Frequency in Middle of Magnon Band Gap in a Layered Ferromagnetic Superlattice

The frequency in middle of magnon energy band in a five-layer ferromagnetic superlattice is studied by using the linear spin-wave approach and Green's function technique. It is found that four energy gaps and corresponding four frequencie in middle of energy gaps exist in the magnon band along K_x direction perpendicular to the superlattice plane. The spin quantum numbersand the interlayer exchange couplings all affect the four frequencies in middle of the energy gaps. When all interlayer exchange couplings are same, the effect of spin quantum numbers on the frequency ω_g1 in middle of the energy gap Δω₁₂ is complicated, and the frequency ω_g1 depends on the match of spin quantum numbers in each layer. Meanwhile, the frequencies ω_g2, ω_g3, and ω_g4 in middle of other energy gaps increase monotonously with increasing spin quantum numbers. When the spin quantum numbersin each layer are same, the frequencies ω_g1, ω_g2, ω_g3, and ω_g4 all increasemonotonously with increasing interlayer exchange couplings.     

Effects of competition between the anisotropy and the spin quantum number on the magnon energy gap in a four-layer ferromagnetic superlattice

The magnon energy bands are studied for a four-layer ferromagnetic superlattice, with regard to the effects of the competition between the anisotropy and the spin quantum number. A special attention is also paid on the effects of the symmetry of the system. It is found that three modulated energy gaps exist in the magnon energy band along K_x direction perpendicular to the superlattice plane. The magnetic anisotropy affects significantly the magnon energy gaps. The zero energy gap Δω₂₃ correlates with the conditions between anisotropy constants, D₁+D₃=D₂+D₄ and D₁=D₃ (or D₂=D₄), while the disappearance of the magnon energy gaps Δω₁₂ and Δω₃₄ corresponds to a translational symmetry of x-direction in a unit cell. When the parameters of the system deviate from these conditions, the energy gaps Δω₁₂, Δω₂₃ and Δω₃₄ become larger. There is a competition effect of the anisotropy and the spin quantum number on the magnon energy gaps Δω₁₂ and Δω₂₃. When the symmetry of the system is higher, the competition can achieve a balance to cause the zero energy gap.     

Frequency in Middle of Magnon Band Gap in a Layered Ferromagnetic Superlattice

The frequency in middle of magnon energy band in a five-layer ferromagnetic superlattice is studied by using the linear spin-wave approach and Green＇s function technique. It is found that four energy gaps and corresponding four frequencie in middle of energy gaps exist in the magnon band along Kx direction perpendicular to the superlattice plane. The spin quantum numbers and the interlayer exchange couplings all affect the four frequencies in middle of the energy gaps. When all interlayer exchange couplings are same, the effect of spin quantum numbers on the frequency wg1 in middle of the energy gap Δw12 is complicated, and the frequency wg1 depends on the match of spin quantum numbers in each layer. Meanwhile, the frequencies wg2, wg3, and wg4 in middle of other energy gaps increase monotonously with increasing spin quantum numbers. When the spin quantum numbers in each layer are same, the frequencies wg1, wg2, wg3, and wg4 all increase monotonously with increasing interlayer exchange couplings.     

Quantum competitions between the effects of the interlayer exchange couplings and the magnetically structural symmetry in a four-layer ferrimagnetic superlattice

The magnon energy spectra, the sublayer magnetization and the quantum fluctuations in a ferrimagnetic superlattice consisting of four different magnetic sublayers are studied by employing the linear spin-wave approach and Green's function technique. The effects of the interlayer exchange couplings and the spin quantum numbers on the sublayer magnetization and the quantum fluctuations of the systems are discussed for three different spin configurations. The roles of quantum competitions among the interlayer exchange couplings and the symmetry of the different spin configurations have been understood. The magnetizations of some sublayers increase monotonously, while those of others can exhibit their maximum, and the quantum fluctuations of the whole superlattice system can show a minimum when one of the antiferromagnetic interlayer exchange couplings increases. This is due to the quantum competition/transmission of effects of the interlayer exchange couplings. When the spin quantum number of sublayers varies, the system goes through from a quantum region of small spin numbers to a classical region of large spin numbers. The quantum fluctuations of the system exhibit a maximum as a function of the spin quantum number of a sublayer, which is related with higher symmetry of the system. It belongs to the type III Shubnikov group of magnetic groups. This magnetically structural symmetry consists of not only the symmetry of space group, but also the symmetry of the direction and strength of spins.     

