A Monte-Carlo model of thermally activated single-domain particles

The majority of routine magnetic measurements utilised to investigate the characteristics of marine sediments are performed at room temperature. In contrast, most mathematical models of the behaviour of magnetic particles consider thermal activation to be a complicating factor and assume a temperature of absolute zero. This kind of disparity between reality and mathematical models is not uncommon and ultimately it can cause problems when comparing the results we obtain in the laboratory with model predictions.

Shown in the graphic above are model predications for the orientation of the magnetization in a 10 nm uniaxial magnetite particle. Red colours show a high probability of finding a magnetic pole occurring at that position and blue colours show low probability. At the low temperature (10 Kelvin), thermal activation plays only a small role and the magnetization will lie along the longest axis of the particle. As the system is heated (150 K and 300 K) the probability of finding the magnetisation in a different orientation increases due to the randomising effect of the thermal activation.

Recently I completed work on a series of models based on Boltzmann statistics, which allow the randomising effects of temperature to be included in the calculation of magnetic behaviour. The model is written around a Monte Carlo routine that is used to minimise the energy of the magnetic system whilst allowing the introduction of randomising effects, which mimic the effects of thermal activation in laboratory measurements. These results could be used to reinterpret a number of magnetic parameters and how they behave as a function of temperature.