The high-frequency complex susceptibility of ferrofluids deduced from fits to lower frequency measurements

Application of the fluctuation dissipation theorem to the frequency-dependent, complex magnetic susceptibility data, chi(omega) = chi'(omega) - i chi ''(omega), allows the after-effect function or magnetization decay, b(t), of ferrofluids or other particulate systems to be determined. Here it is demonstrated that, by means of the simple expedient of fitting the measured complex susceptibility profiles to suitably adapted classical models, data in the 10-100 GHz frequency band can be determined from measurements made in the 100 MHz to 6 GHz frequency range. Transformation of the fitted data thus, for the first time, allows b(t) to be investigated in the 10(-10) s and 10(-11) s time regions. The results of applying this technique to two ferrofluid samples and a magnetic tape sample are presented; in the case of the ferrofluids the complex susceptibility data, chi(omega), are fitted to the equations of Raikher and Shliomis and of Debye, suitably modified to include a distribution of particle size, r, and anisotropy constant, K, whereas for the magnetic tape sample, the fit is realized by means of the Landau-Lifshitz equations suitably modified to cater for a distribution of K. It is demonstrated that a more accurate after-effect function is obtained in the cases in which the fitted profiles are transformed and that, by application of a varying polarizing magnetic field to the ferrofluid samples, b(t) of the fitted data is shown to be oscillatory in form with the transverse relaxation time, tau(perpendicular to) having a periodic time approximately equal to the time obtained from the resonant frequency, f(res) = omega(0)/(2 pi), f(res) corresponding to the frequency at which the chi'(omega) component goes from a positive to a negative value. The region of 10(-10) s to 10(-11) s corresponds to a time region which is generally associated with the precessional decay time, tau(0), which is a pre-factor of Brown's equations for Neel relaxation. It is considered that the technique presented has the potential to be a useful tool for investigating and verifying the value of this parameter.