Modulation of the electronic and magnetic properties of an MnCrNO2 ferromagnetic semiconductor MXene.

Because the single-layer CrI<sub>3</sub> is a half semiconductor with indirect band gap and magnetic anisotropy, it has received much attention in the spintronic, magneto-electronic and magnetic storage applications. However, the knowledge of the dependence of carrier mobility and optical property on strain is still rather limited. The uniaxial and biaxial strain dependence of electronic, transport, optical and magnetic properties of single-layer CrI<sub>3</sub> are systematically investigated by using first-principles calculations, and the results are compared with experimental results. The electronic structures under different strains are first calculated by using the accurate HSE06 functional, then the carrier mobility is estimated by the deformation potential theory and the dielectric function is obtained to estimate the optical absorption especially in the visible light range. Finally, the magnetic anisotropy energy used to estimate the magneto-electronic properties is studied by the Perdew-Bueke-Ernzerhof functional including the spin-orbit coupling. It is found that the ferromagnetic CrI<sub>3</sub> is an indirect and half semiconductor with band gap 2.024 eV,<inline-formula><tex-math id="M1">\begin{document}$ \Delta {\text{CBM}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20221019_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20221019_M1.png"/></alternatives></inline-formula>= 1.592 eV, <inline-formula><tex-math id="M2">\begin{document}$ \Delta {\text{VBM}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20221019_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20221019_M2.png"/></alternatives></inline-formula>= 0.238 eV and can be driven into AF-Néel antiferromagnetic phase by applying –6% to –8% (compressive) biaxial stain, exhibiting excellent agreement with the results from the literature. It is found that of single-layer CrI<sub>3</sub> has very low carrier mobility with a value within 10 cm<sup>2</sup>·V<sup>–1</sup>·s<sup>–1</sup> due to the large effective mass and small in-plane stiffness can be remarkably increased by increasing biaxial compression strain attributed to the reduced effective mass. A high electron mobility 174 cm<sup>2</sup>·V<sup>–1</sup>·s<sup>–1</sup> is obtained in the zigzag direction by applying a –8% biaxial strain reaching the level of monolayer MoS<sub>2</sub>. The calculated imaginary component of dielectric function along the <i>x </i>(<i>y</i>) direction having two peaks (I, II) in the visible light range is obviously different from that along the <i>z</i> direction, indicating that the single-layer CrI<sub>3</sub> has optical anisotropy, demonstrating the good agreement with results from the literature. It is found that the imaginary part of dielectric function shows that an obvious redshift and peak (I, II) values strongly increase with the increase of compressive strain (biaxial), showing good agreement with the calculated electronic structures and indicating that monolayer CrI<sub>3</sub> possesses high optical adsorption of visible light under a compressive biaxial strain. Furthermore, it is found that the magnetic anisotropy energy of monolayer CrI<sub>3</sub> mainly stemming from the orbital magnetic moment of Cr ions remarkably increases from 0.7365 to 1.08 meV/Cr with g compressive strain increasing. These results indicate that the optoelectronic property of single-layer CrI<sub>3</sub> can be greatly improved by applying biaxial compressive strain and the single-layer CrI<sub>3</sub> is a promising material for applications in microelectronic, optoelectronic and magnetic storage.

Due to their novel spin and valley properties, two-dimensional (2D) ferrovalley materials are expected to be promising candidates for next-generation spintronic and valleytronic devices. However, they are subject to various defects in practical applications. Therefore, the electronic, valley, and magnetic properties may be modified in the presence of the defects. In this work, utilizing first-principles calculations, we systematically studied the effects of defects on the electronic, valley, and magnetic properties of the 2D ferrovalley material VSi2N4. It has been found that C doping, O doping, and N vacancies result in the half-metallic feature, Si vacancies result in the metallic feature, and V vacancies result in a bipolar gapless semiconductor. These defect-induced electronic properties can be effectively tuned by changing defect concentration and layer thickness. Since the impurity bands do not affect the K and K' valleys, valley polarization is well maintained in O-doped and N-defective systems. Importantly, these defects play a crucial role in modifying the magnetic properties of the pristine VSi2N4, especially the magnitude of local magnetic moments and the magnetic anisotropy energy. Detailed analysis of the density of states demonstrates that the variations of the total magnetic moment and magnetic anisotropy energy with biaxial strain are determined by the electronic states near the Fermi level rather than the type of defect, which provides a new understanding of the effects of defects on the magnetic properties of 2D materials. Moreover, the layer thickness can affect the magnetic coupling between defects and surrounding V atoms. Our results offer insight into the electronic, valley, and magnetic properties of VSi2N4 in the presence of various point defects.

