Dynamics of magnetic nanoparticles in a viscous fluid driven by rotating magnetic fields

The rotational dynamics of magnetic nanoparticles in rotating magnetic fields in the presence of thermal noise is studied both theoretically and by performing numerical calculations. Equations for the dynamics of particles with uniaxial magnetic anisotropy are studied and the phase lag between the rotating magnetic moment and the driving field is obtained. It is shown that for large enough anisotropy energy the magnetic moment is locked to the anisotropy axis so that the particle behaves like a rotating magnetic dipole. The corresponding rigid dipole model is analyzed both numerically by solving the appropriate Fokker-Planck equation and analytically by applying an effective field method. In the special case of a rotating magnetic field applied analytic results are obtained in perfect agreement with numerical results based on the Fokker-Planck equation. The analytic formulas derived are not restricted to small magnetic fields or low frequencies and are therefore important for applications. The illustrative numerical calculations presented are performed for magnetic parameters typical for iron oxide.

Figure 1

Phase lag $\varphi$ (upper panel) and in-plane magnetization $m$ (lower panel) versus reduced anisotropy parameter $K_1/K_{10}$ for different values of the magnetic radius $r_m$: $r_m=19$ nm (circles, black), 14 nm (squares, blue), and 10 nm (diamonds, red). $\alpha =0.01, \tilde{\eta }=1.0, r_d/r_m=2.5, F=4$ kHz, $B=5$ mT. The horizontal lines indicate the values obtained within the RDM.

Figure 2

Phase lag $\varphi$ and magnetic moment $m$ versus frequency. Parameters: $\tilde{\eta }=1.0,T=300,r_m=15.0,B_0=5$ mT. Upper panel: $r_d/r_m=1.5$, lower panel $r_d/r_m=4.5$. Dots, black and squares, red: numerical solution of the FPE. Solid lines, blue: present paper, dashed-dotted lines, green: Ref. [24].

Figure 3

Phase lag $\varphi$ and magnetic moment $m$ versus frequency. Parameters: $r_d/r_m=2.5, r_m=19$ nm. Upper panel: $B=2.5$ mT, $\tilde{\eta }=1.0$; middle panel: $B=5$ mT, $\tilde{\eta }=1.0$; lower panel: $B=5$ mT, $\tilde{\eta }=8.0$. Dots, black and squares, red: numerical solution of the FPE. Solid lines, blue: present paper, dashed-dotted lines, green: Ref. [24].

Figure 4

Phase lag $\varphi$ and magnetic moment $m$ versus $r_d/r_m$. Parameters: $\tilde{\eta }=1.0,T=300,r_m=19.0,B=5.0$ mT, $F=4$ kHz. Dots, black and squares, red: numerical solution of the FPE. Solid lines, blue: present paper, dashed-dotted lines, green: Ref. [24].