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ABSTRACTHerein, Fe3O4and Co0.6Fe2.4O4nanoparticles were prepared by using the coprecipitation method. In order to prove the synthesis of the spinel ferrites and to calculate the structural parameters of the sample, the X-Ray Diffraction (DRX) technique was investigated. Nano-particles morphology and their distribution were analysed using Transmission Electron microscopy (TEM). Spherical morphology with average particle size around 13 nm was observed. The magnetic properties were carried out using MPMS SQUID device, from the magnetic hysteresis loops; we can reveal that the insertion of cobalt modified the magnetic behaviour of Fe3O4by increasing the saturation magnetisation and coercive field of Fe3O4nanoparticle due to the high magnetic moment of cobalt cation.

•Ab initio calculations are used to investigate the DOS of Mn2Sn thin films.•The FLAPW, HTSE, MFT methods are used.•The exchange interaction and critical temperature of Mn2Sn thin films are deduced for different thicknesses.

In this paper, we analyzed the physical characteristics of the ternary alloys RE2Rh3Ge (RE = Pr and Sm) using the first principles calculation based on functional density theory integrated in the WIEN2K code. The calculated formation energies of Pr2Rh3Ge and Sm2Rh3Ge are −5.3827 and −5.2782 eV/atom, respectively, showing that these alloys may exist stably. The results of the band structure and density of states indicate that all of the compounds tested are magnetic metals, and their magnetism is mostly related to the contribution of Pr and Sm atoms. The total magnetic moments of Pr2Rh3Ge and Sm2Rh3Ge are 4.07245 and 11.16161 μB/f.u, respectively. Thermodynamic parameters such as heat capacity at constant pressure, entropy, Debye temperature, lattice volume, compressibility coefficients, and Grüneisen parameter alloys were calculated using the Gibbs algorithm and studied in depth over a large temperature range of 0–900 K. The Debye temperature increases with increasing pressure and decreases with decreasing temperature. Moreover, the Debye temperatures calculated at P = 0 GPa and T = 300 K are equal to be 342 and 322 K for Pr2Rh3Ge and Sm2Rh3Ge, respectively. The optical characteristics such as the real and imaginary portions of the dielectric function, the absorption coefficient, the energy-loss function, and the refractive index were investigated and discussed in more depth.

The mean field theory (MFT) and high temperature series expansions (HTSEs) of the magnetic susceptibility are used to investigate the magnetic properties in simple cubic (sc) antiferromagnetic with spins S = 1 and S = 3/2 films by using both the Ising and the XYmodels. The films consisting of l= 2, 3, 4, 5, 6 and infinite (∞) interacting layers are studied up to sixth order series in x= βJwhere $\beta = \tfrac{1} {{k_B T}} $, for free-surface boundary conditions. The effects of finite size on the critical-point behavior are studied by extrapolation of the high-temperature series. The Néel temperature TN(l) as a function of the spin layers numbers lis obtained by using HTSEs of the magnetic susceptibility series, the Padé approximant method and the MFT theory. The critical exponent γassociated with the magnetic susceptibility is deduced. The Néel temperatures TN(l) for the l-layers films are estimated from the divergence of the staggered susceptibility with exponents γ(1) and γ(2) for the Ising and the XYmodels, respectively. This is consistent with the basic assumptions of scaling laws. The shift exponents of the Néel temperature for the Ising and the XYmodels, respectively, are estimated.

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 done in the framework of the random phase approximation and are given for both nearest and next-nearest neighbour exchange integrals J1 and J2, respectively. Our results are given up to order six in β = (kBT)–1 and are used to study the paramagnetic region of the ferromagnetic spinel CdCr2xIn2–2xS4. The critical temperature Tc 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 Padé 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 and can be compared with other theoretical studies based on the 3D Heisenberg model.