SF_6分子最高占据轨道对称性的判断

量化计算是理论研究分子的重要手段,对于具有高对称群的分子,采用子群计算是常用的方法.分子的电子态或分子轨道等的对称性在子群的表示中会出现重迭,从而不能从子群的结果直接给出电子态或分子轨道对称性的归属.本文以如何判断SF6基态1 A_(1g)的电子组态中最高占据轨道的对称性为例来解决这个问题.针对某些文献中的SF6基态1 A1g的电子组态中,最高占据轨道对称性是T_(1g)却写成T_(2g)的问题,采用Molpro量化计算软件,对SF6基态的平衡结构,进行了HF/6-311G*计算,得到了能量三重简并的最高占据轨道的函数表达式,进而运用O_h群的对称操作作用在三个轨道函数上,得到各操作的矩阵表示,于是得到特征标,最后确定了最高占据轨道为T_(1g)对称性.     

Stereodynamics study of reactions N(~2D)+HD→NH+D and ND+H

The product polarizations of the title reactions are investigated by employing the quasi-classical trajectory (QCT) method. The four generalized polarization-dependent differential cross-sections (PDDCSs) $({2\pi } / \sigma )(\d\sigma _{00} / \d\omega _t )$, $({2\pi } / \sigma )(\d\sigma _{20} / \d\omega _t )$, $({2\pi } / \sigma )(\d\sigma _{22 + } / \d\omega _t )$, and $({2\pi } / \sigma )(\d\sigma _{21 - } / \d\omega _t )$ are calculated in the centre-of-mass frame. The distribution of the angle between ${{\bm k}}$ and ${{\bm j^\prime }}$, $P(\theta _r )$, the distribution of the dihedral angle denoting ${{\bm k}}${--}$\bm k^\prime $--$\bm j^\prime $ correlation, $P(\phi _r )$, as well as the angular distribution of product rotational vectors in the form of polar plots $P(\theta _r ,\phi _r )$ are calculated. The isotope effect is also revealed and primarily attributed to the difference in mass factor between the two title reactions.     

Magnetization and magnetic phase diagrams of a spin-1/2 ferrimagnetic diamond chain at low temperature

We used the Jordan–Wigner transform and the invariant eigenoperator method to study the magnetic phase diagram and the magnetization curve of the spin-1/2 alternating ferrimagnetic diamond chain in an external magnetic field at finite temperature. The magnetization versus external magnetic field curve exhibits a 1/3 magnetization plateau at absolute zero and finite temperatures, and the width of the 1/3 magnetization plateau was modulated by tuning the temperature and the exchange interactions. Three critical magnetic field intensities H_(CB), H_(CE) and H_(CS) were obtained, in which the H_(CB) and H_(CE) correspond to the appearance and disappearance of the 1/3 magnetization plateau, respectively, and the higher H_(CS) correspond to the appearance of fully polarized magnetization plateau of the system. The energies of elementary excitation ωσ,k(σ = 1, 2, 3) present the extrema of zero at the three critical magnetic fields at 0 K, i.e., [hω_(3,k)(HCB)]_(min)= 0, [hω_(2,k)(H_(CE))]_(max)= 0 and [hω _(2,k)(H_(CS))]_(min)= 0, and the magnetic phase diagram of magnetic field versus different exchange interactions at 0 K was established by the above relationships. According to the relationships between the system's magnetization curve at finite temperatures and the critical magnetic field intensities, the magnetic field-temperature phase diagram was drawn. It was observed that if the magnetic phase diagram shows a three-phase critical point, which is intersected by the ferrimagnetic phase, the ferrimagnetic plateau phase, and the Luttinger liquid phase, the disappearance of the1/3 magnetization plateau would inevitably occur. However, the 1/3 magnetization plateau would not disappear without the three-phase critical point. The appearance of the 1/3 magnetization plateau in the low temperature region is the macroscopic manifestations of quantum effect.     

