Thermal fluctuations of magnetic nanoparticles: Fifty years after Brown

The reversal time, superparamagnetic relaxation time, of the magnetization of fine single domain ferromagnetic nanoparticles owing to thermal fluctuations plays a fundamental role in information storage, paleomagnetism, biotechnology, etc. Here a comprehensive tutorial-style review of the achievements of fifty years of development and generalizations of the seminal work of Brown [Phys. Rev. 130, 1677 (1963)] on thermal fluctuations of magnetic nanoparticles is presented. Analytical as well as numerical approaches to the estimation of the damping and temperature dependence of the reversal time based on Brown's Fokker-Planck equation for the evolution of the magnetic moment orientations on the surface of the unit sphere are critically discussed while the most promising directions for future research are emphasized. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4754272]