The resonance decay function method in the determination of the pre-factor of the Néel relaxation time of single-domain nanoparticles

Abstract

In its simple form, the relaxation time of the Néel relaxation process of the magnetic moment of single-domain particles is given by τ N = τ 0N exp(σ), σ being the ratio of the anisotropy energy to thermal energy. The pre-factor, τ 0N , is normally given a value of 10 -9 s, but values ranging from 10 -8 to 10 -12 s have been reported in literature. Here, by means of the field and frequency dependence of the complex magnetic susceptibility, χ(ω,H)= χ'(ω,H)-i χ''(ω,H), of a magnetic fluid sample, in the MHz -GHz range, in conjunction with the determination of the sample decay function, b(t), the pre-factor τ 0N is determined. b(t) is readily obtained through the inverse Fourier transformation relationship which exists between b(t) and χ'' (ω).

Experimental Investigations on the Ferromagnetic Resonance and Absorbing Properties of a Ferrofluid in the Microwave Range

“…By fitting with a straight line, the experimental dependence f res (H) from Figure 6, and using Equation (2), we were able to determine the anisotropy field H A and the gyromagnetic ratio of the particle γ; the values obtained being: H A = 38.75 kA/m and γ = 2.25 × 10 5 s −1 A −1 m. From Equation (1), we determine that the effective anisotropy constant, K eff = 1.16 × 10 4 J/m 3 , which agrees with the values obtained in the literature [36,37] for magnetite particles. Taking into account both the value obtained for γ, and the relation (3) valid for high values of the magnetic field H > H A , we were able to determine the damping parameter of the Landau-Lifshitz equation α L , and using the value g = 2, specific to a kerosene-based ferrofluid with magnetite particles [5,8,33], we obtained the value, α L = 0.194.…”

“…Knowing the values of the fres, corresponding to each H value, from Figure 5, we were able to obtain the dependence of fres on H, which is linear, as can be seen in Figure 6, being in accordance with Equation ( 2). By fitting with a straight line, the experimental dependence fres(H) from Figure 6, and using Equation ( 2), we were able to determine anisotropy field HA and the gyromagnetic ratio of the particle γ; the values obtained being: HA = 38.75 kA/m and γ = 2.25 × 10 5 s −1 A −1 m. From Equation ( 1), we determine that the effective anisotropy constant, Keff = 1.16 × 10 4 J/m 3 , which agrees with the values obtained in the literature [36,37] for magnetite particles. Taking into account both the value obtained for γ, and the relation ( 3) valid for high values of the magnetic field H > HA, we were able to determine the damping parameter of the Landau-Lifshitz equation αL, and using the value g = 2, specific to a kerosenebased ferrofluid with magnetite particles [5,8,33], we obtained the value, αL = 0.194.…”

Experimental Investigations on the Ferromagnetic Resonance and Absorbing Properties of a Ferrofluid in the Microwave Range

“…Knowing the values of the fres, corresponding to each H value, from Figure 5, we were able to obtain the dependence of fres on H, which is linear, as can be seen in Figure 6, being in accordance with Equation (2). By fitting with a straight line, the experimental dependence fres(H) from Figure 6, and using Equation (2), we were able to determine the anisotropy field HA and the gyromagnetic ratio of the particle γ; the values obtained being: HA = 38.75 kA/m and γ = 2.25 × 10 5 s −1 A −1 m. From Equation (1), we determine that the effective anisotropy constant, Keff = 1.16 × 10 4 J/m 3 , which agrees with the values obtained in the literature [36,37] for magnetite particles. Taking into account both the value obtained for γ, and the relation (3) valid for From Figure 5, it is observed that the investigated ferrofluid sample presents the ferromagnetic resonance phenomenon, highlighted by the transition of the real part of the complex magnetic permeability, µ ′ (f ), from a superaunit value to a subunit value at the resonant frequency, f res [8,33].…”

Particle Size Controlled Magnetic Loss in Magnetite Nanoparticles in RF-Microwave Region

“…Our results do not follow this approach. Here the anisotropy constant, includes the effects from magnetocrystalline nature, size, shape and interparticle interaction [40] and is called effective anisotropy constant 𝐾 𝑒𝑓𝑓 . The nanoparticle synthesized here are not perfectly spherical, but they are slightly elongated which can be observed in TEM images, so shape anisotropy contributes to constant 𝐾 𝑒𝑓𝑓 [41].…”