The investigation of two-dimensional (2D) intrinsic ferromagnetic material is important in the field of spintronics. In this study, the Mn2Ge2Te6 monolayer (ML) with intrinsic ferromagnetism was fabricated by using the density functional theory (DFT). The Mn2Ge2Te6 ML is a half metal (HM) with a spin-β bandgap of 1.462 eV. Biaxial strain could be applied to tune the electronic and magnetic properties of Mn2Ge2Te6. The magnetic moment (MM), magnetic exchange parameter (J), band structures, and magnetic anisotropy energy (MAE) could be effectively controlled by the biaxial strains (ε). This modulation originates that the states near the Fermi level mainly come from the contribution of in-plane atomic orbitals. The MM of Mn monotonously increases as the tensile strains increase. The energy difference between different magnetic orders (ΔE) and J also change with the strains. The antiferromagnetic-stripy order always has the lowest energy under the strains. As the strains change, ΔE and J monotonously change as the direct exchange and super-exchange interactions between Mn atoms vary. As the tensile strain decreases and compressive strain increases (−2.1%<ε<8%), the gap of spin-β electrons monotonously decreases. The Mn2Ge2Te6 ML changes from a HM to a normal spin-unpolarized metal under larger compressive strains (ε>−2.1%). When the tensile strains are applied, the MAE monotonously increases to the largest value of −22.3 meV (ε=12%). As the compressive strains increase, the MAE monotonously decreases. Last, the Mn2Ge2Te6 ML changes from an in-plane magnetic anisotropy into a perpendicular magnetic anisotropy under a larger compressive strain (−11%). The change of MAE direction origins that the contribution of hybridization between Te's py and pz orbitals is changed when the strain changes. Our results offer crucial insights into the potential of strain modulation in a 2D Mn2Ge2Te6 ML, paving the way for future advancements in this field.

Tuning electronic, magnetic and optical properties of Cr-doped antimonene via biaxial strain engineering

Two-dimensional (2D) intrinsic van der Waals ferromagnetic semiconductor (FMS) crystals with strong perpendicular magnetic anisotropy and high Curie temperature (TC) are highly desirable and hold great promise for applications in ultrahigh-speed spintronic devices. Here, we systematically investigated the effects of a biaxial strain ranging between -8% and +8% and doping with different charge carrier concentrations (≤0.7 electrons/holes per unit cell) on the electronic structure, magnetic properties, and TC of monolayer CrSeBr by combining first-principles calculations and Monte Carlo (MC) simulations. Our results demonstrate that the pristine CrSeBr monolayer possesses an intrinsic FMS character with a band gap as large as 1.03 eV, an in-plane magnetic anisotropy of 0.131 meV per unit cell, and a TC as high as 164 K. At a biaxial strain of only 0.8% and a hole density of 5.31 × 1013 cm-2, the easy magnetization axis direction transitions from in-plane to out-of-plane. More interestingly, the magnetic anisotropy energy and TC of monolayer CrSeBr are further enhanced to 1.882 meV per unit cell and 279 K, respectively, under application of a tensile biaxial strain of 8%, and the monolayer retains its semiconducting properties throughout the entire range of investigated strains. It was also found that upon doping monolayer CrSeBr with holes with a concentration of 0.7 holes per unit cell, the perpendicular magnetic anisotropy and TC are increased to 0.756 meV per cell and 235 K, respectively, and the system tends to become metallic. These findings will help to advance the application of 2D intrinsic ferromagnetic materials in spintronic devices.

