# What is the rotating magnetic magnetic field

## Rotating magnetic fields

In addition to the switched and the alternating magnetic field, the rotating magnetic field represents a further possibility for the magnetic manipulation of magnetic nanoparticles (MNP), which are dissolved in an aqueous medium and relax according to Brown. The magnetic torque between the rotating magnetic field and the magnetization of the magnetic nanoparticles causes the particles to rotate at the same frequency as the rotating magnetic field. In the alternating magnetic field, however, the MNP change their orientation according to their magnetic moment and the applied magnetic field at the rate of the selected frequency without entering into a defined rotational movement. The rotational movement of the MNP or the magnetic moment has a phase difference φ to the rotating magnetic field (Figure 1), which is largely caused by the rotational friction between the particle shell and the medium. The absolute phase angle depends here φ also on the frequency and field strength of the rotating magnetic field as well as on the parameters (temperature, viscosity, charge) of the medium. Thus, by determining the phase angle between the rotating magnetic field and the magnetization of the magnetic nanoparticles, a statement can be made about the ratio of magnetic core to particle shell if the temperature and viscosity of the medium are kept constant. In contrast to the alternating magnetic field, the rotating magnetic field is generated with the help of a 2-axis Helmholtz coil system (Figure 1).

##### Figure 1: Helmholtz coils for generating alternating and rotating magnetic fields for the magnetic manipulation of MNP.

The two Helmholtz coils are arranged perpendicular to one another and are operated with two sinusoidal currents shifted by 90 ° to one another. The principal dependency of the phase angle φ the frequency and field strength of the rotating magnetic field is illustrated in Figure 2 using the example of an aqueous suspension of iron oxide particles with a hydrodynamic diameter (particles including shell) of 120 nm. It can be clearly seen here that an increasing frequency causes an increase in the phase angle, whereas a greater field strength reduces the phase angle. In the case of the alternating magnetic field, analogously to the rotating magnetic field, a phase angle can be determined for the fundamental frequency of the manipulating magnetic field which, in comparison, has a significantly lower dependence on the field strength. This is made clear by the smaller spread of the blue curves (ACF) in Figure 2. The measurements shown are recorded with a measuring system developed at the institute, which enables the analysis of the MNP dynamics in rotating as well as alternating magnetic fields up to a frequency of 5 kHz and 10 mT with the help of Fluxgate magnetic field sensors.