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In this paper, we investigated the structural, elastic, topological-electronic properties as well as optical properties of two half-Heusler (HH) heavy fermions-based compounds: HoPtBi and HoPdBi. We accomplished our calculations in the framework of density functional theory (DFT), based on the full potential linearized augmented plane wave (FP-LAPW). Both compounds are antiferromagnetic (AFM) type-II as reported by experimental data so we carried out our study in the AFM type-II configuration. Considering the spin-orbit coupling, we found that the hydrostatic pressure leads to a phase transition from the trivial semimetal to the topological semimetal (TSM) because of band inversion for HoPdBi with no apparent effect of hydrostatic pressure on the topological phase for HoPtBi. We also studied their optical properties, without and with hydrostatic pressure. The first peak in reflectivity, absorption, optical conductivity spectra and energy loss factor are strongly influenced by the hydrostatic pressure. Both compounds exhibit a considerable first absorption peak in the visible and ultraviolet ranges and they are best candidates for solar cells considered essential in renewable energy.

We investigate the frustration effects on small-world networks by studying antiferromagnetic Ising model in two dimensions. When the rewiring is constrained to those sites such that the interaction still occurs between spins in distinct sublattices and frustration does not take place, we observe that the system behaves as in previous investigations of ferromagnetic Ising model. However, when the rewiring procedure does not only produce interactions between spins in distinct sublattices, small-world configurations can effectively produce geometrical frustration and we attain a different critical behavior. In the frustrated case, the critical temperature decreases with the augment of the rewiring probability and the magnetic ordering presents two different regimes for low and high p.

The S=1/2 Heisenberg chain with bond alternation and randomness of antiferromagnetic (AFM) and ferromagnetic (FM) interactions is investigated by quantum Monte Carlo simulations of loop/cluster algorithm. Our results have shown interesting finite temperature magnetic properties of this model. The relevance of our study to former investigation results is discussed.

We have investigated the magnetic and magnetotransport properties of monophasic double perovskites Sr₂FeMO₆(M = Mo, W). Magnetic measurements indicate that SFMO is a ferromagnet and SFWO is an antiferromagnet with T_N = 35 K at H = 5 T. Large magnetoresistance ratio (MR) of ~ 22% (H = 3 T) at room temperature (RT) was observed in the SFWO compound. However, the SFMO compound did not show any significant MR even at high fields and RT (MR~1%; H = 3 T and 300 K). The changes observed by physical measurements are supported by band structure calculations to explain the interaction between the 3d(Fe), 4d(Mo) and 5d(W) orbitals of transition metal ions and oxygen ions.

The double perovskite (Sr₂CrWO₆) has been prepared in polycrystalline state by solid state reaction. At room temperature, the crystal structure is cubic (space group: Fm3m) with lattice parameter of 7.8200(2) (Å). Both ρ(H=0) and ρ(H=5T) show a semiconductor-like behavior over the whole temperature range up to 5 K. The highest MR(magnetoresistance) value of 55% (H=5T) was observed at 25 K. The valence state of Cr was determined by the X-ray absorption spectroscopy at Cr-L edge. The results, compared to the standard sample, show that the valence state of Cr is 3+.

An effective mean-field theory based on cumulant expansion was used to deal with antiferromagnetic Heisenberg model on planar triangular lattice. The corrections of expansion were performed to the third order. By using the equation of the mean field condition, curves of internal energy E specific heat C staggered helicity K (order parameter) and the variational ratio of staggered helicity X were obtained when the proper values of effective external field were achieved. The calculated results showed that there were two phases (which were ordered antiferromagnetic phase and the disordered phase) in the spin system. The first order critical point is -kT_c/J_s = 1.65, the second is -kT_c/J_s = 1.35 and the third is -kT_c/J_s = 1.29, obviously closer to that of Monte Carlo simulation order by order. And also, the analytic expansion curves derived from this method exhibited higher proximity order by order to the Monte Carlo simulation. Such results showed that this method was a useful tool to obtain thermodynamically observables of spin system.

