Generalized Spin-Glass Relaxation

Abstract

Spin relaxation close to the glass temperature of CuMn and AuFe spin glasses is shown, by neutron spin echo, to follow a generalized exponential function which explicitly introduces hierarchically constrained dynamics and macroscopic interactions. The interaction parameter is directly related to the normalized Tsallis non-extensive entropy parameter, q, and exhibits universal scaling with reduced temperature. At the glass temperature q = 5/3 corresponding, within Tsallis' q-statistics, to a mathematically defined critical value for the onset of strong disorder and non-linear dynamics. However the stretched exponential form does not adequately describe the relaxation of either structural or magnetic glasses close to T g and below, where selfsimilarity in time (i.e. fractal behaviour in time) occurs. This is demonstrated in Monte Carlo calculations by Ogielski [8], based upon a 3d ±J Ising spin glass model, which show that close to the spin glass temperature the time dependent spin autocorrelation function should take a phenomenological modified Kohlrausch form which incorporates a power law dependence:in which β increases from 1/3 at T g to 1 at ∼ 4T g , x increases from 0 below T g to 0.5 at high temperatures and the relaxation time, τ , diverges at T g . This prediction is also largely supported by neutron spin echo (NSE) measurements [11]. The origins and implications of such non-exponential relaxation remain the subject of some debate, not least because it can be demonstrated that Kohlrausch-like relaxation may arise from either a statistical distribution of independent (parallel) relaxation channels, or from more complex hierarchically constrained dynamics [12]. For a detailed physical insight it is necessary to explore global models of glassy relaxation which attempt intrinsically to embody both distributed dynamics and the interactions that may lead to hierarchical relaxation.Such a model was introduced by Weron [13] in an attempt to explain the apparently universal power law for dielectric relaxation. Weron's rigorous probabilistic approach, based on the cluster model of Dissado and Hill [14], considers a hierarchical progression of relaxation which results in a continuously changing energy landscape. The hierarchy is introduced through the formation of finite clusters which arise from interactions between relaxing dipoles, with each cluster being represented by an effective dipole related to its internal structure. The time taken for polarization fluctuations to reach equilibrium is a random variable that for each relaxing dipole depends upon two other random variables, namely the waiting time and the dissipation rate. Through these variables Weron accounts for the effects of both intercluster and intra-cluster interactions with the characteristic timescale of any relaxing entity being restricted by the structural reorganization of the surrounding clusters and derives a generalized relaxation functionwhere β is associated with the fractal geometry of the system and k(> 0) is an effective interaction par...

Monitoring a simple hydrolysis process in an organic solid by observing methyl group rotation

“…where R* is the characteristic relaxation rate and β is the stretching parameter [11,22,[29][30][31][32][33][34][35]. If the relaxation is exponential to within experimental uncertainty, β = 1 and R* is labeled R. This occurs in pure compounds like 1 and 2 at temperatures below the maximum in the relaxation rate [2,[8][9][10][22][23][24][25][26][27][28].…”

Nonextensive statistical mechanics and high energy physics

“…If x has the physical dimensions of an [energy] 1/η , an effective temperature T q can be defined through β q = 1 kT q . If x has the physical dimensions of a [time], a characteristic relaxation time τ q can be defined through β q = 1 (τ q ) 1/η (see [37] for such an example). In the x → ∞ limit, we straightforwardly verify that, for q > 1,…”

“…We briefly mention here some selected ones: cold atoms in optical lattices [17], trapped ions [18], asteroid motion and size [19], motion of biological cells [20], edge of chaos [21][22][23][24][25][26][27][28][29][30][31], restricted diffusion [32], defect turbulence [33], solar wind [34], dusty plasma [35,36], spin-glass [37], overdamped motion of interaction particles [38], tissue radiation [39], nonlinear relativistic and quantum equations [40], large deviation theory [41], long-range-interacting classical systems [42][43][44][45][46], microcalcification detection techniques [47], ozone layer [48], scale-free networks [49][50][51], among others.…”

Structural and magnetic properties of the cobaltate series (BaSr)4−xLa2xCo

“…The stretched exponential function has traditionally been used to model relaxation in spin glasses or structural glasses, and a generalization has been discussed recently. 35,36 In the modeling procedure, the Fourier Transform (time to energy) of the stretched exponential relaxation function was computed with sufficient precision using a numerical procedure adapted to the particular shape of the function. 37 The β parameter was set to 0.25 and held fixed throughout, because, as it is a phenomenological parameter, a possible temperature dependence will add too much uncertainty to the fitting to give dependable results for the relaxation time.…”