This system is based on a common design where the sample is positioned in one of a coupled pair of detection coils that are themselves surrounded by a single primary coil. However, a number of commercial and home-built systems exist for this purpose, where typically a set of primary and secondary coils are used to generate the AC field and detect the induced magnetization, respectively.Ī schematic representation of the principle components of the home-made instrument developed at Keele University is shown in Fig. While it is relatively straightforward to design an instrument to measure the AC susceptibility at a fixed frequency, measurements across a broad-band frequency range are more difficult. In order to do this, an inductive coil arrangement is typically used. The measurement of frequency-dependent AC susceptibility is extremely useful for evaluating the Brownian and Néel relaxation of magnetic nanoparticles. Hence an AC magnetic field operating at this frequency (i.e., sufficiently weak to be within the linear response region) will also generate the greatest heating effect.
As discussed in the previous section, under this condition the corresponding elliptical hysteresis loop has its maximum area. This point also corresponds to the maximum of the χ′′ component, and the observation of such peaks can therefore be used to determine the relaxation time of the particles from the knowledge that at this frequency, ωτ R = 1. When the angular period of the AC field cycle is matched to the relaxation time, the phase angle is 45° and the two susceptibility components have equal magnitude ( Fig. The relative amplitudes of the χ′ and χ′′ components reflect the phase shift at different time scales, while the magnitude of the phasor, χ ~, decreases nonlinearly with increasing frequency. 7.6 shows an example of the theoretical frequency-dependent AC susceptibility that would be obtained from an assembly of nanoparticles, where a single relaxation mode occurs within the frequency range.
Measurements of the in-phase and out-of-phase components of AC susceptibility as a function of frequency enable the magnetization relaxation to be probed at different time scales. The inset schematic representation shows how the magnitude and phase angle of the complex AC susceptibility phasor varies with frequency. Theoretical frequency-dependent AC susceptibility curves calculated for particles with a single relaxation mode.
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