M. Hamedoun

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.

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 superexchange and covalency parameters of ZnxCd1−xCr2Se4

Abstract The cationic substitutions effects at different concentrations, within the ZnxCd1−xCr2Se4 lattice (0.35⩽x⩽0.58), on the electronic transfer in chromiums ion are investigated. For this purpose, after taking into account the exchange integrals, we use the Anderson–Kanamori theory of superexchange to determine the transfer integrals bσσ and bπσ. Using the conventional molecular orbital model, the covalency-mixing parameters λσ and λπ, the electron spin transfer coefficients f i (i=σ , π, s) and the total charge C are evaluated. The bσσ and bσπ variation with x, agrees with the passage of the system from ferromagnetic to antiferromagnetic order. For the compound presenting re-entrant behaviour (0.45⩽x⩽0.58), fs exhibits anomalies. The C increasing with x is consistent with the expected decrease in covalency of the non-magnetic cation in a tetrahedral site.

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.

Magnetic studies in spinel solid solutions ZnxCd1−xCr2Se4 (0.35 ⩽ x ⩽ 0.45)

Abstract Magnetization measurements were presented in this paper for the spinel solid solutions ZnxCd1−xCr2Se4 for x = 0.35,0.41 and 0.45. The Cr moment is 2.8 μB/Cr where the magnetization saturates for fields up to 10 kOe at low temperature. Using mean field theory and spin wave theory, we find a satisfactory agreement for the values of the nearest-neighbour (n.n) exchange integral.

Magnetization studies of amorphous Fe80 − xTmxB20 alloys

Abstract We have carried out magnetic studies at fields up to 18 kOe of melt- spun amorphous Fe 80 − x Tm x B 20 alloys. Magnetization and Curie temperatures were investigated. We have extracted the anisotropy constant from the coercivity.

Physical properties of Co(Mn)Fe2O4 nanomaterials

CoFe2O4 and MnFe2O4 ferrite nanoparticles were prepared by the co-precipitation method. The structural evolutions of the nanophase have been studied. The refinement result showed that the type of cationic distribution over the tetrahedral and octahedral sites in the nanocrystalline lattice is a partially inverse spinel. The morphology of the samples has been determined using transmission electron microscopy and the magnetic properties of the samples are given. The gap energy is calculated using the Korringa–Kohn–Rostoker method combined with a coherent potential approximation and using optical measurements for CoFe2O4 and MnFe2O4. This study has been extended theoretically to the mixed spinel ferrites, FeCoMnxFe1−xO4. Indeed, the saturation magnetization, the critical temperature, exchange interactions and Curie constant for the cation distribution , have been calculated. The high temperature series expansion combined with the Pade approximant are used to determine the critical temperature and critical exponent (γ) associated with the magnetic susceptibility of mixed spinels.

STUDY OF CRITICAL BEHAVIOUR IN DILUTED FERROMAGNETIC: THIN FILMS AND SEMI-INFINITES FILMS

By using the high-temperature series expansion technique, we have analyzed the phase transition and the critical phenomena of a ferromagnetic thin film and ferromagnetic semi-infinite film, through three models: Ising, XY and Heisenberg. The critical reduced temperature τC(v) is studied as a function of the thickness of the film. In the case of the magnetic film and semi-infinite film, on the simple cubic lattice and the face-centered cubic lattice, τC(v) is studied as a function of the exchange interactions in the bulk, and on the surface. A critical value of the surface exchange interaction in the film above which the surface and the interface magnetism appears is obtained. The dependence of the reduced critical temperature on the thickness of the film has been investigated. These shifts of the critical temperatures TC(L) from the bulk value can be described by a power law. The obtained values for the simple cubic lattice and face centered cubic ferromagnetic thin film are in qualitative accordance with the universality class hypothesis. The critical exponent associated with the magnetic susceptibility is studied as a function of interactions. In a defined range of the exchange interactions, the obtained values for Heisenberg, XY and Ising models, for simple cubic thin film are comparable to the universal ones and are independent of the film thickness. The asymmetry of the structure and the competition of the effects of the exchange coupling, are important for the magnetic properties of the system. A critical value of the surface exchange interaction above which the surface magnetism appears is obtained. For the dependence of the critical parameter of surface reduced coupling as a function of the dilution x and the ratio of the exchange interaction between the surface and nearest neighbour layer to the bulk one R1 for the three studied models has been investigated. The magnetic phase diagrams are obtained for two structures. The percolation threshold is defined as the concentration xp at which τC=0. In the case of the thin film, the obtained values are xp≈0.2 in the bulk and xp≈0.4 at the surface. For the case of the semi-infinite film, the value obtained in the surface and the nearest layer at the surface is xp≈0.2.

Thermodynamic properties of the ferromagnetic spinel ZnpCd1−pCr2Se4

Abstract The magnetic properties of the B-spinel ferromagnetic Zn p Cd 1− p Cr 2 Se 4 compound are studied via a cluster series expansion approximation with nearest and next-nearest exchange integrals J 1 and J 2 , respectively. Using the minimization of the free-energy expressions, the magnetization, the magnetic susceptibility, the two-spin correlation functions and the specific heat are obtained and computed numerically as a function of temperature and for each composition of the system. The magnetization curves are used to determine the critical temperatures T c . Using the power laws in the vicinity of the critical regions the critical exponents β , γ and α associated, respectively, with the magnetization, the magnetic susceptibility and the specific heat are numerically calculated. The critical temperatures T c obtained are in very good agreement with those predicted by the magnetic measurements and the values of the critical exponents may be compared with other theoretical results based on the 3D Heisenberg model.

Critical behaviour and magnetic interactions in the diluted systems ZnxHg1−xCr2Se4 (0⩽x⩽1)

Abstract We study the magnetic properties and the critical behaviour of the B-spinel Zn x Hg 1− x Cr 2 Se 4 in the concentration range 0⩽ x ⩽1. Using the mean field theory and the probability distribution of the interactions, the exchange integrals were calculated up to second nearest neighbours. The critical region is studied by the high-temperature series expansion extrapolated with the Pade approximants method. The critical temperatures the critical exponents associated with the magnetic susceptibility ( γ ) and the correlation length ( ν ) are obtained. The values of T c and T N obtained by this method are in accordance with those predicted by magnetic measurements. The values of γ and ν are sensitive to the dilution ratio x . For the compounds situated in the long-range order (LRO) region (0⩽ x ⩽0.4 and 0.6⩽ x ⩽1), they are close to those of 3D Heisenberg model. For a concentration situated in the perturbed phase ( x =0.5), γ and ν deviate rapidly from the values predicted by this model and approach the values found in re-entrant systems.