Constant-magnetic-field effect in Néel relaxation of single-domain ferromagnetic particles

Coffey, W. T.; Crothers, D S F; Kalmykov, Yuri P.; Waldron, J T

doi:10.1103/physrevb.51.15947

Cited by 111 publications

(115 citation statements)

References 13 publications

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“…The same departure was found in the classical limit. 7,8 The physical reason for the disagreement between int −1 and ⌳ 1 is the intrawell processes entering into scene at a finite h = B z / D͑2S −1͒. Formally, at h Ӷ 1, the quantity ⌽ m 2 / P m+1͉m N m ͑0͒ in Eq.…”

Section: Lowest Eigenvalue ⌳mentioning

confidence: 99%

“…The first two quantities and are equivalent to those used in the description of magnetic nanoparticles. [7][8][9] The "reduced field" h is B z measured in terms of the field for barrier disappearance D͑2S −1͒; it differs from the usual classical definition h cl = / ͑2 ͒ due to the discreteness of the energy levels.…”

Section: Classical Limitmentioning

confidence: 99%

“…More interesting is the longitudinal response; its analysis revealed that an one-mode relaxation picture with time scale ⌳ 1 −1 is not valid in general. 7,8 A satisfactory description, however, is provided by a two-mode response, one mode corresponding to the overbarrier flux and the other, with a characteristic scale ⌳ w −1 , describing the faster intrawell dynamics. 9 Quantum mechanically, spin reversal can take place by thermal activation or tunneling ͑or a combination of both͒.…”

Section: Introductionmentioning

confidence: 99%

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Longitudinal relaxation and thermoactivation of quantum superparamagnets

Zueco

García‐Palacios

2006

Phys. Rev. B

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The relaxation mechanisms of a quantum nanomagnet are discussed in the framework of linear response theory. We use a spin Hamiltonian with a uniaxial potential barrier plus a Zeeman term. The spin, having arbitrary S, is coupled to a bosonic environment ͑phonons͒. From the eigenstructure of the relaxation matrix, we identify two main mechanisms: namely, thermal activation over the barrier, with a time scale ⌳ 1 −1 , and a faster dynamics inside the potential wells, with characteristic time ⌳ w −1 . This permits to introduce a simple analytical formula for the response, which agrees well with exact numerical results and covers experiments even under moderate to strong fields in the superparamagnetic range. In passing, we generalize known classical results for a number of quantities ͑e.g., integral relaxation times, initial decay time, Kramers' rate͒, results that are recovered in the limit S → ϱ.

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Section: Lowest Eigenvalue ⌳mentioning

confidence: 99%

Section: Classical Limitmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Longitudinal relaxation and thermoactivation of quantum superparamagnets

Zueco

García‐Palacios

2006

Phys. Rev. B

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“…In order to obtain these results we shall use the approach of Coffey, Kalmykov, and Waldron 12 for the solution of the infinite hierarchy of differential-recurrence relations which has already allowed us to obtain the exact solution for the longitudinal relaxation. 16 This approach is based on matrix continued fractions and essentially constitutes a further development of Risken's method. 10 It has also been used in the theory of dielectric and Kerr effect relaxation.…”

Section: Introductionmentioning

confidence: 99%

Transverse complex magnetic susceptibility of single-domain ferromagnetic particles with uniaxial anisotropy subjected to a longitudinal uniform magnetic field

Kalmykov

Coffey

1997

Phys. Rev. B

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The infinite hierarchy of differential-recurrence relations for the equilibrium transverse correlation functions appropriate to magnetic relaxation of single-domain ferromagnetic particles with uniaxial anisotropy subjected to a uniform external magnetic field H 0 is derived by averaging Gilbert's equation. Exact expressions in terms of matrix continued fractions for the transverse complex magnetic susceptibility are obtained with the aid of linear-response theory by solving the infinite hierarchy. The principal features of the spectra are emphasized in figures showing the real and imaginary parts of the complex magnetic susceptibility. The accuracy and the range of the applicability of analytical results based on the effective eigenvalue method is established. It is shown that this method provides in general a good approximation to the exact solution with the exception of the range of low-to-intermediate barrier heights of the anisotropy potential where at small H 0 there exists essentially a spread of the precession frequencies of the magnetization.

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“…3. Here, the effect of the depletion 19,23 of the shallower of the two potential wells of a bistable potential ͑5͒ by a bias field is apparent: at fields above the critical field h c at which the depletion occurs, it is possible to make the LF peak disappear ͑curves 3 and 3Ј͒. Such behavior of ͑ ͒ implies that if one is interested solely in the low-frequency ( р1) part of ͑ ͒, where the effect of the HF modes may be completely ignored ͑so that the relaxation of the magnetization at long times may be approximated by a single exponential with the characteristic time ͒, then the Debye-like relaxation formula, viz.,…”

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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Constant-magnetic-field effect in Néel relaxation of single-domain ferromagnetic particles

Cited by 111 publications

References 13 publications

Longitudinal relaxation and thermoactivation of quantum superparamagnets

Longitudinal relaxation and thermoactivation of quantum superparamagnets

Transverse complex magnetic susceptibility of single-domain ferromagnetic particles with uniaxial anisotropy subjected to a longitudinal uniform magnetic field

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

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