Theoretical investigations of the local distortion and electron paramagnetic resonance parameter for CdCl2:V2+ and CsMgX3:V<sup>2+（X=Cl,Br） systems

This paper systematically investigates the local distortion and electron paramagnetic resonance (EPR) parameter for CdCl 2 :V 2+ and CsMgX 3 :V 2+ (X=Cl, Br) systems on the basis of the complete energy matrix, in which not only the contributions due to the spin–orbit coupling of the central ions but also that of the ligands are considered. To describe the difference of overlapping between d-orbits and p orbit, two spin–orbit coupling coefficients are introduced. By simulating the crystal field parameter and EPR parameter, the local distortion parameters are studied and the relationships between the EPR parameter and the spin–orbit coupling coefficients as well as divergent parameter are discussed. These results show that the local structures exhibit compression distortion for CdCl 2 :V 2+ and elongation distortions for CsMgX 3 :V 2+ (X=Cl, Br), respectively. It notes that the empirical formula R ≈ R H + (r i-r h )/2 is not suitable for CdCl 2 :V 2+ and CsMgX 3 :V 2+ (X=Cl, Br) systems. The contributions of ligand to spin–orbit coupling interaction cannot be neglected for strong covalent systems, especially for V 2+ doped in CsMgBr 3 :V 2+ .     

Zero-field splitting parameters and local structures for tetragonal Cr2＋ centers in Cr2＋-doped ZnSe semiconductors

The inter-relation between zero-field splitting （ZFS） parameters and local lattice structures of the （CrSe4）6 clusters in ZnSe semiconductors has been established by using the complete diagonalization （of the energy matrix） method. On the basis of this, the local lattice distortions, the ZFS parameters D, a, F and the optical spectrum for Cr2＋ ions doped into ZnSe are theoretically investigated, and the contributions of the spin singlets have been taken into account. The calculated ZFS parameters are in good agreement with the experimental values. From our calculations, the tetragonal distortion parameters AR = 0.091A and Aθ = 4.28° of Cr2＋ in ZnSe are acquired, and the results suggest that there exists a tetragonal expansion distortion for the local lattice structure of （CrSe4）6- clusters in ZnSe crystals. The influence of the spin singlets on ZFS parameters is also discussed, indicating that the contributions to ZFS parameters a and F cannot be ignored.     

Topological superfluid in a two-dimensional polarized Fermi gas with spin-orbit coupling and adiabatic rotation

We study the properties of superfluid in a two-dimensional(2 D) polarized Fermi gas with spin–orbit coupling and adiabatic rotation which are trapped in a harmonic potential. Due to the competition between polarization, spin–orbit coupling, and adiabatic rotation, the Fermi gas exhibits many intriguing phenomena. By using the Bardeen–Cooper–Schrieffer(BCS) mean-field method with local density approximation, we investigate the dependence of order parameter solution on the spin–orbit coupling strength and the rotation velocity. The energy spectra with different rotation velocities are studied in detail. Besides, the conditions for the zero-energy Majorana fermions in topological superfluid phase to be observed are obtained. By investigating distributions of number density, we find that the rotation has opposite effect on the distribution of number density with different spins, which leads to the enhancement of the polarization of Fermi gas. Here,we focus on the region of BCS pairing and ignore the Fulde–Ferrell–Larkin–Ovchinnikov state.     

Investigations of the electron paramagnetic resonance parameters and the tetragonal local structure for (VCl6)4- coordination complex in MCl:V2+ (M=Na, K, Rb) systems

By simulating the electron paramagnetic resonance (EPR) and optical spectra on the basis of the 120×120 complete energy matrix, this paper determines the local lattice structure parameters R1 and R2 for MCl:V2+ (M=Na, K, Rb) systems at 77 K, 195 K and RT (room temperature 295 K or 302 K), respectively. The theoretical results indicate that there exists a compressed distortion in MCl:V2+ systems. Meanwhile, it finds that the structure parameters R1, R2 and |△R| (= R1-R2) increase with the rising temperature. Subsequently, from the analysis it concludes that the relation of EPR parameter D vs.△R is approximately linear. Finally, the effects of orbital reduction factor k on the g factors for the three systems have been discussed.     

