Study of the spin correlation and the percolation threshold in the B-site spinel

High-temperature series expansion of the correlation function on the B- spinel lattice are computed up to order 6 in β = 1/(kBT) for Heisenberg model including both the nearest and next-nearest-neighbor interactions J1 and J2 respectively. The behavior with the temperature and the site dilution is presented. The approach is applied to the experimental results of the B-spinel ZnCr2xAl2-2xS4. The critical temperature and the critical exponents for the susceptibility and the correlation length are deduced by applying the Padé approximant methods. The following estimates are obtained for the familiar critical exponents: γ=1.382±0.012 and ν = 0.691±0.011. These values are not sensitive to the dilution ratio x. The bond percolation threshold xp is determined by studying the disorder variation of the correlation length ξ. The xp is considered as the concentration at which ξ vanishes. The obtained values are xp =0.27 when only J1 is considered and 0.23 when both J1 and J2 are considered.High-temperature series expansion of the correlation function on the B- spinel lattice are computed up to order 6 in β = 1/(kBT) for Heisenberg model including both the nearest and next-nearest-neighbor interactions J1 and J2 respectively. The behavior with the temperature and the site dilution is presented. The approach is applied to the experimental results of the B-spinel ZnCr2xAl2-2xS4. The critical temperature and the critical exponents for the susceptibility and the correlation length are deduced by applying the Padé approximant methods. The following estimates are obtained for the familiar critical exponents: γ=1.382±0.012 and ν = 0.691±0.011. These values are not sensitive to the dilution ratio x. The bond percolation threshold xp is determined by studying the disorder variation of the correlation length ξ. The xp is considered as the concentration at which ξ vanishes. The obtained values are xp =0.27 when only J1 is considered and 0.23 when both J1 and J2 are considered

Critical Properties and Exchange Interactions of Antiferromagnetic A-spinel Lattice: A Study Through High-temperature Series Expansions

We derive high- temperature series expansions for the spin correlation functions of the A-spinel lattice. The development is extended to the order 6 in β = 1/KBT with nearest-neighbour and next-nearest neighbour interactions. The results are given for various neighbour correlation functions (up to the third). The behaviour with the temperature is presented. The critical region is studied by applying the Padé approximants method to the corresponding high- temperature series expansion of the magnetic susceptibility and the correlation length. The approach is applied to the experimental results of the particular system A-spinel CoCo2O4 . The following estimates are obtained for the familiar critical exponents:  γ =  1.382±0.010 and ν =  0.701±0.012.We derive high- temperature series expansions for the spin correlation functions of the A-spinel lattice. The development is extended to the order 6 in β = 1/KBT with nearest-neighbour and next-nearest neighbour interactions. The results are given for various neighbour correlation functions (up to the third). The behaviour with the temperature is presented. The critical region is studied by applying the Padé approximants method to the corresponding high- temperature series expansion of the magnetic susceptibility and the correlation length. The approach is applied to the experimental results of the particular system A-spinel CoCo2O4 . The following estimates are obtained for the familiar critical exponents:  γ =  1.382±0.010 and ν =  0.701±0.012

Study of critical properties in B-spinel ZnxCd1-xCr2Se4 (0.35 ≤ x ≤ 0.58)

The critical behaviour of the B-spinel ZnxCd1-xCr2Se4 systems is studied in the concentration range 0.35≤x≤0.58. The mean field theory and the ferromagnetic spin-wave theory at low temperatures are combined to calculate the exchange integrals up to the third nearest neighbours. The ferromagnetic critical region is studied by the high-temperature series expansion (H.T.S.) extrapolated with the Padé (P.A) approximants method. The critical temperatures T c and the critical exponents associated with the magnetic susceptibility (γ) and the correlation length (ν) are estimated. The obtained values of T c are in good agreement with those obtained by magnetic measurements. The values of γ and ν are sensitive to the dilution ratio x. For the compounds situated in the ferromagnetic region ( 0.35≤x≤0.41), they are close to those of 3D Heisenberg model. For the compounds presenting re-entrant behaviour ( 0.41≤x≤0.58 ), γ and ν deviate slowly from those of this model and approach the values found in re-entrant systems.The critical behaviour of the B-spinel ZnxCd1-xCr2Se4 systems is studied in the concentration range 0.35≤x≤0.58. The mean field theory and the ferromagnetic spin-wave theory at low temperatures are combined to calculate the exchange integrals up to the third nearest neighbours. The ferromagnetic critical region is studied by the high-temperature series expansion (H.T.S.) extrapolated with the Padé (P.A) approximants method. The critical temperatures T c and the critical exponents associated with the magnetic susceptibility (γ) and the correlation length (ν) are estimated. The obtained values of T c are in good agreement with those obtained by magnetic measurements. The values of γ and ν are sensitive to the dilution ratio x. For the compounds situated in the ferromagnetic region ( 0.35≤x≤0.41), they are close to those of 3D Heisenberg model. For the compounds presenting re-entrant behaviour ( 0.41≤x≤0.58 ), γ and ν deviate slowly from those of this model and approach the values found in re-entrant systems

