Giant Transversal Particle Diffusion in a Longitudinal Magnetic Ratchet

We study the transversal motion of paramagnetic particles on a uniaxial garnet film, exhibiting a longitudinal ratchet effect in the presence of an oscillating magnetic field. Without the field, the thermal diffusion coefficient obtained by video microscopy is $D_0\approx 3\times {10}^{-4}\mu {\mathrm{m}}^2/\mathrm{s}$. With the field, the transversal diffusion exhibits a giant enhancement by almost four decades and a pronounced maximum as a function of the driving frequency. We explain the experimental findings with a theoretical interpretation in terms of random disorder effects within the magnetic film.

Figure 1

(a) Schematic illustrations of a traveling paramagnetic particle on top of the FGF, the stray field of the BWs, and the oscillating external field $\mathit{H}$ for two different times $t=-\pi /2\omega$ and $t=\pi /2\omega$. (b) Corresponding potentials $V(x,t)$ (arb. units) entailing particle motion in $x$ direction and calculated from Eq. (1) of Ref. 16. The middle graph corresponds to $H=0$. (c) Gray: Three optical microscope snapshots of the FGF and the traveling particle at $t=0$, 2.8, and 5.6 s $\omega =18.8{\mathrm{s}}^{-1}$, $H=1500\mathrm{A}/\mathrm{m}$, $\vartheta =\pi /7$). Black (blue) line: Corresponding particle trajectory $x(t)$. Gray (green) line: Corresponding path in the $x\mathrm{\text{−}}y$ plane. See also Video2 in 17.

Figure 2

Transversal mean square displacement $⟨\Delta y^2⟩$ versus time (log-log-plot). Black (blue) line: Experimental results for the same system as in Fig. 1. Gray (red) line:  Same but without external field. The approach of a straight line with slope $\alpha =1$ for large times indicates convergence in $D_y$; the curves starting from the dashed lines were used to calculate $D_y$. Inset: The power spectra $S(\nu )≔|Y(\nu ){|}^2$, where $Y(\nu )$ is the Fourier transform of one representative trajectory $y(t)$. The convergence towards a straight line with slope $\beta =-2$ for small $\nu$ indicates normal (as opposed to anomalous) diffusion [19].

Figure 3

Transversal diffusion coefficient $D_y$ versus driving frequency $\omega$ in units of $D_0=3.2\times {10}^{-4}\mu {\mathrm{m}}^2/\mathrm{s}$ (undriven diffusion). Dots: Experimental findings for the same system as in Fig. 1. Line: Theoretical approximation (1) with fit parameters $\sigma =1.8\pm 0.2\mu \mathrm{m}$ and $k=2.9\pm 0.1{\mathrm{s}}^{-1}$.

Figure 4

Exploration time ${\tau }_e$ versus driving frequency $\omega$. Circles: Experimental results. Line: Theoretical approximation ${\tau }_e=\pi /\omega -{\tau }_j$ with ${\tau }_j=0.02\mathrm{s}$. Inset: Experimental particle trajectories $x(t)$ for different driving frequencies $\omega$. ${\tau }_e$ (red bars) indicates the exploration time between two jumps in $x$ direction, during which the particle moves along one given BW.