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The recent claimed room-temperature superconductivity in Cu-doped lead apatite at ambient pressure is under debate. To identify its physical origin, we conducted a detailed analysis of the crystal structure, band structure, lattice dynamics and magnetic properties of the parent Pb${}_{10}$(PO₄)₆O compound and the two different phases of Pb₉Cu(PO₄)₆O (LK-99) compound. Our results show that the parent Pb${}_{10}$(PO₄)₆O compound is an indirect band gap semiconductor, where Cu doping at the 4f site of Pb leads to a semiconducting to half-metallic transition. Two half-filled flat bands spanning the Fermi energy levels are present in the 4f phase of LK-99, which are mainly formed by hybridization of the d orbitals of Cu with the 2p orbitals of O. In addition, 6h phase of LK-99 always has spin polarization at the bottom of the conduction band and at the top of the valence band, making the material a magnetic semiconductor. Our theoretical research reveals recent experimental reports on the different transport properties of LK-99.

The quest for novel low-dimensional materials has led to the discovery of graphene and thereafter, a tremendous attention has been paved in designing of its fascinating properties aiming in fabricating electronic devices. Using first-principles calculations, we study the structure, energetic and electronic as well as magnetic properties of graphene induced by the interactions in presence of both external and internal foreign agents in detail. We find that a variety of tunable electronic states, e.g., semiconductor-to-half-metal-to-metal and magnetic behaviors can be achieved under such hierarchical interactions and their influence. We also find that the nature and compositions of foreign substances play a key role in governing the electro-magnetic characteristics of these nanomaterials. In this review, we suggest a few routes for engineering the tunable graphene properties suitable for future electronic device applications.

The site preference, electronic structure and magnetic properties of Mn₂RhAl have been studied by first-principles calculations. Both the Cu₂MnAl-structure and the Hg₂CuTi-type have been tested. For the compound Mn₂RhAl, the Hg₂CuTi structure is the more stable one with a lattice parameter of 5.80 Å. The Mn₂RhAl alloy is predicted to be a half-metal with 100% spin polarization of the conduction electrons at the Fermi level (E_F). The calculated total magnetic moment is 2.00 μ_B per unit cell, which is in line with the Slater–Pauling curve of M_t = Z_t-24. The Mn(A) and Mn(B) atom-projected spin moments are -1.54 μ_B and 3.16 μ_B, respectively. The resulting moment is mainly determined by the antiparallel aligned Mn(A) and Mn(B) spin moment. Whereas, the small spin magnetic moment of Rh is small and only 0.38 μ_B and the Al atom is almost nonmagnetic. Such an alloy may be a promising material for future spintronics devices.

In order to promote suitable material to be used in spintronics devices, this study purposes to evaluate the magnetic properties of the titanium and vanadium-doped zinc-blende ZnO from first-principles. The calculations of these properties are based on the Korringa–Kohn–Rostoker (KKR) method combined with the coherent potential approximation (CPA), using the local density approximation (LDA). We have calculated and discussed the density of states (DOSs) in the energy phase diagrams for different concentration values, of the dopants. We have also investigated the magnetic and half-metallic properties of this doped compound. Additionally, we showed the mechanism of the exchange coupling interaction. Finally, we estimated and studied the Curie temperature for different concentrations.

Half-metallic, optical and thermodynamic phase diagrams of two-dimensional Mn₂ZrZ (Z = Ge, Si) have been calculated by density functional theory (DFT) framework with full-potential linear augmented plane-wave (FP-LAPW) method. The spin-polarized electronic computations show that these layers have metallic behavior with a spin polarization less than 100%. It is observed that with increasing thickness of the layers, both the thermodynamic and energy stabilities increased, and the graphene-like layers of Mn₂ZrGe with a thickness of 7.6955 Å and Mn₂ZrSi with a thickness of 7.551 Å are completely stable thermodynamically. The optical responses of Mn₂ZrZ (Z = Ge, Si) have anisotropy at infrared region versus the optical direction and have high metallic nature in this optical range. The plasmonic frequencies have occurred after the visible edge and the refraction index becomes lower than one after the ultra-violet edge.

The ab initio study of electronic, magnetic properties and Curie temperature of AlAs doped by single and double impurities is investigated using LDA–KKR–CPA method. It is shown that the Al substituted by V and/or Ti induces a half-metallic character and ferromagnetism in the system for different concentrations except co-doping by x=y=0.035. The stability of magnetism between the ferromagnetic and DLM states as well as the mechanism of exchange interaction are discussed. The density of states are plotted in the energy diagram for different concentrations of dopants. The co-doping with (V, Ti) increases Curie temperature in AlAs with respect to single substituant. The finding of this work confirms that the new compounds have a great potential for spintronic devices.