Unveiling the tunable electronic, optoelectronic, and strain-sensitive gas sensing properties of Janus ZrBrCl: Insights from DFT study

Effective modulating the electronic and magnetic properties of VI3 monolayer: A first-principles calculation

In recent years, two-dimensional (2D) materials have attracted considerable attention due to their outstanding optical and electronic properties, and they have shown great potential applications in next-generation solar cells and other optoelectronic devices. In this work, density functional theory (DFT) is used to systematically study the electronic and optoelectronic properties of the heterojunction formed by 2D BAs and I-AsP monolayers, as well as the response of this heterojunction under biaxial strain and electric field. The calculation results show that in the ground state, the four vertically stacked BAs/I-AsP heterostructures all have stable geometric structures, and their band gaps range from 0.63 to 0.86 eV. Compared with their constituent monolayers, these heterostructures have the increased optical absorption coefficients (the absorption coefficient in the <i>x</i>-direction reaches 10<sup>6</sup> cm<sup>–1</sup>), and they can effectively separate the photogenerated electron-hole pairs. Of the four structures, the A1 structure exhibits the smallest interlayer spacing, the smallest binding energy, and the highest stability. It has a type-I band alignment and a structure of a direct-band-gap semiconductor with band gaps of 0.86 eV (PBE) and 1.26 eV (HSE06), which can be used in the field of light-emitting diodes. The band gap and band type of the heterostructure can be effectively changed by applying biaxial strain and electric field. Under the application of biaxial tensile or compressive strain in a range of –10% to 8%, the band gap increases accordingly. When the tensile strain is greater than 8%, the band gap starts to decrease. When the biaxial strain <i>ε</i> ≤ –3% and <i>ε</i> > 8%, the heterojunction transitions from a type-I band alignment to a type-II band alignment. Under tensile strain, the absorption spectrum undergoes a red shift, while compressive strain leads to a blue shift of the absorption spectrum. Similarly, the externally applied electric field linearly affects the band gap of the BAs/I-AsP heterojunction in a range from –0.5 to 0.5 V/Å, and the band gap decreases as the electric field increases. When a positive electric field with <i>E</i> ≥ 0.2 V/Å is applied, the band alignment of the heterojunction can also transition from type-I to type-II. The BAs/I-AsP heterojunction has strong absorption properties in the ultraviolet and visible light ranges. Based on the Scharber model, the theoretical power conversion efficiency (PCE) <i>η</i> of the BAs/I-AsP heterojunction is found to be greater than 13%, which is higher than those of 2D heterojunction materials such as Cs<sub>3</sub>Sb<sub>2</sub>I<sub>9</sub>/InSe (<i>η</i> = 3.3%), SiPGaS/As (<i>η</i> = 7.3%) and SnSe/SnS (<i>η</i> = 9.1%). This further expands the application scope of the BAs/I-AsP heterojunction, making it expected to play an important role in the field of photodetectors and solar cells.

Two-dimensional (2D) ferromagnetic (FM) materials with valley polarization are highly desirable for use in valleytronic devices. The 2D Janus materials have fascinating physical properties due to their asymmetrical structures. In this work, the electronic structure and magnetic properties of Janus RuXY (X, Y = Br, Cl, F, I, X ≠ Y) monolayers are systematically studied using first-principles calculations. RuBrCl, RuBrF, and RuClF monolayers are all FM semiconductors. The valley polarization is present in the band structure and this is determined by the spin orbit coupling (SOC). The valley splitting energy of the RuClF monolayer is as large as 204 meV, with a perpendicular magnetic anisotropy (PMA) energy of 1.918 mJ m-2 and a Curie temperature of 316 K. Therefore, spontaneous valley polarization at room temperature will be seen in the RuClF monolayer. The Curie temperature of the RuBrF monolayer is higher than that of the RuClF, but the magnetic anisotropy energy (MAE) is in-plane magnetic anisotropy (IMA). The valley splitting energy of the RuBrCl monolayer is higher and the PMA energy is lower than that of the RuClF monolayer. The Curie temperature was only 197 K. The valley polarization was modulated in the RuXY monolayers at different biaxial strains, during which the semiconductor properties are still maintained. The PMA of the RuClF and RuBrCl monolayers is enhanced by the biaxial compressive strains, which are mainly attributed to the variation of the (dyz, d2z) orbital matrix elements of the Ru atoms. The MAE of the RuBrF monolayer is tuned from IMA into PMA at a biaxial strain of -6%. These results show an example of a 2D Janus ferrovalley material.

