nanoparticles: Two-level theory

The magnetic moment of a single-domain nanoparticle can be effectively switched on an ultrashort time scale by means of oscillating (microwave) magnetic fields. This switching technique can be further improved by using fields with time-dependent frequency (autoresonance). Here, we provide a full theoretical framework for the autoresonant switching technique, by exploiting the analogy between the magnetization state of an isolated nanoparticle and a two-level quantum system, whereby the switching process can be interpreted as a population transfer. We derive analytical expressions for the threshold amplitude of the microwave field, with and without damping, and consider the effect of thermal fluctuations. Comparisons with numerical simulations show excellent agreement.

Figure 1

Geometric configuration of the nanoparticle with its magnetic moment $\mathbf{M}$, the static field ${\mathbf{B}}_{\mathrm{dc}}$, and the time-dependent ac field ${\mathbf{B}}_{\mathrm{ac}}\left(t\right)$.

Figure 2

Threshold amplitude as a function of the chirp rate ${\alpha }^{3/4}$. The red dots are numerical results obtained by solving the full LLG equation. The straight line is the theoretical result from Eq. (17).

Figure 3

Amplitude of the $|A_2{|}^2$ level in the two-parameter space $\left(\epsilon ,a_1^{-0.5}\right)$, obtained from numerical solutions of Eqs. (14) and (15). Regions where $|A_2{|}^2$ is larger are those of efficient population transfer (i.e., efficient magnetization switching).

Figure 4

Rescaled threshold amplitude ${\mu }_{\mathrm{th}}$ as a function of the damping $\nu$. Simulation data are represented by red dots; the solid lines correspond to the theoretical result to first (blue) and second (black) order in $\nu$, from Eq. (21).

Figure 5

Width of the threshold for the driving field in the presence of thermal noise, as a function of the square root of the temperature. The red dots are numerical results obtained by solving the full LLG equation. The straight line is the theoretical result of Eq. (27).