Local structure distortion and spin Hamiltonian parameters for Cr3＋-Vzn tetragonal defect centre in Cr3＋ doped KZnF3 crystal

The quantitative relationship between the spin Hamiltonian parameters (D, g_‖, Δg) and the crystal structure parameters for the Cr³⁺—V_Zn tetragonal defect centre in a Cr³⁺:KZnF₃ crystal is established by using the superposition model. On the above basis, the local structure distortion and the spin Hamiltonian parameter for the Cr³⁺—V_Zn tetragonal defect centre in the KZnF_3 crystal are systematically investigated using the complete diagonalization method. It is found that the V_Zn vacancy and the differences in mass, radius and charge between the Cr³⁺ and the Zn²⁺ ions induce the local lattice distortion of the Cr³⁺ centre ions in the KZnF₃ crystal. The local lattice distortion is shown to give rise to the tetragonal crystal field, which in turn results in the tetragonal zero-field splitting parameter D and the anisotropic g factor Δg. We find that the ligand F^- ion along [001] and the other five F^- ions move towards the central Cr³⁺ by distances of Δ₁ = 0.0121 nm and Δ₂ = 0.0026 nm, respectively. Our approach takes into account the spin—orbit interaction as well as the spin—spin, spin—other-orbit, and orbit—orbit interactions omitted in the previous studies. It is found that for the Cr³⁺ ions in the Cr³⁺:KZnF₃ crystal, although the spin—orbit mechanism is the most important one, the contribution to the spin Hamiltonian parameters from the other three mechanisms, including spin—spin, spin—other-orbit, and orbit—orbit magnetic interactions, is appreciable and should not be omitted, especially for the zero-field splitting (ZFS) parameter D.     

SU(3) spin–orbit-coupled Bose–Einstein condensate confined in a harmonic plus quartic trap

We consider a SU(3) spin–orbit coupled Bose–Einstein condensate confined in a harmonic plus quartic trap.The ground-state wave functions of such a system are obtained by minimizing the Gross–Pitaevskii energy functional, and the effects of the spin-dependent interaction and spin–orbit coupling are investigated in detail.For the case of ferromagnetic spin interaction, the SU(3) spin–orbit coupling induces a threefold-degenerate plane wave ground state with nontrivial spin texture.For the case of antiferromagnetic spin interaction, the system shows phase separation for weak SU(3) spin–orbit coupling, where three discrete minima with unequal weights in momentum space are selected, while hexagonal honeycomb lattice structure for strong SU(3) SOC, where three discrete minima with equal weights are selected.     

Fabrication and magnetic properties of 4SC(NH_2)_2–Ni_(0.97)Cu_(0.03)Cl_2 single crystals

Single crystals of 4SC(NH2)2–Ni1-xCux Cl2(x = 0.03)(Cu-DTN) containing spin S = 1/2 Cu2+and S = 1 Ni2+cations are synthesized by slow evaporation methods. Structural characterization demonstrates that the Cu-DTN is of a tetrahedral structure with lattice parameter c being 9.0995 ?A, which is 1.32% expansion compared with that of parent material DTN due to the larger radius of the Cu ion. Direct current(DC) susceptibility measurements show that both the antiferromagnetic exchange interaction at low temperature and the large anisotropy of susceptibilities are suppressed after doping the Cu ion, which could be related to the structural distortion and the increase of the super-exchange paths in Cu-DTN.     

Composite solitons in SU(3) spin–orbit-coupling Bose gases

We study solitons in a spin-1 Bose–Einstein condensates with SU(3) spin–orbit coupling. We obtain the ground state and the metastable solution for solitons with attractive interactions by the imaginary-time evolution method. Compared with the SU(2) spin–orbit coupling, it is found that the solitons in SU(3) spin–orbit coupling show a new feature due to breaking the symmetry. The solitons called the composite solitons have mixing manifolds of ferromagnetic and antiferromagnetic states. This has stimulated people to study the topological excitation properties of SU(3) spin–orbit coupling and it is expected to find new quantum phases.     

Quantum spin Hall and quantum valley Hall effects in trilayer graphene and their topological structures

The present study pertains to the trilayer graphene in the presence of spin orbit coupling to probe the quantum spin/valley Hall effect. The spin Chern-number C_s for energy-bands of trilayer graphene having the essence of intrinsic spin–orbit coupling is analytically calculated. We find that for each valley and spin, C_s is three times larger in trilayer graphene as compared to single layer graphene. Since the spin Chern-number corresponds to the number of edge states,consequently the trilayer graphene has edge states, three times more in comparison to single layer graphene. We also study the trilayer graphene in the presence of both electric-field and intrinsic spin–orbit coupling and investigate that the trilayer graphene goes through a phase transition from a quantum spin Hall state to a quantum valley Hall state when the strength of the electric field exceeds the intrinsic spin coupling strength. The robustness of the associated topological bulk-state of the trilayer graphene is evaluated by adding various perturbations such as Rashba spin–orbit(RSO) interaction αR, and exchange-magnetization M. In addition, we consider a theoretical model, where only one of the outer layers in trilayer graphene has the essence of intrinsic spin–orbit coupling, while the other two layers have zero intrinsic spin–orbit coupling.Although the first Chern number is non-zero for individual valleys of trilayer graphene in this model, however, we find that the system cannot be regarded as a topological insulator because the system as a whole is not gaped.     