The goal of this paper is to study the effect of the small amount of molybdenum-doped ${\mathrm{\text{SnO}}}_2$ on the magnetism behavior of that system. We utilized the density functional theory (DFT): DFT framework within MACHIKANEYAMA2002V09 package based on Coherent Potential Approximation (CPA). Inducing the magnetism in the diluted magnetic semiconductors (DMS) with a low dopant concentration at adequate room-temperature is a challenge, so, we restricted the Mo impurity at 2%. In addition, the small amount of Mo-doped ${\mathrm{\text{SnO}}}_2$ is found optimal in many studies related to other fields.

The ferromagnetic stability is observed in ${\mathrm{\text{Sn}}}_{0.98}{\mathrm{\text{Mo}}}_{0.02}{\mathrm{\text{O}}}_2$ system, since the $t_{2g}^{+}$ state of Mo element is found around the Fermi level and is 100% spin polarized, the half-metallic characteristic is useful in magnetoelectronic applications. Within the mean-field approximation (MFA) we predict the Curie temperature, as an obtained value, the $T_C=372.78$ K, consequently, the present system showed potential promise for real applications.

We use the Kondo lattice model to investigate the possibility of ferromagnetism and half-metallicity in local moment systems. Using the spectral density approach and making use of the fact that the spontaneous magnetization of local moment and the itinerant electron polarization are coupled, we derive an expression for the paramagnetic susceptibility. The magnetic ordering temperature is determined from the singularities of the susceptibility. The magnetic phase diagram is constructed in T - n (band filling) plane. It is found that ferromagnetism is possible only for small values of n. It is also found that the temperature drives the transition of the system from half-metal to metal.

We have investigated the electronic and magnetic properties of electron-doped Sr_2-xLa_xFeReO₆ (x = 0.0, 0.25, 0.5) using first-principles density functional theory within the generalized gradient approximation (GGA) and GGA + U schemes. Our results reveal that the symmetry of the La-doped compounds is decreased from tetragonal I4/m for perfect sample to monoclinic P2₁/n. With increasing La content the absolute magnetic moment of the Re site increases distinctly and the doped electrons are considered to occupy mainly the down-spin Re 5d band from the band calculation. Electronic doping is found to enhance the Curie temperature (T_c) and stabilize the ferromagnetic half-metallic ground states of Sr₂FeReO₆. And it is found that the increase of T_c is mainly caused by the increase of ferromagnetic interaction between the Fe–O–Fe.

Combining the first-principles noncollinear calculations of scattering matrices with Andreev approximation, we investigated the spin-triplet Andreev reflection (AR) spectra for the interface between half-metallic ferromagnet Co₂MnSi and s-wave BCS superconductor Al with and without interfacial roughness, where the orientations of magnetic moments near the interface are randomly distributed. The calculated results show that the AR spectra have peak structures near zero bias for the clean interface with relative weak magnetic disorder. With the increasing degree of interfacial roughness or magnetic disorder, these subgap peaks of conductance spectra will be washed out. The results also show that the value of subgap conductance spectrum can be raised significantly by the magnetic disorder. Finally, our calculations reveal that the long-range spin-triplet AR in Co₂MnSi/Al(001) interface can be enhanced by a small amount of interfacial roughness.

In this study, we have investigated the structural, electronic, magnetic and elastic properties of the full-Heusler ${\mathrm{\text{Cr}}}_2\mathrm{\text{MnAl}}$ alloy in the framework of density functional theory with generalized gradient approximation (GGA). The calculated results showed that ${\mathrm{\text{Cr}}}_2\mathrm{\text{MnAl}}$ was stable in ferrimagnetic configuration and crystallized in the ${\mathrm{\text{Hg}}}_2\mathrm{\text{CuTi}}$-type structure. From the band structure and density of states calculation results, we concluded that ${\mathrm{\text{Cr}}}_2\mathrm{\text{MnAl}}$ belongs to a kind of half-metallic compound with an indirect band gap of 0.37 eV. Immediately thereafter, we have analyzed the origin of half-metallic band gap. The total magnetic moment of ${\mathrm{\text{Cr}}}_2\mathrm{\text{MnAl}}$ at the stable state is $-2{\mu }_B$ per formula unit, obeying the Slater–Pauling rule $M_t=Z_t-24$. In addition, various mechanical properties have been obtained and discussed based on the three principle elastic tensor elements $C_{11},C_{12}$ and $C_{44}$ for the first time in the present work. We expect that our calculated results may trigger the application of ${\mathrm{\text{Cr}}}_2\mathrm{\text{MnAl}}$ in future spintronics field.

