Percolation model for relaxation in random systems

Chamberlin, Ralph V.; Haines, Donald N.; Kingsbury, D.

doi:10.1016/0022-3093(91)90297-j

Cited by 11 publications

(7 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The key distinction of our approach is that we consider the response of low-energy, internal degrees of freedom (examples include magnons, phonons, and polaritons) for which the energylevel spacing decreases with increasing domain size. Our model gives better agreement with the observed resDonse from dozens of different materials, including magnetic relaxation in random ferromagnets, spin glasses, and oxide superconductors (7,15) as well as the dielectric response or structural relaxation of liquids, glasses, polymers, and metals (6,7,16). Here we show that this model accurately describes the primary magnetic response of singlecrvstal Fe.…”

supporting

confidence: 57%

Slow Magnetic Relaxation in Iron: A Ferromagnetic Liquid

Chamberlin

Scheinfein

1993

Science

View full text Add to dashboard Cite

The remanent magnetization of single-crystal iron whiskers has been measured from 10(-5) to 10(4) seconds after the removal of an applied field. The observed response is accurately modeled by localized magnon relaxation on a Gaussian size distribution of dynamically correlated domains, virtually identical to the distribution of excitations in glass-forming liquids. When fields of less than 1 oersted are removed, some relaxation occurs before 10(-5) second has elapsed; but when larger fields are removed, essentially all of the response can be accounted for by magnon relaxation over the available time window. The model provides a physical picture for the mechanism and observed distribution of Landau-Lifshitz damping parameters.

show abstract

supporting

confidence: 57%

Slow Magnetic Relaxation in Iron: A Ferromagnetic Liquid

Chamberlin

Scheinfein

1993

Science

View full text Add to dashboard Cite

show abstract

“…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.…”

mentioning

confidence: 72%

Remanent magnetization of a simple ferromagnet

Chamberlin

Holtzberg

1991

Phys. Rev. Lett.

View full text Add to dashboard Cite

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...

show abstract

“…As a consequence, in theoretical attempts to model relaxation it has been commonly assumed that the empirical relaxation laws reflect a kind of general behavior which is independent of the details of systems under study [7,10,11,38,40,62,64,66]. In recent attempts to find the origins of the nonexponential relaxation patterns the idea of complex systems as "structures with variations" [18] that are characterized through a large diversity of elementary units and strong interactions between them is of special importance.…”

Section: Introductionmentioning

confidence: 99%

“…Intuitively, one expects "averaging principles" like the law of large numbers to be in force. However, it turns out to be very hard to make this intuition precise in concrete examples of stochastic systems with a large number of locally interacting components [11,21,32,33,40,50,62,63,67].…”

Section: Introductionmentioning

confidence: 99%

Limit theorems for randomly coarse grained continuous-time random walks

Jurlewicz

2005

Dissertationes Math.

View full text Add to dashboard Cite

Percolation model for relaxation in random systems

Cited by 11 publications

References 11 publications

Slow Magnetic Relaxation in Iron: A Ferromagnetic Liquid

Slow Magnetic Relaxation in Iron: A Ferromagnetic Liquid

Remanent magnetization of a simple ferromagnet

Limit theorems for randomly coarse grained continuous-time random walks

Contact Info

Product

Resources

About