Thermal fluctuations of magnetic nanoparticles: Fifty years after Brown

Abstract

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] 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. V C 2012 American Institute of Physics. [http://dx

A quantitative study of particle size effects in the magnetorelaxometry of magnetic nanoparticles using atomic magnetometry

“…The forefactor is given by ≈ − . Generalisations (see, e.g., [33]) of Brown's expression (27) to other crystalline structures lead to similar expressions in which t 0 and e σ − also appear as key constituents.…”

On the superparamagnetic size limit of nanoparticles on a ferroelectric substrate

“…To address the issue of the magnetization stability of the Fe nanoparticles against thermal fluctuations we calculate the MFPTs. It is known [37], that for zero magnetic field the FM MFPT is given by equation…”

“…In view of the already realized experiment [32] it is well conceivable that the suggested system in Fig. 1 [21,34,35,36,37], and here we extend the approach as to include the influence of the magnetoelectric coupling. The starting point is the Landau-Lifshitz-Gilbert (LLG) equation [14,15] describing the classical dynamics of the magnetization M(t) of a FM nanoparticle…”

Spin Relaxation in Phase Space

“…Also on a nanoscale level, we have magnetic fluids composed of single domain ferromagnetic particles in a colloidal suspension. Here relaxation experiments detect [4,5] both the Arrhenius or solid state like (Néel) mechanism [6] of relaxation of the magnetization which may overcome via thermal agitation anisotropy potential barriers inside the particle and the Debye orientational relaxation [7,8] due to physical Brownian rotation of the suspended particles in the presence of thermal agitation. Here quantum effects are expected to be much smaller.…”

“…In the more recent treatment formulated by Brown [23,24] (now known as the Néel-Brown model [6,9]), which explicitly treats the system as a gyromagnetic one and which includes nonequilibrium effects due to the loss of magnetization at the barrier, the time evolution of the magnetization of the particle ( ) t M is described by a classical (magnetic) Langevin equation. This is the phenomenological Landau-Lifshitz [25] or Gilbert equation [26,27] augmented by torques due to random white noise magnetic fields h(t) characterizing the giant spin-bath interaction, viz., Fokker-Planck equation is [5,6] …”