Generalized Pair Approximation Research Articles

Generalized pair approximation in the description of the ac conductivity of a dense disordered array of quantum dots

AbstractThe frequency dependence of the hopping conductivity of dense arrays of semiconductor quantum dots of size $ \bar a $ substantially exceeding the edge‐to‐edge separation $ \bar w $ between the neighboring quantum dots is considered. It is shown that at low frequencies in a wide frequency range the conductivity obeys a fractional power law and its magnitude depends on the structural characteristics of the material. The possibility of the deviations from universality related to the material structure is discussed. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Phenomenological parameters for a magneto-optical characterization of Cd1−xMnxTe with moderate magnetic ion concentration

The modified Brillouin function approach is improved in order to obtain a correct description of the low-temperature behavior of the Zeeman splittings in Cd1−xMnxTe. This work is based on computer simulations, within the extended generalized pair approximation, of the two relevant phenomenological parameters, i.e. the effective spin and the temperature shift for moderate magnetic ion concentration. A significant temperature dependence of the temperature shift is predicted.

Randomness of the magnetic ion distribution in dilute magnetic semiconductor epilayers grown by molecular beam epitaxy

We have applied our extended generalized pair approximation to dilute magnetic semiconductor epilayers grown by molecular beam epitaxy and in this paper we have compared our calculations of the heavy-hole exciton Zeeman splitting with those we measured on Zn 1− x Mn x Se and those measured by other authors on Cd 1− x Mn x Te epilayers. It appears that there can be found experimental results, including ours, which exhibit a systematic tendency to lie well below the corresponding theoretical curves based on random distribution. We can clearly attribute this reduced paramagnetic behavior to a non-random distribution of the magnetic ions and we present a way to determine the degree of non-random distribution.

Description of the exchange effects in dilute magnetic semiconductor quantum structures

Based on our extended generalized pair approximation, a theoretical method is presented which realistically describes the exchange-interaction effects in dilute magnetic semiconducting quantum structures with moderate magnetic ion concentrations ( x ⩽ 10%). As an illustration of our approach, we have calculated the Zeeman splittings in Cd 1− x Mn x Te showing clearly the correlation between the mean spin projection of magnetic ions and the related p—d and d—d exchange integrals. On the other hand, our analysis of the Zeeman splittings in Cd 1− x Mn x Te/Cd 1− x− y Mn x Mg y Te quantum structures with different well widths demonstrates that the data are well described, within the experimental error, with the bulk values of the sp—d and d—d exchange-interaction constants.

Magnetic ion statistics and thermodynamics in dilute magnetic semiconductor quantum structures

We have extended our generalized pair approximation applicable, in principle, to diluted magnetic semiconductors, in which the spatial distribution of the magnetic ions may be assumed to be random and homogeneous, to systems with a variable magnetic ion concentration. Using our model, which may be called the extended generalized pair approximation, we have developed a quantitative description of the magnetization in dilute magnetic semiconductor quantum structures with moderate magnetic ion concentration (x10%). The latest models describing the radial dependence of the exchange interaction, clustering, and interface mixing are also discussed.

Application of Generalized Pair Approximation to Diluted Magnetic Semiconductor Quantum Structures

Application of Generalized Pair Approximation to Diluted Magnetic Semiconductor Quantum Structures

Magnetic properties of ( Cd1− x− yZnyMnx) 3As2

We have studied the specific heat, magnetization and susceptibility of the tetragonal diluted magnetic semiconductor (DMS) ( Cd 1− x− y Zn y Mnx x ) 3 As 2 (CZMA) with various compositions in dc magnetic fields up to 17 T and in the temperatu range 1.3−300 K. The complicated crystal structure of CZMA has inspired us to generalize the pair approximation, widely used in analysis of the magnetic behaviour of II-VI DMSs, for an arbitrary structure. The resulting model, which may be called the generalized pair approximation (GPA), has been subsequently applied to interpret the results of our magnetic measurements performed on CZMA. Based on theoretical analyses concerning the Mn-Mn interaction in DMSs, which show that the dominant roles in this process are played by superexchange and the Bloembergen-Rowland exchange, we have obtained satisfactory agreement between our approach and experiment by using the analytical formulae with only two adjustable parameters, i.e. the first nearest-neighbour exchange constants for both mechanisms, which appear to be strongly dependent on Zn content.