Investigations on spectroscopic parameters, vibrational levels, classical turning points and inertial rotation and centrifugal distortion constants for the X1∑+g state of sodium dimer

The density functional theory (B3LYP, B3P86) and the quadratic configuration-interaction method including single and double substitutions (QCISD(T), QCISD) presented in Gaussian03 program package are employed to calculate the equilibrium internuclear distance $R_{\rm e}$, the dissociation energy $D_{\rm e }$ and the harmonic frequency $\omega _{\rm e}$ for the $X{}^{1}\Sigma^{ + }_{\rm g}$ state of sodium dimer in a number of basis sets. The conclusion is gained that the best $R_{\rm e}$, $D_{\rm e}$ and $\omega _{\rm e}$ results can be attained at the QCISD/6-311G(3df,3pd) level of theory. The potential energy curve at this level of theory for this state is obtained over a wide internuclear separation range from 0.16 to 2.0~nm and is fitted to the analytic Murrell--Sorbie function. The spectroscopic parameters $D_{\rm e}$, $D_{0}$, $R_{\rm e}$, $\omega _{\rm e}$, $\omega _{\rm e}\chi _{\rm e}$, $\alpha _{\rm e}$ and $B_{\rm e}$ are calculated to be 0.7219~eV, 0.7135~eV, 0.31813~nm, 151.63~cm$^{ - 1}$, 0.7288~cm$^{ - 1}$, 0.000729~cm$^{ - 1}$ and 0.1449~cm$^{ - 1}$, respectively, which are in good agreement with the measurements. With the potential obtained at the QCISD/6-311G(3df,3pd) level of theory, a total of 63 vibrational states is found when $J=0$ by solving the radial Schr\"{o}dinger equation of nuclear motion. The vibrational level, corresponding classical turning point and inertial rotation constant are computed for each vibrational state. The centrifugal distortion constants ($D_{\upsilon }\, H_{\upsilon }$, $L_{\upsilon }$, $M_{\upsilon }$, $N_{\upsilon }$ and $O_{\upsilon })$ are reported for the first time for the first 31 vibrational states when $J=0$.     

Investigation of analytical harmonic frequency and potential energy function,vibrational levels for the X^2∑^＋ and A^2Л states of CN radical

This paper calculates the equilibrium structure and the potential energy functions of the ground state （X^2∑^＋） and the low lying excited electronic state （A^2Л） of CN radical are calculated by using CASSCF method. The potential energy curves are obtained by a least square fitting to the modified Murrell-Sorbie function. On the basis of physical theory of potential energy function, harmonic frequency （ωe） and other spectroscopic constants （ωeχe, βe and αe） are calculated by employing the Rydberg-Klei-Rees method. The theoretical calculation results are in excellent agreement with the experimental and other complicated theoretical calculation data. In addition, the eigenvalues of vibrational levels have been calculated by solving the radial one-dimensional SchrSdinger equation of nuclear motion using the algebraic method based on the analytical potential energy function.     

Ru thickness-dependent interlayer coupling and ultrahigh FMR frequency in FeCoB/Ru/FeCoB sandwich trilayers

The antiferromagnetic (AFM) interlayer coupling effective field in a ferromagnetic/non-magnetic/ferromagnetic (FM/NM/FM) sandwich structure, as a driving force, can dramatically enhance the ferromagnetic resonance (FMR) frequency. Changing the non-magnetic spacer thickness is an effective way to control the interlayer coupling type and intensity, as well as the FMR frequency. In this study, FeCoB/Ru/FeCoB sandwich trilayers with Ru thickness ($t_{\rm Ru}$) ranging from 1 Å to 16 Å are prepared by a compositional gradient sputtering (CGS) method. It is revealed that a stress-induced anisotropy is present in the FeCoB films due to the B composition gradient in the samples. A $t_{\mathrm{Ru}}$-dependent oscillation of interlayer coupling from FM to AFM with two periods is observed. An AFM coupling occurs in a range of $2 {\rm Å} \le t_{\rm Ru} \le 8 {\rm Å}$ and over 16 $\mathrm{Å}$, while an FM coupling is present in a range of $t_{\rm Ru}< 2$ Å and $9 {\rm Å} \le t_{\rm Ru} \le 14.5 Å$. It is interesting that an ultrahigh optical mode (OM) FMR frequency in excess of 20 GHz is obtained in the sample with ${t}_{\mathrm{Ru}}= 2.5 \mathrm{Å}$ under an AFM coupling. The dynamic coupling mechanism in trilayers is simulated, and the corresponding coupling types at different values of $t_{\mathrm{Ru}}$ are verified by Layadi's rigid model. This study provides a controllable way to prepare and investigate the ultrahigh FMR films.     