Evaluation Of The Heavy Metals Accumulate In Samples Of TheSediments, Soils And Plants By Icp­oes With The Average Sebou

The urban, industrial and artisanal wastes liquid of the town of Fez have a very remarkable impact in the valley of Sebou. For that, various samples of sediments, agricultural grounds and plants were collected upstream like downstream from the junction Oued Fez- Oued Sebou along about thirty the kilometers; and analyzed by the method of the optical spectrometry of emission to source of plasma in inductive coupling (ICP-OES). These analyses enabled us to evaluate the contents of heavy metals such as: Ba, Zn, Cr, Ni, Co, Cd, Pb, Cu and others. All the results record a high degree of contamination of the metal elements to the state of trace in samples of sediments, grounds and plants irrigated with worn water containing of the particles of suspended materials. We could establish significant correlations of each metal for the various compartments of the ecosystem.The urban, industrial and artisanal wastes liquid of the town of Fez have a very remarkable impact in the valley of Sebou. For that, various samples of sediments, agricultural grounds and plants were collected upstream like downstream from the junction Oued Fez- Oued Sebou along about thirty the kilometers; and analyzed by the method of the optical spectrometry of emission to source of plasma in inductive coupling (ICP-OES). These analyses enabled us to evaluate the contents of heavy metals such as: Ba, Zn, Cr, Ni, Co, Cd, Pb, Cu and others. All the results record a high degree of contamination of the metal elements to the state of trace in samples of sediments, grounds and plants irrigated with worn water containing of the particles of suspended materials. We could establish significant correlations of each metal for the various compartments of the ecosystem

Phase diagrams of site diluted ferromagnetic semi infinite system

The spin correlations functions of face-centered cubic semi-infinite system are investigated by using the high  temperature series expansions extrapolated with the Padé approximant method for Heisenberg, XY and Ising models. The magnetic phase diagrams tc(n) versus the dilution x are obtained. The value obtained of the percolation threshold is. Xp≈0.2 The Xp is defined as the concentration at which tc =0The spin correlations functions of face-centered cubic semi-infinite system are investigated by using the high  temperature series expansions extrapolated with the Padé approximant method for Heisenberg, XY and Ising models. The magnetic phase diagrams tc(n) versus the dilution x are obtained. The value obtained of the percolation threshold is. Xp≈0.2 The Xp is defined as the concentration at which tc =

Study of Magnetic Superexchange in diluted Systems Znx Cd1-xCr2Se4 ( 0.35 ≤ x ≤ 0.58 )

The effects of cationic substitutions at different concentrations within the lattice Znx Cd1-xCr2Se4 (0.35≤x≤0.58) on the electronic transfer in chromium ions are investigated. For this propose, after taking into account the exchange integrals, we use the Anderson’s-Kanamori theory of superexchange to determine the transfer integrals bσσ and bπσ . With the use of the conventional molecular orbital model the covalency-mixing parameters, λσ and λπ, the electron spin transfer coefficients, ƒ i (i=σ, π, s ), and the total charge, C, transferred from ligand to the chromium ions, are evaluated. The variation of bσσ and bσπ with x agree with the passage of the system from ferromagnetic to antiferromagnetic order. For the compound presenting re-entrant behaviour (0.45≤x≤0.58), f s exhibits anomalous. The increasing in C with x is consistent with the expected decrease in covalency of the non magnetic cation in tetrahedral site.The effects of cationic substitutions at different concentrations within the lattice Znx Cd1-xCr2Se4 (0.35≤x≤0.58) on the electronic transfer in chromium ions are investigated. For this propose, after taking into account the exchange integrals, we use the Anderson’s-Kanamori theory of superexchange to determine the transfer integrals bσσ and bπσ . With the use of the conventional molecular orbital model the covalency-mixing parameters, λσ and λπ, the electron spin transfer coefficients, ƒ i (i=σ, π, s ), and the total charge, C, transferred from ligand to the chromium ions, are evaluated. The variation of bσσ and bσπ with x agree with the passage of the system from ferromagnetic to antiferromagnetic order. For the compound presenting re-entrant behaviour (0.45≤x≤0.58), f s exhibits anomalous. The increasing in C with x is consistent with the expected decrease in covalency of the non magnetic cation in tetrahedral site

