Percolation model for relaxation in random systems

Chamberlin, Ralph V.; Haines, Donald N.

doi:10.1103/physrevlett.65.2197

Cited by 72 publications

(24 citation statements)

References 29 publications

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“…on a distribution of finite domains has been shown to give excellent agreement with observed magnetic relaxation in spin glasses [11], stress relaxation in ionic glasses [12,13], and dielectric susceptibility of glass-forming liquids [14,15]. The model is based on standard domain-size distributions and elementary finite-size quantization, thus providing a common link between fundamental excitations and observed dynamic response.…”

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confidence: 69%

Remanent magnetization of a simple ferromagnet

Chamberlin

Holtzberg

1991

Phys. Rev. Lett.

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We have measured the remanent magnetization of single-crystal EuS from 10""* to 10'' sec after removing an applied field. Using a recent model for magnon relaxation on finite domains, the data yield size-scaling exponents of ^=-0.10 ±0.02 and f=0.669 ±0.004, in excellent agreement with exact theoretical predictions. As a function of temperature, the remanent magnetization is a maximum above the Curie transition, and, for some thermal histories, becomes negative in the ferromagnetic regime. The behavior is consistent with a percolation backbone that is negatively coupled to the finite domains.PACS numbers: 75.50. Dd, 64.60.Ak, 75.40.Gb, 75.60.Lr Relaxation of the remanent magnetization in ferromagnetic materials has previously been attributed to rotation of individual domains, wall motion between domains, or relaxation of a continuum of internal degrees of freedom. Most models of domain rotation [1,2] consider activation over a smooth distribution of barrier heights, resulting in logarithmic time dependences, for which the 1949 measurements of Street and Woolley [3] remain the most cited evidence [4,5]. Power-law behavior is predicted by scaling theories for domain growth [6] and internal dynamics [7]. Other treatments yield Kohlrausch-Williams-Watts stretched-exponential relaxation [8]. All of these empirical formulas have divergent slope at short times, and hence they can only be approximations valid over a limited range. Complete numerical solution of semiclassical Ising [9] and Heisenberg [10] models generally exhibit relaxation times that increase with domain size. We have measured the magnetic relaxation of ferromagnetic EuS from 10""* to 10"^ sec after removing an applied field. The quality and range of the data are suflficient to demonstrate significant deviations from all of these previously proposed relaxation mechanisms.A recent model for relaxation of quantized excitations (magnons, phonons, polaritons, etc.) on a distribution of finite domains has been shown to give excellent agreement with observed magnetic relaxation in spin glasses [11], stress relaxation in ionic glasses [12,13], and dielectric susceptibility of glass-forming liquids [14,15]. The model is based on standard domain-size distributions and elementary finite-size quantization, thus providing a common link between fundamental excitations and observed dynamic response. Here we show that the remanent magnetization of single-crystal EuS is dominated by finite-size quantized magnons.Macroscopic ferromagnetic samples segregate into mesoscopic domains to reduce their magnetic dipolar energy. The lowest-energy domains (Goldstone modes), which form as metastable droplets in an otherwise ordered system, generally have a positive surface tension and a negative energy term proportional to volume.Minimizing the free energy leads to a domain-size distribution of the form [16-18] ris^-s'^&xp( -s^). The size-scaling exponents, 0=~^and f=T, are exact theoretical predictions for isotropic low-energy excitations, regardless of local structure or natur...

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confidence: 69%

Remanent magnetization of a simple ferromagnet

Chamberlin

Holtzberg

1991

Phys. Rev. Lett.

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“…Therefore, all the dipoles ͑or spins͒ within the correlated domain have the same average level of excitation. [14][15][16][17][18] Since the initial response ( P s ) and the relaxation rate ( s ) are directly related to the size of a given correlated domain, the net response P(t) can be written using the following linear response terms with the weighted sum over all the domains:…”

Section: Chamberlin's Correlated Domain Modelmentioning

confidence: 99%

Correlated domain model of deuterated dipole glass

Kim

Jang

1999

Phys. Rev. B

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The low-frequency dielectric relaxation of the deuterated rubidium ammonium dihydrogen phosphate ͑DRADP͒ dipole glass was investigated by examining the complex dielectric permittivity above the glass freezing temperature. We show that none of the well-known Debye-type relaxation functions that include the Cole-Cole, Cole-Davidson, and Kohlrausch-Williams-Watts functions adequately describe the observed dielectric relaxation behavior of the DRADP. We then examine the Chamberlin's correlated domain model as a possible description of the DRADP dipole glass. The experimental data and the computational results based on the correlated domain model qualitatively agree with each other with common features of ͑i͒ a long tail at the lower-frequency side and ͑ii͒ increase in the asymmetry of ⑀Љ() spectrum with decreasing temperature. Finally, we discuss the fitting results of the DRADP dipole glass in comparison with glass-forming liquids and other polar glasslike systems. ͓S0163-1829͑99͒03034-9͔ PHYSICAL REVIEW B 1 SEPTEMBER 1999-II VOLUME 60, NUMBER 10 PRB 60 0163-1829/99/60͑10͒/7170͑8͒/$15.00 7170

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“…The time evolution of physical properties of such a Ôstructure with variationsÕ is non-predictable or anomalous, and the main feature of all dynamical processes in such systems is their stochastic background. Hence, unlike the classical exponential relaxation law, the widely prevailing universal law (1) with its fractional power-law dependence cannot be explained in the framework of any intuitively simple physical concept [11][12][13][14][15][16][17][18][19][20]. The need to find the connections between the macroscopic, universal property (1) and the random, local properties of the relaxing complex system requires introduction into the theoretical analysis of advanced stochastic methods [9,13,16,[18][19][20].…”

Section: Introductionmentioning

confidence: 99%