N. Benzakour

High-temperature series expansion of the spin correlation functions in B-spinel lattice

High-temperature series expansion of the spin correlation functions on the B-spinel lattice are computed to order 6 in for Heisenberg model having both nearest- and next-nearest-neighbour exchange integrals. The results are given for various neighbour correlations (up to the third). The behaviour with the temperature and the site dilution is presented. The obtained results provide a useful tool for a straightforward interpretation and understanding of experimental data. The approach is applied to the experimental results of the B-spinel in the dilution range . The critical temperature and the critical exponents for the susceptibility and the correlation length are deduced by applying the Pade approximant methods. The following estimates are obtained for the familiar critical exponents: and . These values are not sensitive to the dilution ratio x. The transition temperatures as a function of x obtained by the present theory are found to be in excellent agreement with the experimental ones.

Phase transition in Heisenberg magnetic films

Abstract The phase transitions of a ferromagnet spin- S Heisenberg thin film are examined using the high-temperature series expansions technique extrapolated with Pade approximants method. The critical reduced temperature of the system τ c = k B T c /2 S ( S +1) J b is studied as function of the thickness of the film and the exchange interactions in the bulk, and within the surfaces J b , J s and J ⊥ , respectively. A critical value of surface exchange interaction above which the surface magnetism appears is obtained. The dependence of the reduced critical temperature on the film thickness L has been investigated. The effects of an amorphous magnetic surface on the critical properties of the film have been studied. The results show that the magnetic order of the thin film may be destroyed by a higher amorphization on the surface layers.

Magnetic properties and percolation threshold in diluted B-spinel ZnCr2xAl2−2xS4: a study through high-temperature expansions

By making use of high-temperature series expansions (HTSE) of the correlation functions, we study the thermal and disorder variation of the short-range order (SRO) in the particular B-spinel ZnCr2xAl2−2xS4. We developed the HTSE for the q-dependent static structure factor S(q) to the order 6 in reciprocal temperature including both the nearest- and next-nearest-neighbour interactions J1 and J2, respectively. Respecting the experimental fact that the broad diffuse peak of the neutron is situated at the particular wave vector and is insensitive to the temperature for a given ratio of dilution x, we have estimated the thermal variation of J1 and J2 in the case of the pure compound. The bond percolation threshold xp of the ZnCr2xAl2−2xS4 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 taken into account.

Magnetic structure and ground states in spinel B-site lattice

Abstract The ground states of diluted spinel AB2xB′2−2xX4 are studied as a function of x in the range 0.85 ⩽ x ⩽ 1 by means of a classical minimization of the exchange energies taking into account exchange integrals up to the fourth nearest neighbors J4. At low temperature, the magnetic structure observed in the spinel solid solution ZnCr2xAl2−2xS4 is well represented in the obtained ground states. The values of the relative exchange integrals, the intraplanar and the interplanar interactions are deduced. The disappearance of the long-range order is shown to be due to the decrease of the relative interplanar and intraplanar interactions when diluting Cr by Al.

Zn Doping Effect on Magnetic Properties of Znx Cd1−xCr2S4 Systems by High-Temperature Series Expansions

The effect of Zn doping on the magnetic properties of CdCr2S4 systems is studied by mean field theory and high-temperature series expansion (HTSE). The nearest neighbouring and the next-neighbouring super-exchange interactions J1(x) and J2(x) are evaluated for the spinel system ZnxCd1−xCr2S4 in the range 0≤x≤1. The intra-planar and the inter-planar interactions are deduced. The HTSE combined with the Pade approximant method (PA) is applied to the spinel system ZnxCd1−xCr2S4. The magnetic phase diagram, i.e. TC versus dilution x, is obtained. The critical exponents associated with the magnetic susceptibility γ and the correlation length ν are deduced. The obtained theoretical results are in agreement with the experimental data obtained by magnetic measurements.

Effect of Co-Substitution on Magnetic Properties in Spinels GeNi2O4 Systems

The magnetic properties of spinel GeNi2-2xCo2xO4 systems in the range 0 ≤ x ≤ 1 are studied by mean Geld theory and high-temperature series expansions. The nearest neighbouring and the next-neighbouring super-exchange interactions J1(x) and J2(x) are evaluated for these systems in the range 0 ≤ x ≤ 1, by using the first theory. The intra-planar and the inter-planar interactions and the exchange energy are deduced. The second theory is applied in the spinel GeNi2-2xCo2xO4 systems, combined with the Pade approximants method, to determine the magnetic phase diagrams (Tn versus dilution x) in the range 0 ≤ x ≤ 1. The obtained theoretical results are in agreement with experimental data obtained by magnetic measurements. The critical exponents associated with the magnetic susceptibility γ and the correlation lengths v are deduced.

Variation of exchange interaction in the GeNi2-xCoxO4 systems and in the CoRh2O4 nanoparticle

The magnetic properties of the spinels GeNi2-xCoxO4 systems in the range 0 ≤ x ≤ 2 have been studied by mean field theory (MFT) and high-temperature series expansions. The nearest neighbouring and the next-neighbouring super-exchange interactions J1 (x) and J2 (x) are evaluated for the spinel GeNi2-xCoxO4 systems in the range 0 ≤ x ≤ 2. The exchanges interactions are calculated for different sizes of CoRh2O4 nanoparticle by using the MFT. The intra-planar and the inter-planar interactions and the exchange energy are deduced for GeNi2-xCoxO4 and CoRh2O4. The second theory has been applied to the spinel GeNi2-xCoxO4 systems, combined with the Pade approximant method, we have obtained the magnetic phase diagrams (TN versus dilution x) in the range 0 ≤ x ≤ 2. The obtained theoretical results are in agreement with experimental ones obtained by magnetic measurements. The critical exponents associated with the magnetic susceptibility (γ) and the correlation lengths (ν) are deduced. The obtained theoretical results are in agreement with the experimental data obtained by magnetic measurements. The critical exponent associated to the correlation lengths (ν) is deduced for different sizes of CoRh2O4 nanoparticle.

Exchange integrals and magnetic short range order in the system CdCr2S4(1−x)Se4x

Abstract High-temperature series expansions are derived for the magnetic susceptibility and two-spin correlation functions for a Heisenberg ferromagnetic model on the B-spinel lattice. The calculations are developed in the framework of the random phase approximation and are given for both nearest and next-nearest neighbour exchange integrals J 1 and J 2 , respectively. Our results are given up to order 6 in β =( k B T ) −1 and are used to study the paramagnetic region of the ferromagnetic spinel CdCr 2 S 4(1− x) Se 4 x . The critical temperature T c and the critical exponents γ and ν associated with the magnetic susceptibility χ ( T ) and the correlation length ξ ( T ) respectively are deduced by applying the Pade approximant methods. The results as a function of the dilution x obtained by the present approach are found to be in excellent agreement with the experimental ones.