We investigate the band structure, magnetism and density of states of half-Heusler compounds $\mathrm{\text{CoCr}}Z$$(Z=\mathrm{\text{Si}},\mathrm{\text{Ge}},\mathrm{\text{P}},\mathrm{\text{As}})$ based on the first-principle calculations. Combined with molecular orbital hybridization theory, we discuss the influence of the main-group element on half-metallic properties of $\mathrm{\text{CoCr}}Z$. It is found that the replacement of Ge for Si in CoCrSi can adjust the position of the Fermi level, and while it has no impact on the energy gap width and magnetic structure. However, the substitution of P for Si can effectively adjust the magnetism without disrupting its half-metallicity. Our results demonstrate that the electronic structure of $\mathrm{\text{CoCr}}Z$ is mainly dependent on the number of valence electrons of the main-group element.

The electronic properties of zigzag and armchair SiC nanoribbons are studied using a theoretical method. The spin-unrestricted electronic behavior of an armchair and zigzag SiC nanoribbon containing Si and C vacancy in the supercell was investigated. Spin-polarized electronic structure calculations show that armchair SiC nanoribbon was classified as a nonmagnetic semiconductor while zigzag SiC nanoribbon presents a half-metallic electronic structure. Our results suggest that SiC nanoribbon containing point vacancy may be a good candidate for spintronics due to its half-metal properties.

In this work, we have used the full-potential linearized augmented plane wave (FP-LAPW) method implemented in the WIEN2k code combined with the generalized gradient approximation (GGA) of the density functional theory (DFT) to study the structural, elastic, mechanical, electronic, magnetic, and thermodynamic properties of the parent ternary inverse Heusler compounds based on Titanium and Cobalt Ti₂CoGa, Ti₂CoCu in the Hg₂CuTi-type structure and their quaternary alloys Ti₂CoGa${}_{1-x}$Cu_x ($x=0.25$, 0.5, 0.75) for the chosen concentrations using a supercell with 16 atoms. We have calculated the structural properties, such as the lattice parameters, bulk modulus, and its first derivative, which are in good agreement with those that have been obtained based on other published theoretical methods. Also, we calculated the elastic constants of the studied Heusler alloys, and we found that these materials are elastically stable, ductile, and anisotropic. Therefore, the electronic and magnetic properties indicate that Ti₂CoGa exhibits a half-metallic (HM) ferromagnetic behavior, while Ti₂CoCu shows a metal and a non-magnetic (NM) character. Their quaternary alloys are found to be nearly HM ferromagnetic materials, with a magnetic moment mainly due to the atom Ti. Furthermore, the quasi-harmonic Debye model, which incorporates the lattice vibrations, was used to estimate the thermodynamic effects on some macroproperties of the Ti₂CoGa${}_{1-x}$Cu_x alloys. Successful results were achieved for the variations of the primitive cell volume, bulk modulus, heat capacities, and Debye temperature with pressure and temperature, respectively, in the ranges of 0–30GPa and 0–1400K. To our knowledge, no analogous investigations on the mechanical and thermodynamic properties of the Ti₂CoGa${}_{1-x}$Cu_x ($x=0.25$, 0.5 and 0.75) alloys have been performed to date. As a result, it is predicted that Ti₂CoGa${}_{1-x}$Cu_x Heusler alloys will be promising candidates for actual applications in spintronic devices.

We performed first-principles calculation to show that a host–guest silicon nanostructure can exhibit half-metallic properties, wherein the host is a single-walled hexagonal silicon nanotube while the guest is a hybrid atomic chain of Mn and Co (encapsulated in the host nanotube). The calculated electronic band structures indicate that the Fermi level intersects only in the spin-up band, whereas the spin-down band exhibits semiconducting characteristics.