The spin-1/2 antiferromagnetic (AFM) Heisenberg model is considered in the mean-field approximation in terms of the spin operators ${Ŝ}_x,{Ŝ}_y$ and ${Ŝ}_z$ in the matrix forms with the introduction of bilinear exchange interaction ($J_{\mu }$), the Dzyaloshinskii–Moriya interaction (DMI) (${\mathrm{\Delta }}_{\mu }$) and external magnetic fields ($H_{\mu }$) into the Hamiltonian in three dimensions. The thermal changes of sublattice magnetizations $M_{\mu }^A$ and $M_{\mu }^B$ are investigated in the isotropic case to identify the critical behaviors displayed by the system. The phase diagrams are illustrated on various planes of system parameters for given coordination numbers $q=3,4$ and 6. In addition, the graphs of the magnetization components in the same directions were drawn against each other and very interesting results were obtained. The model exhibits the ordered phases, i.e., AFM, ferromagnetic (FM), and a phase with random or oscillatory behavior (R). The phase transitions are observed between FM and R phases when for all ${\mathrm{\Delta }}_{\mu }\ne 0.0$, between FM and AFM when ${\mathrm{\Delta }}_{\mu }=0.0$ only and, AFM and R at low temperatures for very small ${\mathrm{\Delta }}_{\mu }$ and $H_{\mu }$ values.

Single phase MgTi₂O₄ compound was synthesized by spark plasma sintering (SPS) method. The temperature dependence of the magnetic susceptibility and specific heat measurements show that MgTi₂O₄ takes place in phase transition at 258 K. Magnetic entropy measurements show that the change of magnetic entropy ΔS_M is positive and ΔS_M increases more quickly than H^2/3 near the transition; while ΔS_M is negative and |ΔS_M| (the absolute value) increases slowly with applied field increasing at lower temperature. The change of ΔS_M at different temperature range is suggested to be related not only to spin entropy change, but also orbital entropy change. The magnetic phases of MgTi₂O₄ are suggested to be Pauli paramagnetic, collinear antiferromagnetic and non-collinear antiferromagnetic order with temperature decrease.

The antiferromagnetic (AFM) spin-3/2 Heisenberg model is explored by using a mean-field approach (MFA) with the inclusion of spin operators for a square lattice. The considered Hamiltonian consists of the bilinear exchange interaction $J_z$ and Dzyaloshinskii–Moriya interaction (DMI) ${\mathrm{\Delta }}_m$ parameters between the nearest-neighbor (NN) spins along the z- and y-axes and external magnetic field components $H_x$ and $H_z$ acting along the x- and z-axes, respectively. After obtaining the mathematical formulation of the magnetization components along the x- and z-directions in the MFA, their thermal changes are inspected to obtain the phase diagrams on the (${\mathrm{\Delta }}_m$, T) and (H, T) planes for the given values of $H=H_x=H_z$ and ${\mathrm{\Delta }}_m$, respectively, with $J_z=-1$ which leads to AFM interactions. It is found that the model not only presents the AFM and ferromagnetic (FM) phases but also the random (R) phase regions created by the existence of ${\mathrm{\Delta }}_m$ interaction. These three phases are observed to coexist for the appropriate values of given system parameters. The phase lines exhibit reentrant behavior when only the FM and R phases are present.

The electronic and magnetic properties of Na_0.5CoO₂ are studied within the hybrid density functional methods. A charge-ordered antiferromagnetic insulating state is unambiguously identified as the ground state of Na_0.5CoO₂. The electronic structures of the ground state are very similar to our previous GGA+U (U = 4eV) results, except for the large band gap discrepancy. Our results suggest that the hybrid density functional methods capture the main physics of the strong correlation in Na_xCoO₂ system.

Understanding of different magnetic configurations for the FeAs₂ iron pnictide compound is carried out using first-principles studies based on spin density functional theory (DFT) within the generalized gradient approximation (GGA), including the spin–orbit coupling (SOC). The calculated stable phase is in the marcasite (Pnnm) with nonmagnetic spin-ordering. We find that the FeAs₂ compound in the nonmagnetic (NM) marcasite phase undergoes pressure-induced phase transition to the antiferromagnetic (AFM1) marcasite phase at 12GPa, then to the AFM CuAl₂ ($I$4/mcm) phase at 63GPa. The phase transition is also accompanied by semiconducting (marcasite phase) to metallic (CuAl₂ phase) transition. The calculated electronic density of states profile shows the hybridization of the Fe-3$d$ and As-4$p$ orbitals plays an important role in determining the electronic and magnetic characters of this compound. The associated phase transition results in increased Fe-3d orbitals around the Fermi energy level.