Local structure distortion and spin Hamiltonian parameters of oxide-diluted magnetic semiconductor Mn-doped ZnO

The local structure distortion, the spin Hamiltonian (SH) parameters, and the electric fine structure of the ground state for Mn²⁺(3d⁵) ion in ZnO crystals are systematically investigated, where spin--spin (SS), spin--other--orbit (SOO) and orbit--orbit (OO) magnetic interactions, besides the well-known spin--orbit (SO) coupling, are taken into account for the first time, by using the complete diagonalization method. The theoretical results of the second-order zero-field splitting (ZFS) parameter D, the fourth-order ZFS parameter (a-F), the Zeeman g-factors: g_// and g_⊥, and the energy differences of the ground state: \delta₁ and \delta₂ for Mn²⁺ in Mn²⁺: ZnO are in good agreement with experimental measurements when the three O^2- ions below the Mn²⁺ ion rotate by 1.085^o away from the [111]-axis. Hence, the local structure distortion effect plays an important role in explaining the spectroscopic properties of Mn²⁺ ions in Mn²⁺: ZnO crystals. It is found for Mn²⁺ ions in Mn²⁺: ZnO crystals that although the SO mechanism is the most important one, the contributions to the SH parameters, made by other four mechanisms, i.e. SS, SOO, OO, and SO～SS～SOO～OO mechanisms, are significant and should not be omitted, especially for calculating ZFS parameter D.     

V4+ in SrTiO3: A Jahn-Teller impurity

EPR results of V⁴⁺, with $\text{S =}\text{1}\text{2}$, in SrTiO₃ are reported. The tetragonal local symmetry of the impurity ion is related to strong T_2g × ?_g coupling as evidenced by intensity variations in the presence of stress. At 4.2 K the V⁴⁺ EPR behaviour is related to the intrinsic local strain in SrTiO₃.     

EPR parameters and local lattice structure study of V ions in CdCl2 and CsMgCl3 crystals

The local lattice structure and EPR parameters (D, g_‖, g_⊥) have been studied systematically on the basis of the complete energy matrix for a d³ configuration ion in a trigonal ligand field. By simulating the calculated optical and EPR spectra data to the experimental results, the local distortion parameters (ΔR, Δθ) are determined for V²⁺ ions in CdCl₂ and CsMgCl₃ crystals, respectively. The results show that the local lattice structure of CdCl₂:V²⁺ system exhibits a compression distortion (ΔR=−0.0868 Å) while that of CsMgCl₃:V²⁺ system exists an elongation distortion (ΔR=0.0165 Å). The different distortion may be ascribed to the fact that the radius of V²⁺ ion is smaller than that of Cd²⁺ ion or larger than that of Mg²⁺ ion. Moreover, the relationships between EPR parameter D and local structure parameters (R, θ) as well as the orbital reduction factor k and g‐factors (g_‖, g_⊥) are discussed.     

EPR of V2+ in SrCl2

The X-band EPR spectrum of SrCl₂:V has been measured at liquid nitrogen temperature. A signal associated with V²⁺ in a site of trigonal symmetry is observed. The EPR data have been explained using the spin hamiltonian $\textcolor{red}{}\text{= μ}{}_{\mathrm{\beta }}\text{H}\text{g}\text{?}\text{S}\text{+ D[S}{}^2{}_{\mathrm{z}}\text{?}\text{1}\text{3}\text{S(SH)] +}\text{S}\text{A}\text{?}\text{I}$, with D ? hv, g_∥ = 1.957 ± 0.004, g₆ = 1.954 ± 0.004, A_∥ = 230 ± 5 MHz, A₆ = 235 ± 5 MHz. This V²⁺ defect is similar to those previously reported in fluoride crystals with the fluorite structure.     

Al2O3:V3+晶体局域结构及其自旋哈密顿参量研究

提出了解释掺杂离子局域结构畸变的配体平面移动模型，建立了此模型下晶体微观结构与自旋哈密顿参量之间的定量关系.在考虑自旋与自旋、自旋与另一电子轨道和轨道与轨道作用等微小磁相互作用的基础上，采用全组态完全对角化方法，对Al₂O₃晶体中V³⁺的局域结构和自旋哈密顿参量进行了系统的研究.结果表明，V³⁺掺入Al₂O₃晶体后，上下配体氧平面间距离增大了0.0060 nm.从而成功地解释了Al₂O₃:V³⁺晶体的自旋哈密顿参量.在此基础上，研究了三角晶场下3d²离子自旋哈密顿参量的微观起源.研究发现，自旋三重态对自旋哈密顿参量的贡献是主要的，微小磁相互作用对自旋哈密顿参量的贡献只与自旋三重态有关.     