We compute the phase diagram of the non-metallic compounds ZnCr2pAl2—2pS(Se)4 and Zn1—pCdpCr2S(Se)4, for which we consider the bond-diluted Ising model on the spinel B-site (S.B.S.) lattice with competitive exchange interactions, and show that quenched randomness may cause fundamental changes in their low-temperature magnetic behaviour. Dilution and competition are found to be responsible of the spin glass phase and the percolation behaviour. The possible appearance of a reentrant spin glass phase is also mentioned.

We compute the phase diagram of the non-metallic compounds ZnCr2pAl2—2pS4 (I) and Zn1—pCdpCr2Se4 (II). We consider the bond-diluted Ising model on the spinel B site (S.B.S.) lattice with competitive exchange interactions, i.e. the ferromagnetic exchange interaction J1 between nearest neighbours (n.n.) and the antiferromagnetic superexchange interaction J2 between next-nearest neighbours (n.n.n.) (or and the more distant superexchange interactions Ji (i > 1)). Dilution and competition are found to be responsible of the spin glass phase and the percolation behaviour.

We study the magnetic properties and the critical behaviour of the B-spinel CdCr2xIn2—2xS4 systems in the range of concentration 0.9 ≤ x ≤ 1. Using the mean-field theory combined with the probability distribution of interaction, the exchange integrals were calculated up to the second nearest neighbours. The critical temperature and the critical exponents for the magnetic sysceptibility and the correlation length γ and ν, respectively, are deduced by applying the high-temperature series expansion (HTS) extrapolated with the Padé approximants (PA) method. The obtained values of Tc are in good agreement with those predicted by the magnetic measurements. The values of γ and ν are sensitive to the dilution ratio x. For the compounds situated in the region 0.98 ≤ x ≤ 1, they are close to those of the 3D Heisenberg model. For the concentration x = 0.9, γ and ν deviate slowly from the values predicted by this model and approach the values found in re-entrant systems.

We study the critical behaviour of the B-spinel ZnxCd1–xCr2Se4 systems in the concentration range 0.35 ≤ x ≤ 0.58. Using the mean field theory and the ferromagnetic spin-wave theory at low temperatures, the exchange integrals were calculated up to the third nearest neighbours. The ferromagnetic critical region is studied by the high-temperature series expansion extrapolated with the Padé approximants method. The critical temperatures Tc and the critical exponents associated with the magnetic susceptibility (γ) and the correlation length (ν) are estimated. The obtained values of Tc 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 the 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.

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 J1and J2, respectively. Respecting the experimental fact that the broad diffuse peak of the neutron is situated at the particular wave vector q0=[000.79]and is insensitive to the temperature for a given ratio of dilution x, we have estimated the thermal variation of J1and J2in the case of the pure compound.

The spinel solid solutions ZnxCd1—xCr2Se4 have been studied by mean of macroscopic magnetization measurements in the range 0.35 ≤ x ≤ 0.45. The ferromagnetic scaling properties permit to determine the critical temperature TC and the critical exponents β, γ, and δ. Whereas the compounds with x = 0.35 and 0.41 exhibit exponents compatible with a 3D Heisenberg ferromagnetic model, a slight increase of β, γ and a decrease of δ were found for x = 0.45. The Kadanoff scaling law γ = β(δ — 1) is satisfied by the experimental data. Using the mean-field theory and the spinwave theory at low temperatures, the exchange integrals were calculated up to the third nearest neighbours.

The magnetic properties of chromite ACr2S4(A=Zn, Cd and Hg) spinels have been investigated. The first, second and the third nearest-neighbor exchange interactions are included into a Metropolis-based Monte Carlo calculation for the three-dimensional Ising model. Transition temperatures have been deduced from the variation of magnetizations and magnetic susceptibilities for three spinel systems. The magnetic hysteresis cycles have been deduced for three systems. Critical exponents associated with the magnetization, magnetic susceptibility and specific heat have been determined. Superparamagnetism behavior has been obtained below the transition temperature. The results of our simulations are in good agreement with other results.

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