Complex magnetic susceptibility setup for spectroscopy in the extremely low-frequency range.

A sensitive balanced differential transformer was built to measure complex initial parallel magnetic susceptibility spectra in the 0.01-1000 Hz range. The alternating magnetic field can be chosen sufficiently weak that the magnetic structure of the samples is only slightly perturbed and the low frequencies make it possible to study the rotational dynamics of large magnetic colloidal particles or aggregates dispersed in a liquid. The distinguishing features of the setup are the novel multilayered cylindrical coils with a large sample volume and a large number of secondary turns (55 000) to measure induced voltages with a good signal-to-noise ratio, the use of a dual channel function generator to provide an ac current to the primary coils and an amplitude- and phase-adjusted compensation voltage to the dual phase differential lock-in amplifier, and the measurement of several vector quantities at each frequency. We present the electrical impedance characteristics of the coils, and we demonstrate the performance of the setup by measurement on magnetic colloidal dispersions covering a wide range of characteristic relaxation frequencies and magnetic susceptibilities, from chi approximately -10(-5) for pure water to chi>1 for concentrated ferrofluids.