EPR spectra of NaCl:V2+ and KCl:V2+ above room temperature

Measurements above 300 K of the temperature variation of EPR spectra in NaCl and KCl, doped with divalent vanadium, are analysed. A new isotropic spectrum in KCl:V²⁺, which appears above 500 K, due to vanadium in cubic surroundings, is reported.     

Spin--orbit ab initio curves of 80Se2+ ion and theassignment of photoelectron spectra of 80Se2 molecule

This paper carries out ab initio calculations to study the ^80Se2（X^3Σg^-） state and ^80Se2^＋（X^2Πg）, ^80Se2^＋（a^4Πg） states by using completed active space self-consistent field and multi-reference second order perturbation theory. The electronic curves of these states including spin-orbit coupling are calculated, and then the spectroscopic parameters are obtained. The photoelectron spectra of ^80Se2 molecule in gas phase are assigned according to Franck-Condon analysis based on calculated potential energy curves. The ionization energies of ^80Se2 molecule are determined by the present calculation.     

Density functional study on chirospectra of hydrogen-bonded systems X-（H2O）3（X=F,Cl,Br,I）

This paper calculates the molecular structures,infrared,Raman,circular dichroism spectra and optical rotatory powers of some hydrogen-bonded supramolecular systems as a cyclic water trimer,(H2O)3 and its pyramidal halide complexes,X-(H2O)3(X = F,Cl,Br,I) with the gradient-corrected density functional theory method at the B3LYP/6-311++G(2d,2p) and B3LYP/Aug-cc-pVTZ levels.It finds that the complexation of halide anions with the water trimer can efficiently modulate the chirally optical behaviors.The calculated vibrational circular dichroism spectrum illuminates that the vibrational rotational strength of S(+)-(H2O)3 mostly originates from the O-H rocking modes,whereas chirality of S(-)-X-(H2O)3(X = F,Cl,Br,I) has its important origin in the O-H stretching modes.The calculated optical rotatory power demonstrates that S(+)-(H2O)3 and S(+)-F(H2O)3 are positively chiral,whereas S(-)-X-(H2O)3(X = Cl,Br,I) are negatively chiral.With the polarizable continuum model,calculated bulk solvent effect in the solvents water and carbontetrachloride and argon shows that the positive chirality of S(+)-(H2O)3 is enhanced and the negative chirality of S(-)-X-(H2O)3(X = Cl,Br,I) and the positive chirality of S(+)-F(H2O)3 are reduced with an augmentation of the solvent dielectric constant.     

EPR and optical spectra of Ni2+-VAg in silver chloride and silver bromide

The optical absorption and EPR spectra of Ni²⁺-V_Ag centres in the AgCl:Ni²⁺ and AgBr:Ni²⁺ systems have been investigated theoretically on the basis of the complete energy matrices including the electron–electron repulsion interaction, the ligand field interaction, the spin–orbit coupling interaction, and Zeeman interaction. Because the charge compensation forms a silver ion vacancy (V_Ag) which makes the attractive force acted on the each ligand ion different, it was determined that the Ni–X (X = Cl, Br) distance next to V_Ag is shorter than others for both AgCl:Ni²⁺ and AgBr:Ni²⁺ systems in the tetragonal symmetry. Besides, it was found that the local lattice structure of (NiX₆)^4? clusters in AgCl and AgBr crystals exhibit a compression distortion. This compression distortion may be ascribed to the fact that the Ni²⁺ ion has a smaller ionic radius and more effective charge than the Ag⁺ ion.     

掺入Ni2+和V3+对α-Al2O3晶体光谱精细结构、晶体局域结构和零场分裂参量的影响

应用晶体场理论和不可约张量算符方法构造了3d2/3d8态离子在C3v对称晶场中包含自旋-轨道相互作用、自旋-自旋相互作用、自旋-其它轨道相互作用和其它轨道-其它轨道相互作用四种微观磁效应的45阶可完全对角化的能量哈密顿矩阵.利用该矩阵,计算了V³⁺∶α-Al₂O₃和Ni²⁺∶α-Al₂O₃晶体的光谱精细结构、晶体局域结构和零场分裂参量,研究了掺入两种互补态离子Ni²⁺和V³⁺对同种晶体的光谱精细结构、晶体局域结构和零场分裂参量的影响,理论计算值和实验值相符.研究发现：掺杂没有改变晶体的光谱精细结构和能级分裂条数,但改变了能级间距|掺杂也没有改变晶体的对称性,但使晶体局域结构发生了一定程度的畸变| Ni²⁺∶α-Al₂O₃晶体局域结构的伸长畸变量大于V³⁺∶α-Al₂O₃晶体,键角的变化量小于V³⁺∶α-Al₂O₃晶体.