Study of the magnetic order in chromium spinel systems

We present a study of the magnetic properties of the A1-x CuxCr2X4 (A=Dp,Zn,....; X=S,Se,O,...)chromium spinel systems. Using the mean field theory, we have evaluated the nearest neighbour, the next-neighbour super-exchange, and the third next nearest neighbour interaction J1(x), J2(x) and J3(x), respectively for the Zn1-xCuxCr2Se4and J1(x), J2(x) for the Cd1-xCuxCr2Se4systems in the whole range of concentration 0≤x≤1. By using the high-temperature series expansions combined with the Padé approximants method, we have obtained the magnetic phase diagrams in Tc versus dilution c. A spin glass phase is predicted for intermediate range of concentration. The obtained results are in agreement with experimental ones obtained by magnetic measurements for the systems studied. The critical exponents associated with the magnetic susceptibility g and the correlation lengths n have been deduced. The obtained values are comparable to those of 3D Heisenberg model, and are insensitive to the dilution c.We present a study of the magnetic properties of the A1-x CuxCr2X4 (A=Dp,Zn,....; X=S,Se,O,...)chromium spinel systems. Using the mean field theory, we have evaluated the nearest neighbour, the next-neighbour super-exchange, and the third next nearest neighbour interaction J1(x), J2(x) and J3(x), respectively for the Zn1-xCuxCr2Se4and J1(x), J2(x) for the Cd1-xCuxCr2Se4systems in the whole range of concentration 0≤x≤1. By using the high-temperature series expansions combined with the Padé approximants method, we have obtained the magnetic phase diagrams in Tc versus dilution c. A spin glass phase is predicted for intermediate range of concentration. The obtained results are in agreement with experimental ones obtained by magnetic measurements for the systems studied. The critical exponents associated with the magnetic susceptibility g and the correlation lengths n have been deduced. The obtained values are comparable to those of 3D Heisenberg model, and are insensitive to the dilution c

Phase diagrams of site diluted semi infinite ferromagnetic film

The magnetic susceptibility of a semi-infinite ferromagnetic films with a simple cubic lattice and the face centered cubic lattice is investigated by the method of exact high-temperature series expansions (HTSE) extrapolated with the Padé approximants method for Heisenberg, XY and Ising models. The magnetic phase diagrams in (tc (ν), c) plane are obtained. The value of the percolation threshold Xp is obtained. The Xp is defined at which tc= 0.The magnetic susceptibility of a semi-infinite ferromagnetic films with a simple cubic lattice and the face centered cubic lattice is investigated by the method of exact high-temperature series expansions (HTSE) extrapolated with the Padé approximants method for Heisenberg, XY and Ising models. The magnetic phase diagrams in (tc (ν), c) plane are obtained. The value of the percolation threshold Xp is obtained. The Xp is defined at which tc= 0

Phase diagrams of nanoparticles of diluted magnetic semiconductors

The magnetic properties of diluted magnetic semi conductors (DMS)Cd1-xMnxTe are investigated. Using the mean field theory, we have evaluated the critical temperature from the nearest neighbour interactions and the energy exchange for the different diameter of the Cd0.5Mn0.5Te nanoparticle. The critical exponents are obtained. The magnetic phase diagrams (Tc versus dilution ) have been determined by the High-temperature series expansions. The critical exponents associated with the magnetic susceptibility (g) and correlation lengths (v) are deduced.The magnetic properties of diluted magnetic semi conductors (DMS)Cd1-xMnxTe are investigated. Using the mean field theory, we have evaluated the critical temperature from the nearest neighbour interactions and the energy exchange for the different diameter of the Cd0.5Mn0.5Te nanoparticle. The critical exponents are obtained. The magnetic phase diagrams (Tc versus dilution ) have been determined by the High-temperature series expansions. The critical exponents associated with the magnetic susceptibility (g) and correlation lengths (v) are deduced