Two-dimensional (2D) van der Waals (vdW) heterostructures have potential applications in new low-dimensional spintronic devices owing to their unique electronic properties and magnetic anisotropy energies (MAEs). The electronic structures and magnetic properties of RuClF/WSe2 heterostructure are calculated using first-principles calculations. The most stable RuClF/WSe2 heterostructure is selected for property analysis. RuClF/WSe2 heterostructure has half-metallicity. Considering spin-orbit coupling (SOC), band inversion is present in the RuClF/WSe2 heterostructure, which is also demonstrated by the weight of the energy contributions. The local density of states (LDOS) of the edge states can provide strong evidence that the RuClF/WSe2 heterostructure has topological properties. The MAE of RuClF/WSe2 heterostructure is in-plane magnetic anisotropy (IMA), which mainly originates from the contribution of matrix element difference in Ru (dxy, dx2-y2) orbitals. The electronic properties and MAE of RuClF/WSe2 heterostructure can be regulated by biaxial strains and electric fields. The band inversion phenomenon is enhanced at electric fields in the opposite direction, which is also modified at different biaxial strains. However, the band inversion phenomenon disappears at the biaxial strains of 6% and an electric field of 0.5 V Å-1. The MAE of RuClF/WSe2 heterostructure is transformed from IMA into perpendicular magnetic anisotropy (PMA) at certain compressive strains and positively directed electric fields. The above results indicate that the RuClF/WSe2 heterostructure has potential applications in spintronic devices.

In the past few years, two-dimensional (2D) high-temperature ferromagnetic semiconductor (FMS) materials with novelty and excellent properties have attracted much attention due to their potential in spintronics applications. In this work, using first-principles calculations, we predict that the H-MnN2 monolayer with the H-MoS2-type structure is a stable intrinsic FMS with an indirect band gap of 0.79 eV and a high Curie temperature (Tc) of 380 K. The monolayer also has a considerable in-plane magnetic anisotropy energy (IMAE) of 1005.70 μeV/atom, including a magnetic shape anisotropy energy induced by the dipole-dipole interaction (shape-MAE) of 168.37 μeV/atom and a magnetic crystalline anisotropy energy resulting from spin-orbit coupling (SOC-MAE) of 837.33 μeV/atom. Further, based on the second-order perturbation theory, its in-plane SOC-MAE of 837.33 μeV/atom is revealed to mainly derive from the couplings of Mn-dxz,dyz and Mn-dx2-y2,dxy orbitals through Lz in the same spin channel. In addition, the biaxial strain and carrier doping can effectively tune the monolayer's magnetic and electronic properties. Such as, under the hole and few electrons doping, the transition from semiconductor to half-metal can be realized, and its Tc can go up to 520 and 620 K under 5% tensile strain and 0.3 hole doping, respectively. Therefore, our research will provide a new, promising 2D FMS for spintronics devices.

