The theory of the Vogel-Fulcher law of spin glasses

Shtrikman, S.; Wohlfarth, E.P.

doi:10.1016/0375-9601(81)90441-2

Cited by 390 publications

(224 citation statements)

References 9 publications

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“…In Ref. [26] is experimentally shown that the effective anisotropy constant depends on the particle concentration (the larger the particle concentration, the larger the value of the effective anisotropy constant), a result which is in agreement with the theoretical models of Shtrikman-Wohlfarth [27] and Dormann-Bessais-Fiorani [9,10]. and the ratio of the anisotropy energy to the thermal energy, σ, the pre-factor, τ 0N =2.06⋅10 -10 s is determined.…”

Section: Resultssupporting

confidence: 76%

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

Fannin

Marin

Couper

2011

Journal of Magnetism and Magnetic Materials

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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).

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Section: Resultssupporting

confidence: 76%

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

Fannin

Marin

Couper

2011

Journal of Magnetism and Magnetic Materials

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“…This fact leads to conclude that there exist some magnetic interactions among particles. The Vogel-Fulcher law better describes a magnetically interacting particle system, 41 = 0 exp͓− KV/k B ͑T ac max − T 0 ͔͒. ͑2͒ Figure 9͑a͒ shows the evolution of the susceptibility peak with variation in frequency to fit the evolution of T ac max with Eq.…”

Section: Discussionmentioning

confidence: 99%

Effects of interparticle interactions in magneticFe/Si3N4granular systems

et al. 2010

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An experimental evidence of the progressive modification in the magnetic behavior of granular Fe/ Si 3 N 4 samples due to interaction effects between particles is reported. Microstructural features and local structure were determined by x-ray absorption spectroscopy and transmission electron microscopy to select granular samples with predetermined cluster size. Fe/ Si 3 N 4 systems have been characterized by ac-and dcmagnetization measurements to study the gradual evolution of magnetic properties of granular systems, where three different behaviors have been observed. As-deposited samples with Fe thickness layers of 2.5 nm, present a modified superparamagnetic behavior, due to very weak interactions between very small Fe clusters separated by a nonmagnetic FeN phase. An evolution of the average blocking temperature at intermediate fields ͑T B ϳ H 3/2 ͒ is observed, similar to noninteracting systems, but first signatures of a frozen spin state at low temperatures appear. Annealed samples exhibit a noticeable modification from the multilayer character to a random three-dimensional organization of Fe clusters embedded in a Si 3 N 4 matrix. After annealing, samples with initial Fe layer thickness of 0.7 nm provide iron cluster in the range of 1.3 nm and exhibit a superspinglass state, with a de Almeida-Thouless evolution of the energy barriers ͑T B ϳ H 2/3 ͒ that is explained in terms of increasing interparticle interactions. Moreover, annealed samples, with initial layer thickness of 1.3 nm, supply iron cluster of near 3 nm that present stronger interactions and yield a superferromagnetic state, likely provided by residual ultrasmall particles between the blocked clusters.

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“…Fits to the frequency dependence of T B (ν) using the Néel-Arrhenius model resulted in un-physically large τ 0 = 1/ν 0 of 10 −15 s for the un-doped and 10 −23 s for the cobalt doped samples, indicating interparticle interactions 28 . To obtain a physically reasonable τ 0 and to account for the effects of interactions on the energy barrier of the magnetization dynamics, the Néel-Arrhenius law is modified by T B → T B − T 0 to obtain a Vogel-Fulcher law 28,29 ν = ν 0 exp[−KV /k B (T B − T 0 )], where T 0 accounts for the effect of interparticle interactions.…”

Section: Susceptometry (Dynamics)mentioning

confidence: 99%

Intra- and interparticle magnetism of cobalt-doped iron-oxide nanoparticles encapsulated in a synthetic ferritin cage

Skoropata

Desautels

Falvo³

et al. 2014

Phys. Rev. B

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We present an in-depth examination of the composition and magnetism of cobalt (Co 2+ )-doped iron-oxide nanoparticles encapsulated in Pyrococcus furiosus ferritin shells. We show that the Co 2+ dopant ions were incorporated into the γ-Fe2O3/Fe3O4 core, with small paramagnetic-like clusters likely residing on the surface of the nanoparticle that were observed for all cobalt-doped samples. In addition, element-specific characterization using Mössbauer spectroscopy and polarized x-ray absorption indicated that Co 2+ was incorporated exclusively into the octahedral B-sites of the spinel-oxide nanoparticle. Comparable superparamagnetic blocking temperatures, coercivities, and effective anisotropies were obtained for 7, 10 and 12% cobalt-doped nanoparticles, and were only slightly reduced for 3% cobalt, indicating a strong effect of cobalt incorporation, with a lesser effect of cobalt content. Due to the regular particle size and separation that result from the use of the ferritin cage, a comparison of the effects of interparticle interactions on the disordered assembly of nanoparticles was also obtained that indicated significantly different behaviours between un-doped and cobalt-doped nanoparticles.

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The theory of the Vogel-Fulcher law of spin glasses

Cited by 390 publications

References 9 publications

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

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

Effects of interparticle interactions in magneticFe/Si3N4granular systems

Intra- and interparticle magnetism of cobalt-doped iron-oxide nanoparticles encapsulated in a synthetic ferritin cage

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