Improved efficiency of heat generation in nonlinear dynamics of magnetic nanoparticles

The deterministic Landau-Lifshitz-Gilbert equation has been used to investigate the nonlinear dynamics of magnetization and the specific loss power in magnetic nanoparticles with uniaxial anisotropy driven by a rotating magnetic field. We propose a new type of applied field, which is “simultaneously rotating and alternating,” i.e., the direction of the rotating external field changes periodically. We show that a more efficient heat generation by magnetic nanoparticles is possible with this new type of applied field and we suggest its possible experimental realization in cancer therapy which requires the enhancement of loss energies.

Figure 1

Orbit map in the rotating frame obtained by solving the LLG equation, below the critical value of anisotropy (there is a single attractive fixed point in the figure). The parameters are ${\alpha }_N=0.1, \omega =-0.01, {\omega }_L=0.2$, and ${\lambda }_{\mathrm{eff}}=1.1$.

Figure 2

The loss energy per cycle as a function of the anisotropy parameter ${\lambda }_{\mathrm{eff}}$ is shown for various frequencies: (a) $\omega =0.15$, (b) $\omega =0.1$, (c) $\omega =0.05$, and (d) $\omega =0.01$. The calculation is based on the attractive fixed point solutions of (6) with ${\alpha }_N=0.1, {\omega }_L=0.2$. The vertical lines indicate the critical value ${\lambda }_c$. Solid and dashed lines correspond to loss energies of steady-state solutions. The upper lines (solid, dashed) always correspond to ${\lambda }_{\mathrm{eff}}<0$ while the lower lines (solid, dashed) are related to ${\lambda }_{\mathrm{eff}}>0$. Dotted lines represent the loss energy per cycle in case of rotating field where the direction is changed periodically.

Figure 3

Calculated loss energy, $E/\left(2\pi {\mu }_0{m}_S{H}_0\right)$, in the first cycle out of the steady states for small anisotropy (${\lambda }_{\mathrm{eff}}=0.05$) as a function of the initial conditions on the ($\theta ,\varphi$) plane.

Figure 4

The loss energy per cycle as a function of the anisotropy parameter ${\lambda }_{\mathrm{eff}}$ is shown for various values of ${\alpha }_N$ (for fixed $\omega$ and ${\omega }_L$).