On the calculation of the Neel relaxation time in uniaxial single-domain ferromagnetic particles

Abstract

Nanometre-sized particles of ferrite, commonly used in magnetic fluids, are single-domain. The direction of magnetic moment of these small, uniaxial, ferromagnetic particles is known to fluctuate due to thermal agitation, and can relax through the Neel-type relaxation mechanism. The relaxation time of such fluctuations is usually determined by means of Brown's equations for high and low barrier heights. More recently, modified equations catering for a continuous range of barrier heights have been proposed. Comparison of these equations shows that, even in the most extreme case only a factor of approximately 1.7 distinguishes the corresponding eigenvalues (which represent the inverse of the relaxation time). It is concluded that the major source of error in predicting the relaxation time arises, not primarily due to the particular equations used, but because of the large uncertainty in obtaining precise experimental data needed to determine the components, f0 and sigma , of these equations. For example, for a small change in anisotropy constant K by a factor of 2.5 (typical values for the system considered here are (2-5)*104 J m-3), the calculated values of Neel relaxation times using Brown's equation differ by a factor of about 37, corresponding to times of 1.6*10-7 to 4.3*10-9. An experimental value of 5*10-9 s determined from the frequency of the maximum of the loss-peak of the imaginary part of the complex susceptibility is at the outer limit of these calculated values.

Decreasing nanofluid droplet heating time with alternating magnetic fields

“…Another important issue is that for larger particle sizes the low barrier Néel expression is not valid anymore. In this case one should use the high barrier Néel equation, 16,17 which will result on another theoretical solution for the energy conservation equation. Such investigation will be performed in the near future.…”

“…first approximation. 16,17 It is important to point out that V is the nanoparticle volume without the coating layer ͑V ϵ D 3 / 6͒, and K is the magnetic anisotropy, which is strongly dependent upon the material, shape and also particle size. 18,19 The process of heat generation in magnetic nanofluids under the influence of a magnetic field is due to in part by the mobility of the nanoparticles inside the fluid and in part by heat conduction from the nanoparticle to the liquid carrier.…”

An Analytic Analysis of the Diffusive-Heat-Flow Equation for Different Magnetic Field Profiles for a Single Magnetic Nanoparticle

“…Again, the maximal temperature rate rise and the maximal temperature are considerably small due to the relaxation time that depends on the volume of the particle. For radii larger or smaller than 9.2 nm, the magnetic heat dissipation starts to decrease as the magnetic relaxation time gets bigger or smaller, respectively, reducing the denominator or the numerator in (15) and (16).…”

“…Because these relaxation mechanisms happen simultaneously, they both contribute to the total magnetization and the heat losses and their total influences can be express by an effective relaxation time, τ e , which is a combination of τ N and τ B [14][15][16].…”

Comparisons of characteristic timescales and approximate models for Brownian magnetic nanoparticle rotations

“…19,20 The equilibrium relaxation time is different for each mechanism and depends on many parameters. 21,22 However, because most applications involve magnetically excited particles, it is more important to examine non-equilibrium timescales determining the speed of movements in varying driving fields-these timescales can be very different from the relaxation time. One only needs to imagine that in a stronger field, the particles will align faster to see why this is true.…”