Rotating magnetic nanorods detect minute fluctuations of magnetic field

Magnetic nanorods rotating in a viscous liquid are very sensitive to any ambient magnetic field. We theoretically predicted and experimentally validated the conditions for two-dimensional synchronous and asynchronous rotation as well as three-dimensional precession and tumbling of nanorods in an ambient field superimposed on a planar rotating magnetic field. We discovered that any ambient field stabilizes the synchronous precession of the nanorod so that the nanorod precession can be completely controlled. This effect opens up different applications of magnetic nanorods as sensors of weak magnetic fields, for microrheology, and generally for magnetic levitation.

Figure 1

(a) System of coordinates and angles used for the description of nanorod dynamics. See explanation of symbols in the text. Time evolution of (b) in-plane and (c) out-of-plane angles for the rotation of nanorods above a critical frequency (${\omega }_C\sim 2.17\mathrm{Hz}$) in the presence of no or small bias fields ($\mu =0-0.06$). Offsets were added to the data for visibility. Rods were initially oriented in plane at ${\theta }_0={90}^{\circ }$ and several different out-of-plane angles (${\varphi }_0$). These rods were then subjected to rotating fields of different frequencies. (Information corresponding to each trajectory is in the table.) The average slopes of the trajectories in the synchronous region are ∼180/π as the time data are normalized by corresponding rotation frequencies.

Figure 2

(a) Phase space for the cyclic flow at $\mathrm{\Omega }=2$, $\mu =0$. (b) Time dependence of ϕ (solid lines) and ψ (dashed lines) corresponding to the phase portrait at $\omega =1.6\mathrm{Hz}$. Color (red, green, and orange) corresponds to certain initial conditions for φ (see legend). The initial condition for ψ is always zero.

Figure 3

(a) Phase space for the spiral flow at $\mathrm{\Omega }=2$, $\mu =0.5$. (b) The time dependence of the angles corresponding to the phase portrait at $\omega =1.6\mathrm{Hz}$. The dashed lines are the ψ trajectory and the solid lines are the ϕ trajectory. Color (red, green, and orange) corresponds to certain initial conditions for φ (see legend). The initial condition for ψ is always zero.

Figure 4

(a) Contours of the steady precession angle ${\varphi }^S$ and (b) experimental (circles with error bars) and theoretical (lines) angles ${\varphi }^S$ at different rotation frequencies.