Justyna Trzmiel

Subordination model of anomalous diffusion leading to the two-power-law relaxation responses

We derive a general pattern of the nonexponential, two-power-law relaxation from the compound subordination theory of random processes applied to anomalous diffusion. The subordination approach is based on a coupling between the very large jumps in physical and operational times. It allows one to govern a scaling for small and large times independently. Here we obtain explicitly the relaxation function, the kinetic equation and the susceptibility expression applicable to the range of experimentally observed power-law exponents which cannot be interpreted by means of the commonly known Havriliak-Negami fitting function. We present a novel two-power relaxation law for this range in a convenient frequency-domain form and show its relationship to the Havriliak-Negami one.

Stretched-exponential photoionization of the metastable defects in gallium doped Cd0.99Mn0.01Te: Statistical origins of the short-time power-law in response data

The subject of the present study is the low temperature nonexponential transients of photoconductivity build-up in gallium doped Cd0.99Mn0.01Te semiconducting mixed crystals possessing metastable defects, so called DX centers. The phototransients were analyzed in terms of two approaches. The first one was the two-exponential fitting that is usually applied to explain the persistent photoeffect build-up in materials with DX centers. The second, implemented in the above-mentioned semiconductors, was the stochastic model of relaxation leading to the stretched-exponential result. The latter fitting was found to be more appropriate for it justifies the short-time power-law exhibited by the phototransient response. According to the stochastic approach this behavior results from a heavy-tailed distribution of photoionized DX centers. The distribution can have its origin in different local arrangements.

Unusual electronic behavior in the polycrystalline metal organic framework [(CH3)2NH2][Na0.5Fe0.5(HCOO)3]

In this study, the dielectric properties of a polycrystalline metal organic framework [(CH3)2NH2][Na0.5Fe0.5(HCOO)3] (DMNaFe) sample were investigated. The DMNaFe sample exhibited a typical relaxor-like relaxation response in addition to a ferroelastic order-disorder phase transition. Analysis of the frequency dependence of the complex permittivity revealed the characteristic two-power-law dipolar glass relaxor behavior of the DMNaFe, indicating complex cluster formation in the material. Moreover, an unusual transformation associated with the ferroelastic phase transition from the generalized Mittag-Leffler relaxation pattern (low-temperature ordered phase) to the Havriliak-Negami one (high-temperature disordered phase) was detected. The relaxation data obtained for the investigated sample were interpreted based on the stochastic approach to relaxation processes.

The frequency-domain relaxation response of gallium doped Cd1-xMnxTe

In this paper the complex dielectric permittivity of gallium doped Cd(0.99)Mn(0.01)Te mixed crystals is studied at different temperatures. We observe a two-power-law relaxation pattern with m and n, the low- and high-frequency power-law exponents respectively, satisfying the relation m < 1-n. To interpret the empirical result we propose a correlated-cluster relaxation mechanism. This approach allows us to find origins of both power-law exponents, m and n.

Experimental evidence of the role of compound counting processes in random walk approaches to fractional dynamics

We present dielectric spectroscopy data obtained for gallium-doped Cd(0.99)Mn(0.01)Te:Ga mixed crystals, which exhibit a very special case of the two-power-law relaxation pattern with the high-frequency power-law exponent equal to 1. We explain this behavior, which cannot be fitted by any of the well-known empirical relaxation functions, in a subordinated diffusive framework. We propose a diffusion scenario based on a renormalized clustering of a random number of spatio-temporal steps in the continuous-time random walk. Such a construction substitutes the renewal counting process, which is used in the classical continuous time random walk methodology, with a compound counting one. As a result, we obtain an appropriate relaxation function governing the observed nonstandard pattern, and we show the importance of the compound counting processes in studying fractional dynamics of complex systems.

Comparison of the two-power-law generalized Mittag-Leffler and Havriliak-Negami dielectric relaxation responses

In this paper analysis of the two-power-law relaxation behavior in terms of the generalized Mittag-Leffler (GML) and Havriliak-Negami (HN) responses is presented. Using the probabilistic representation of the relaxation function, differences and similarities between the GML and HN patterns are investigated by means of the Monte Carlo technique.

Stretched-exponential photoionization of the DX-related centers in indium-and gallium-doped Cd1−xMnxTe alloys

The kinetics of photoconductivity build-up in indium- and gallium-doped Cd1−x Mnx Te mixed crystals was studied at 80 K. The photoconductivity transients are non-exponential, due to the presence of metastable DX centers, formed by both elements in these semiconductors. It has been shown for the first time that the kinetics of the observed photoconductivity transients can be properly described solely by the Kohlrausch–Williams–Watts (KWW) function. This statement has been verified by the careful analysis of the derivatives of the transients. It has been found that they obey short-time power-law behavior, regardless of the donor type and the content of manganese. This asymptotic property can be explained exclusively by the KWW approach. Such an approach results from a broad distribution of relaxation rates related to the DX centers. It is reasonable to assume that, in Cd1−x Mnx Te alloys, the broad distribution arises from the differences in local atomic configurations in the vicinity of the DX centers.

Two-power-law relaxation processes in semiconductors possessing metastable defects

In this paper the two-power-law relaxation behavior of semiconducting materials possessing deep, metastable defects is analyzed in terms of a model leading to new power-law relaxation pattern being a mixture of the generalized Mittag-Leffler (GML) and Havriliak-Negami (HN) responses, which enlarges the class of physically well grounded fitting functions. Applying the probabilistic representation of the relaxation decay, we show that such a mixture can be derived from an extension of the stochastic model of correlated clusters.