This contribution concerning the effect of spin–orbit coupling on the magnetic properties of materials is divided into two chapters. In the first chapter we review the method based on the density functional theory (DFT) within the local density approximation (LDA) used to compute the electronic structure, the magnetic anisotropy, the x-ray absorption spectra, and the x-ray magnetic circular dichroism. We give the major approximations used to derive the Kohn–Sham equations with or without the Hubbard interaction for correlated orbitals. We give also a brief introduction to the generalized gradient approximation (GGA). We then provide a solution of the latter equations using the full-potential linear augmented plane wave (FLAPW) basis set and discuss the so-called LDA+U method, where the Hubbard U is included for localized orbitals. We show how the relativistic effects, such as the spin–orbit coupling, can be introduced into band structure calculations and show their effect on magnetism, i.e., magnetic anisotropy energy (MAE), magneto-optical properties, and x-ray magnetic circular dichroism (XMCD). Then we show a brief derivation of the force theorem for the calculation of the magnetic anisotropy as well as a description of its application to the MAE calculations and show the details of the calculation of the XMCD matrix elements in the electric–dipole approximation. The second chapter of this contribution includes some applications of the method to the computation of the electronic, magnetism, and spectroscopic properties of spintronics materials. In particular , we investigate the electronic structure and x-ray magnetic circular dichroism (XMCD) of Sr2FeMoO6 (SFMO for short) and other useful ferromagnetic half-metals with 100% spin polarization, materials useful for spin injection. In particular, we show that the spin–orbit coupling reduces the spin polarization while the intra-site electronic correlations tend to increase it. For example, SFMO is found to be a half-metallic ferrimagnet with a gap in the spin-up channel. The calculated spin magnetic moments on Fe and Mo sites confirm the ferromagnetic ordering and settle the controversy existing between the earlier experimental works. The orbital magnetism at the Fe and Mo sites agrees quite well with the recent experimental XMCD measurements. The computed L2,3 XMCD at the Fe and the Mo sites compares fairly well with experiment. The XMCD sum rule computed spin and orbital magnetic moments are in good agreement with the values obtained from the direct self-consistent calculations. In the last application, we focus on the GGA+U treatment of the electronic and magnetic structure of Gd and Gd-related compounds, such as GdN and GdFe2. We compare the calculated density of states to the experimental photoemission and inverse photoemission spectra (XPS and BIS) and determine the Fermi surface with and without the Hubbard U and spin–orbit coupling. The GGA+U is found to be the most appropriate for treating the 4f Gd electrons. We have investigated the bulk properties and calculated the XMCD spectra at the L2,3 edges at the Gd site of GdN. The agreement of the calculated spectra with experiment is the indication of the relevance of the XMCD formalism within the one-electron picture. The results also show that the ground-state electronic structure of GdN is that of a half-metal. Finally our computational method is used to determine the magnetic anisotropy aspect of the Gd and its compounds GdN and GdFe2. Using the force theorem, we have calculated the MAE of Gd, GdN, and GdFe2 for different directions of the magnetization. Indeed, owing to the nil spin–orbit interaction of the 4f half-filled shell, the force theorem is expected to be efficient for Gd and Gd compounds MAE calculations. This theorem allows a considerable computational effort gain since the spin–orbit coupling could be calculated only for one self-consistent iteration. Once again, the GGA+U method is found to be the most adequate approach for the force theorem calculations of the Gd MAE. The GGA and GGA-core model treatments of the 4f states have led to a wrong MAE. It turns out that the electronic properties and the magnetic properties of 4f systems are tightly related, and the 4f electrons play a crucial role in the computed magnetic anisotropy. Although the Gd MAE is found to be similar to that of a typical 3d transition metal like hcp Co, the GdN and GdFe2 cubic crystals MAEs are found to be different from that of a pure 3d cubic material like fcc Ni.