Magnetite is a highly utilized transition metal oxide with many interesting magnetic and transport properties. The presence of anti-phase boundaries (APBs) and charge-orbital ordering (COO) are two of the most exciting properties of epitaxial magnetite thin films. Here, epitaxial stepped Fe₃O₄ films were prepared to investigate the competition between APBs and COO via measurements of in-plane anisotropy. The anisotropy was probed for two orthogonal configurations, with magnetic field applied or electrical-contacts aligned either along or perpendicular to the steps. We reveal that the APBs dominate the magnetic and transport properties of the films above the Verwey transition temperature ($T_{\mathrm{\text{V}}})$. However, below $T_{\mathrm{\text{V}}}$ film thickness becomes a decisive factor in determining the magnetic nature of stepped magnetite films, due to its correlation with domain size. When the film is thinner than a critical thickness, the anisotropy is dominated by the APBs, and a higher anisotropy constant and MR ratio are observed when the magnetic field or contacts are oriented along the steps. Conversely, for sufficiently thick films, below $T_{\mathrm{\text{V}}}$, the magnetic and electrical transport properties are dominated by COO. Thus a higher anisotropy constant and MR ratio are observed when the magnetic field or contacts are oriented perpendicular to the steps.

A novel half-metallic family of materials, the multiple Dirac cones half-metals, has received considerable interest from researchers. Benefiting from its novel electronic structure, they are promising candidates for ultra-performance spintronic devices. In this paper, we propose a new half-metallic material, perovskite-type $R\stackrel{-}{3}c$ HoMnO₃, which possesses similar Dirac-like multiple linear band crosses. We investigated its electronic, magnetic and thermodynamic properties in detail on the basis of density functional theory. The excellent band structures are robust enough against spin-orbit coupling and electron and hole doping. Through calculations, we confirmed its multi-aspect stability. Based on the current study, we confirm that HoMnO₃ has potential for next-generation spintronic applications.

Double perovskites are usually strongly correlated electronic systems that offer many multifunctional properties and are most commonly formed in the monoclinic crystal phase. In this study, we used a first-principles DFT approach in studying the optical and magnetic aspects of Ba₂MMoO₆ ($\mathrm{\text{M}}=\mathrm{\text{Mn}}$, Fe) double perovskite structures in a new monoclinic phase in both their pure and oxygen-deficient form and compared it to their natural cubic phase. The structural parameters of our structures were consistent with the available experimental data of the similar Ca₂MMoO₆ compounds. The optical analysis suggests a high dielectric function for both compounds in their pure and defected state. The addition of defects increases the absorption of photons near the visible spectra. We also found the structures to be half-metallic, with a reduction of magnetic strength and half-metallic gaps when oxygen defects are added to the structure. These features suggest a possible application in the optoelectronics and spintronics industry, even when the crystal structures have oxygen vacancies.

Full-Heuslers are a group of materials that have repeatedly attracted the curiosity of scientists and researchers, especially for their use in the field of spintronics. In this work, we undertook a study on the structural, elastic, electronic, magnetic and thermodynamic properties of the full-Heusler Mn₂OsGe alloy using the calculations of the first principles. Two approximations are used: the generalized approximation of the Perdew–Burke–Ernzerhof GGA–PBE gradient for electron-correlation exchange and the new modified Tran-Blaha form of the modified Becke-Johnson mBJ–GGA-PBE potential. As important results, we found that the compound Mn₂OsGe is stable in the CuHg₂Ti structure; on the other hand, we could also verify its mechanical stability at zero temperature and pressure. For the calculation of the electronic properties, we were able to determine the half-metallic ferrimagnetic character of our compound, which exhibits a metallic behavior in the state of the majority spins, and a semiconductor behavior in the state of the minority spins. An integer value of 2${\mu }_B$ has been recorded for a magnetic moment and this conforms to the Slater–Pauling rule.

According to the firs-principles theory-based spin-density functional calculations within the framework of Wu–Cohen generalized gradient approximation (WC-GGA), we examine the structural and electronic properties of ternary alloys of zinc-blende boron phosphide doped with chromium. We compare the materials with aluminum phosphide that exhibits half-metallic properties at various concentrations. The curves of total and partial densities of states and the band structures show that ${\text{B}}_{1-x}$${\text{Cr}}_x$P are purely metallic and can be possible candidates for use in light emitting diodes (LEDs). These compounds are not polarized on spins; the main cause is the nature of chemical bond located between the boron cations and the phosphorus anion, whereas the ternary materials of ${\text{Al}}_{1-x}$${\text{Cr}}_x$P all have various uses in spintronic science according to many studies because of their half-metallicity behavior.