Magnetic susceptibility of (Cd 1−x−yZn yMn x) 3As 2

The magnetic susceptibility of the tetragonal semimagnetic semiconductor (Cd 1− x−y Zn y Mn x ) 3As 2 (CZMA) with various compositions has been measured in the temperature range 4.2–300 K. The paramagnetic part of the measured susceptibility is analysed within our generalized pair approximation (GPA) and treating the total Mn-Mn interaction strength as a sum of superexchange and the Bloembergen-Rowland exchange. As a result, the values of the first nearest-neighbour exchange constants for both mechanisms are determined appearing to be strongly dependent on Zn content. Finally, the results of our susceptibility measurements of CZMA, extended in some cases up to 370 K, are compared with those obtained recently by other authors for (Zn 1− x Mn x ) 3As 2 (ZMA) and (Cd 1− x Mn x ) 3As 2 (CMA) and a possible origin of the observed differences is discussed.

Generalization of the pair approximation and its application to (Zn1-xMnx)3As2.

By taking into account the results of recent studies of (${\mathrm{Zn}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$${)}_{3}$${\mathrm{As}}_{2}$ (ZMA), which is an example of a II-V diluted magnetic semiconductor (DMS) with a very complicated tetragonal crystal structure, we have generalized the pair-approximation model, widely used to analyze the magnetic behavior of II-VI DMS's, for an arbitrary structure. We have subsequently applied our model, which may be called the generalized pair approximation, to reinterpreting the results of magnetic measurements obtained for ZMA. Based on theoretical works that treat the Mn-Mn interaction in DMS's as a sum of superexchange and the Bloembergen-Rowland (BR) mechanism, we have been able to obtain satisfactory agreement between our approach and experiment by introducing only two adjustable parameters, in spite of the complexity of the crystal structure of ZMA. These parameters are the first nearest-neighbor exchange constants for both mechanisms and they have been found to be equal to -53 and -11 K for superexchange and the BR exchange, respectively.

High-field magnetization of (Cd 1− x− yZn yMn x) 3As 2

We have performed measurements of magnetization for two samples of the tetragonal semimagnetic semiconductor (SMSC) (Cd 1− x− yZn yMn x ) 3As 2 (CZMA) with different compositions, in fields up to 40T. Taking into account the complicated crystal structure of CZMA within the generalized pair approximation and basing on theoretical analyses concerning the Mn-Mn interaction in SMSC which show that the dominant roles in this process are played by superexchange and the Bloembergen-Rowland exchange, we have obtained a very good agreement between our calculated dependences and experimental data.

Short-range order and frustration in omphacite: Comparison of three CVM approximations

We compare three cluster variation method (CVM) models for order-disorder in omphacite (Al0.5Mg0.5)[Na0.5Ca0.5]Si2O6: the generalized point approximation (GPA), generalized pair approximation (GPaA) and an approximation that is based on two eight-body clusters (2X8A). The same Hamiltonian (set of pairwise interactions) is used for all three approximations. Pair probabilities predicted by the GPA obey the geometric constraints of the crysal structure (the frustration constraint), but the exclusion of short-range order (SRO) leads to overestimates of the configurational internal energy (〈E〉), and the critical temperature for cation order-disorder (Tc). The GPaA violates the frustration constraint, and it therefore fails to predict a P21/n → C2/c order-disorder transition and yields values for 〈E〉 and SRO that are inconsistent with the omphacite crystal structure. The 2X8A predicts SRO that is consistent with the frustration constraint, and it yields improved (lower) estimates of 〈E〉 and Tc relative to the GPA: 〈E〉2X8A<〈E〉GPA, and Tc(2X8A)≈0.741 Tc(GPA).

Configurational thermodynamics of aluminous pyroxenes: A generalized pair approximation

A pair approximation is used to estimate the effects of short-range order on the thermodynamic properties of aluminous clinopyroxenes on the joins diopside (CaMg-Si2O6)-jadeite (NaAlSi2O6) and diopside-CaTs (CaAl2SiO6). The generalized pair approximation is the simplest model for concentrated solutions which includes short-range order. Short-range order is expected to be especially significant in coupled solid solutions, such as aluminous pyroxenes, since atoms of different valence substitute for each other.

Electrodynamics of Superconductors as a Consequence of Local Gauge Invariance

AbstractThe electromagnetic properties of superconductors are studied in the framework of a quantum gauge‐invariant theory.The formulation is developed in the generalized pair approximation which preserves the Ward‐Takahashi identities. The macroscopic equations which regulate current and electromagnetic fields are derived by means of the boson transformation method. Comparison with previous works is reported.