This contribution concerning the effect of spin–orbit coupling on the magnetic properties of materials is divided into two sections. In the first section we review the method based on the density functional theory (DFT) within the local density approximation (LDA) used to compute the electronic structure, the magnetic anisotropy, the x-ray absorption spectra, and the x-ray magnetic circular dichroism. We give the major approximations used to derive the Kohn–Sham equations with or without the Hubbard interaction for correlated orbitals. We give also a brief introduction to the generalized gradient approximation (GGA). We then provide a solution of the latter equations using the full-potential linear augmented plane wave (FLAPW) basis set and discuss the so-called LDA+U method, where the Hubbard U is included for localized orbitals. We show how the relativistic effects, such as the spin–orbit coupling, can be introduced into band structure calculations and show their effect on magnetism, i.e., magnetic anisotropy energy (MAE), magnetooptical properties, and x-ray magnetic circular dichroism (XMCD). Then we show a brief derivation of the force theorem for the calculation of the magnetic anisotropy as well as a description of its application to the MAE calculations and show the details of the calculation of the XMCD matrix elements in the electric dipole approximation. The second section of this contribution includes some applications of the method to the computation of the electronic, magnetic, and spectroscopic properties of spintronics materials. In particular, we investigate the electronic structure and x-ray magnetic circular dichroism (XMCD) of Sr2FeMoO6 (SFMO for short) and other useful ferromagnetic half-metals with 100% spin polarization, materials useful for spin injection. In particular, we show that the spin–orbit coupling reduces the spin polarization, while the intra-site electronic correlations tend to increase it. For example, SFMO is found to be a half-metallic ferrimagnet with a gap in the spin-up channel. The calculated spin magnetic moments on iron and Mo sites confirm the ferromagnetic ordering and settle the controversy existing between the earlier experimental works. The orbital magnetism at the Fe and Mo sites agrees quite well with the recent experimental XMCD measurements. The computed L2,3 XMCD at the Fe and the Mo sites compares fairly well with the experiment. The XMCD sum rule computed spin and orbital magnetic moments are in good agreement with the values obtained from the direct self-consistent calculations. In the last application, we focus on the GGA+U treatment of the electronic and magnetic structure of Gd and Gd-related compounds, such as GdN and GdFe2. We compare the calculated density of states to the experimental photoemission and inverse photoemission spectra (XPS and BIS) and determine the Fermi surface with and without the Hubbard U and spin–orbit coupling. The GGA+U is found to be the most appropriate for treating the 4f Gd electrons. We have investigated the bulk properties and calculated the XMCD spectra at the L2,3 edges at the Gd site of GdN. The agreement of the calculated spectra with experiment is the indication of the relevance of the XMCD formalism within the one-electron picture. The results also show that the ground-state electronic structure of GdN is that of a half-metal. Finally our computational method is used to determine the magnetic anisotropy aspect of Gd and its compounds GdN and GdFe2. Using force theorem, we have calculated the MAE of Gd, GdN, and GdFe2 for different directions of the magnetization. Indeed, owing to the nil spin–orbit interaction of the 4f half-filled shell, the force theorem is expected to be efficient for Gd and Gd compounds’ MAE calculations. This theorem allows a considerable computational effort gain since the spin–orbit coupling could be calculated only for one self-consistent iteration. Once again, the GGA+U method is found to be the most adequate approach for the force theorem calculations of the Gd MAE. The GGA and GGA-core model treatments of the 4f states have led to a wrong MAE. It turns out that the electronic properties and the magnetic properties of 4f systems are tightly related, and the 4f electrons play a crucial role in the computed magnetic anisotropy. Although the Gd MAE is found to be similar to that of a typical 3d transition metal like hcp Co, the GdN and GdFe2 cubic crystal MAEs are found to be different from that of a pure 3d cubic material like fcc Ni.

Review: 145 refs.

Two-dimensional (2D) ferromagnetic (FM) half-metallic materials have attracted intensive attention due to their unique electronic and magnetic properties and potential applications in spintronic devices. In this study, we predicted a stable 2D half-metallic material monolayer CrSiSe4 using first-principles density functional theory. The structure, electronic and magnetic properties were systematically studied. The calculations show that the monolayer CrSiSe4 is a dynamically stable FM half-metallic material. The spin-dependent transport properties and the Curie temperature up to 239 K are demonstrated. The spin band gap of monolayer CrSiSe4 was about 0.83 eV by the the Heyd–Scuseria–Ernzerhof function calculation. The magnetic anisotropy energy of each Cr atom in the monolayer of CrSiSe4 is −552.3μ eV. When the applied biaxial tensile strain is greater than 2%, monolayer CrSiSe4 spin-up conduction band and valence band will show a band gap at the Fermi level, and the electronic properties change from a half-metal to a semiconductor. Thus, the monolayer CrSiSe4 can provide an ideal candidate material for exploring 2D magnetic and spintronics experiments.