Relaxation time of fine magnetic particles in uniaxial symmetry

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

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“…(14). Equation (92) may be deemed universal, insofar as it accurately describes the magnetization escape rate for all damping a.…”

Section: Reversal Time Of the Magnetization In Superparamagnets Wmentioning

confidence: 99%

Thermal fluctuations of magnetic nanoparticles: Fifty years after Brown

Coffey

Kalmykov

2012

Journal of Applied Physics

233

249

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“…In the 90's the eigenvalue λ 1 became a subject of extensive studies. Efficient numerical procedures were developed [10] and a number of extrapolation formulas with a good overall accuracy were proposed [11,12,13,14].…”

Section: B Interwell Modementioning

confidence: 99%

Linear and nonlinear superparamagnetic relaxation at high anisotropy barriers

Raǐkher

Stepanov

2002

Phys. Rev. B

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The micromagnetic Fokker-Planck equation is solved for a uniaxial particle in the low-temperature limit. Asymptotic series in the parameter that is the inverse barrier height-to-temperature ratio are derived. With the aid of these series, the expressions for the superparamagnetic relaxation time and the odd-order dynamic susceptibilities are presented. The obtained formulas are both quite compact and practically exact in the low (with respect to FMR) frequency range that is proved by comparison with the numerically-exact solution of the micromagnetic equation. The susceptibilities formulas contain angular dependencies that allow to consider textured as well as randomly oriented particle assemblies. Our results advance the previous two-level model for nonlinear superparamagnetic relaxation.

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“…In the second case, this easy axis is given by the common direction along which the constituent organic molecules of the liquid crystal align. The main interest of the theoretical work concentrated on calculating the Kramers transition rate or its inverse, the mean-first-passage time, i.e., the time the dipoles need to flip over the potential barrier [4,[6][7][8]. This quantity is equivalent to the slowest decay rate with which a distribution of dipole orientations relaxes towards thermal equilibrium.…”

mentioning

confidence: 99%

“…Detailed experimental tests of these theoretical models with magnetic or bulk liquid crystal systems are difficult due to the fact that the potential barrier is not tunable as it is an intrinsic material parameter. Furthermore, the applicability of the idealizing theory to the interpretation of relaxation experiments is still under debate [5,7,8].…”

mentioning

confidence: 99%

Rotational diffusion in a bistable potential

et al. 2002

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Abstract. -Using depolarized quasielastic light scattering, we have investigated the rotational diffusion of optically anisotropic colloidal particles in a dilute suspension subject to external electric and magnetic fields (E0, B0). The particles were produced by the polymerization of nematic liquid crystal droplets, leading to birefringent colloidal spheres whose frozen orientational order is rigidly coupled to the particle orientation. The torque on the droplet director u(t) originating from the coupling of E0 and B0 to the particles' anisotropy in the refractive index and in the diamagnetic susceptibility, respectively, leads to a suppression of the orientational fluctuations about the direction of the external field. We observe a strong dependence of the measured relaxation rates on the field strength and on the orientation of the field relative to the scattering plane. We explain our findings by a solution of the Smoluchowski equation describing rotational diffusion in a bistable potential V (u) which has two equivalent minima separated by a potential barrier whose height is proportional to (E0, B0) 2 .Colloidal particles in a solvent do not only experience random forces due to the collisions with the surrounding molecules, but are also imparted random torques that lead to fluctuating particle orientations described by a unit vector u(t) also called particle director. If the colloids possess optical anisotropy, e.g., due to intrinsic birefringence or shape birefringence, these orientational fluctuations can be probed by depolarized quasielastic light scattering [1]. For isolated, freely rotating spherical particles in the limit of high solvent viscosity η, the rotational part of the field auto-correlation function g 2 of the scattered depolarized electric field E VH (t) decays exponentially with time t; the corresponding decay rate is proportional to the rotational diffusion constant D r = k B T /(8πηR 3 ), where k B T is the thermal energy and R is the particle radius.This simple situation changes completely when the rotational symmetry is broken by an external field (such as an electric or magnetic field) that couples to permanent or induced (electric or magnetic) dipoles localized on the particle. The orientational distribution then develops a peak around the direction of the external field, and, consequently, the amplitudes

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Relaxation time of fine magnetic particles in uniaxial symmetry

Cited by 87 publications

References 20 publications

Thermal fluctuations of magnetic nanoparticles: Fifty years after Brown

Thermal fluctuations of magnetic nanoparticles: Fifty years after Brown

Linear and nonlinear superparamagnetic relaxation at high anisotropy barriers

Rotational diffusion in a bistable potential

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