Linear and Nonlinear Susceptibilities of Ferromagnetic Fine Particles in Cu<sub>97</sub>Co<sub>3</sub>Alloy

Bitoh, Teruo; Ohba, Kazuyuki; Takamatsu, Masaki; Shirane, Takashi; Chikazawa, Susumu

doi:10.1143/jpsj.64.1311

Cited by 60 publications

(88 citation statements)

References 23 publications

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“…(1) the function W has a parametric dependency on the vector n so that, in fact, the angular argument of W is (e · n). The magnetodynamic equation underlying the Brown kinetic equation (2) can be either that by Landau & Lifshitz or that by Gilbert. To be specific, we adopt the former one.…”

Section: Superparamagnetic Relaxation Times a Uniaxially Anisotrmentioning

confidence: 99%

“…Since recently, this approach (it originates from the spin glass science) became quite feasible in experimental realization. [2] However, to benefit from it, one needs an adequate model. Surprisingly, until nowadays the Néel [1] concept of superparamagnetic behavior of fine magnetic particles that had been substantially advanced by Brown [3,4] and refined by numerous researchers (see the review article [5] with about 400 references), lacks a nonlinear extension.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Superparamagnetic Relaxation Times a Uniaxially Anisotrmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Linear and nonlinear superparamagnetic relaxation at high anisotropy barriers

Raǐkher

Stepanov

2002

Phys. Rev. B

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“…Previous studies have investigated the similarities and differences of superparamagnetic clusters compared to a spin-glass system. 12,13 However, these studies were not able to vary independently the cluster concentration and diameter. This limitation, resulting from the sample-preparation method, makes it difficult to measure the concentration/cluster volume regime where such a system goes from being superparamagnetic clusters to a more collective or interactive system.…”

mentioning

confidence: 96%

Magnetic properties of cluster-beam-synthesized cobalt: Noble-metal films

Meldrim

Qiang

Liu

et al. 2000

Journal of Applied Physics

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A cluster-beam deposition technique has been used to produce magnetic clusters embedded in a nonmagnetic matrix. We report here on films with cobalt clusters of average diameter of 5.5 nm embedded both in Cu and Ag. Volumetric concentrations of Co ranged from 10% to 50%. Magnetization and low temperature hysteresis loops, both field cooled (FC) and zero-field cooled (ZFC), have been measured between 4.2 and 300 K. The FC and ZFC magnetization bifurcate at or above room temperature with the clusters having a nonzero remanence at room temperature. Low temperature hysteresis loops exhibit a two-phase nature with one phase displaying exchange bias upon field cooling, suggesting the presence of an oxide phase. Conditions under which the oxide is present have been studied.

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“…In the calculations, we have also assumed that all the particles are identical; in order to account for polydispersity, one must average ͑ ͒ over the appropriate distribution function ͑e.g., over the particle volumes; see for details Refs. 25 …”

Section: ͑8͒mentioning

confidence: 99%

Precessional effects in the linear dynamic susceptibility of uniaxial superparamagnets: Dependence of the ac response on the dissipation parameter

et al. 2001

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It is shown that the low-frequency relaxation spectrum of the linear dynamic susceptibility of uniaxial single domain particles with a uniform magnetic field applied at an oblique angle to the easy axis can be used to deduce the value of the damping constant. DOI: 10.1103/PhysRevB.64.012411 PACS number͑s͒: 75.50.Tt, 05.40.Ca, 76.20.ϩq, 76.50.ϩg A single domain ferromagnetic particle is characterized by an internal potential, having several local states of equilibrium with potential barriers between them. If the particles are small ͑ϳ 10 nm͒ so that the potential barriers are relatively low, the magnetization vector M may cross over the barriers due to thermal agitation. The ensuing thermal instability of the magnetization results in the phenomenon of superparamagnetism. 1 This problem is important in information storage, rock magnetism, and the magnetization reversal observed in isolated ferromagnetic nanoparticles. 2 The dynamics of the magnetization M of a superparamagnetic particle is usually described by the Landau-Lifshitz or Gilbert ͑LLG͒ equation 3,4 2whereis the free Brownian motion diffusion time of the magnetic moment, ␣ is the dimensionless damping ͑dissipation͒ constant, M s is the saturation magnetization, ␥ is the gyromagnetic ratio, ␤ϭv/(kT), v is the volume of the particle, and the magnetic field H consists of applied fields ͑Zeeman term͒, the anisotropy field H a , and a random white-noise field accounting for the thermal fluctuations of the magnetization of an individual particle. Here the internal magnetization of a particle is assumed homogeneous. Surface and ''memory'' effects are also omitted in Eq. ͑1͒. These assumptions are discussed elsewhere ͑e.g., Refs. 5-7͒. Furthermore, the description of the relaxation processes in the context of Eq. ͑1͒ does not take into account effects such as macroscopic quantum tunneling ͑a mechanism of magnetization reversal suggested in Ref.1͒. These effects are important at very low temperatures 8,9 and necessitate an appropriate quantum-mechanical treatment, e.g., Refs. 10-12.The various regimes of relaxation of M in superparamagnetic particles are governed by ␣. In general, ␣ is difficult to estimate theoretically, although a few experimental methods of measuring ␣ ͓such as ferromagnetic resonance ͑FMR͒ and the angular variation of the switching field, e.g., Refs. 7 and 8͔ have been proposed. Yet another complementary and potentially promising technique, viz., the nonlinear response of single domain particles to alternating ͑ac͒ stimuli, has recently 13 been suggested in order to evaluate ␣. In particular, it has been shown in Ref. 13 that for uniaxial particles having a strong ac field applied at an angle to the easy ͑Z͒ axis, the nonlinear response truncated at terms cubic in the ac field is particularly sensitive to the value of ␣. On the other hand, the linear response to the ac field does not exhibit such behavior. The explanation of this is reasonably straightforward: the linear ac response may simply be calculated from the after effect solution ...

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Linear and Nonlinear Susceptibilities of Ferromagnetic Fine Particles in Cu₉₇Co₃Alloy

Cited by 60 publications

References 23 publications

Linear and nonlinear superparamagnetic relaxation at high anisotropy barriers

Linear and nonlinear superparamagnetic relaxation at high anisotropy barriers

Magnetic properties of cluster-beam-synthesized cobalt: Noble-metal films

Precessional effects in the linear dynamic susceptibility of uniaxial superparamagnets: Dependence of the ac response on the dissipation parameter

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Linear and Nonlinear Susceptibilities of Ferromagnetic Fine Particles in Cu97Co3Alloy

Cited by 60 publications

References 23 publications

Linear and nonlinear superparamagnetic relaxation at high anisotropy barriers

Linear and nonlinear superparamagnetic relaxation at high anisotropy barriers

Magnetic properties of cluster-beam-synthesized cobalt: Noble-metal films

Precessional effects in the linear dynamic susceptibility of uniaxial superparamagnets: Dependence of the ac response on the dissipation parameter

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Linear and Nonlinear Susceptibilities of Ferromagnetic Fine Particles in Cu₉₇Co₃Alloy