Magnetic susceptibility measurements as a function of temeperature and freqeuncy I: inversion theory

Magnetic measurements as a function of temperature and time are commonly used to reconstruct the volume distribution of superparamagnetic (SP) particles. Knowledge of the temperature dependence of the magnetic moments and the anisotropy energies is necessary for a correct interpretation of the measurements. Temperature dependences are usually derived from bulk magnetic properties. The magnetic properties of small particles, however, are strongly influenced by surface effects related to low-temperature oxidation, reduced coordination of surface spins and interactions with surrounding molecules. These effects are difficult to quantify, especially in rocks and sediments. To address this problem, a method for reconstructing the magnetic properties of weakly interacting assemblages of SP particles is presented. The method is based on the inversion of magnetic susceptibility measurements performed for a range of temperatures at different frequencies. The redundancy of the measurements is used to obtain estimates of the abovementioned temperature dependences, the effective interaction field and the pre-exponential factor in NEel-Brown relaxation theory without using any a priori assumptions on the magnetic properties of the particles. The inversion method was successfully tested on numerical samples representing typical susceptibility measurements of natural and artificial samples. Susceptibility inversion results can provide new insights in the magnetic properties of fine particles relevant in palaeo- and environmental magnetism.