Mixedness of the N-qubit states with exchange symmetry

The mixedness of the N-qubit quantum states with exchange symmetry has been studied, and the results show that the linear entropy of the single qubit reduced density matrix （RDM）, which can describe the mixedness, is completely determined by the expectation values 〈Sz〉 and 〈S±〉 for both the pure and the mixed states. The mixedness of the pure states can be used to describe the bipartite entanglement, as an example we have calculated the mixedness of the Dicke state and the spin squeezed Kitagawa-Ueda state. For the mixed states, we determine the mixedness properties of both the ground states and the thermal states in mean-field clusters of spin-1/2 particles interacting via the anisotropy Heisenberg XXZ interaction, and found for the ferromagnetic case （J 〈 0）, the mixedness will approximate to the pairwise entanglement when the anisotropic parameter △ 〉 △c.     

Coherent interaction and action-counteraction theory in small polaron systems,and ground state properties

Based on the coherent interaction and action-counteraction principles, we investigate the ground state properties for small polaron systems, the coherent-squeezed fluctuation correction, and the anomalous lattice quantum fluctuation, with the new variational generator containing correlated squeezed-coherent coupling and quantum entanglement. Noting that $-2t $ is the T.B.A. energy, for the coherent interaction effect, we find the ground-state energy $E_0$ to be $-2.428t$, in which the coherent squeezed fluctuation correction $-A_0 t$ is $-0.463t $ (where $ t $ is the hopping integral, $\omega $ is the phonon frequency), with the electron-one-phonon coupling constant $g=$1 and the electron-two-phonon coupling constant $g_{1}=-0.1$. However, as a result of the action-counteraction effect, $\tilde{{E}}_{0} $ is $-2.788t$, but $-\tilde{{A}}_{0} t$ is $-0.735t$. As to the polaron binding energy $(E_{\rm P} )$, for the coherent interaction effect, $E_{\rm P} $ is $-1.38\omega $, but for the action-counteraction effect, $\tilde{{E}}_{\rm P}$ is $-1.88\omega $. In particular, the electron-two-phonon interaction noticeably enlarges the coherent interaction and the coherent squeezed quantum fluctuation correction. By intervening with the quantum entanglement, the evolutions of the squeezed coherent state and the lattice quantum fluctuation begin to take control. At that time, we encounter a new quantum phase coherence phenomenon — the collapse and revival of inversion repeatedly for the coherent state in the entangled evolution.     

Potential energy curves and analytical potential energy functions of the metastable states of B2^＋＋

The multi-reference configuration interaction method and aug-cc-pvqz （AVQZ） have been used to calculate potential energy curves （PECs） of the singlet and triplet states of the riu and rig symmetry of B2＋＋. All of the four states （^l∏u, ^1∏g, ^3∏u and ^3∏g） are found to be metastable states, though the potential well of ^3∏u symmetry is very shallow. Based on the PECs, the analytical potential energy functions （APEFs） of these states have been fitted using the least square fitting method and two models of function. The spectroscopic parameters of each state are also calculated, and are compared with other investigations in the literature. The credibility and veracity of the two functions are evaluated. Some ideas to improve the fitting accuracy are presented. Also the vibrational levels for each state are predicted by solving the SchrSdinger equation of nuclear motion.     

用H-W-ECR CVD系统实现氢化非晶硅薄膜在氢气环境下同时进行化学热退火和光诱导退火的研究

为了研究氢化非晶硅薄膜的稳定性，我们设计了一个在原子氢气氛中热退火的同时进行光诱导退火的实验(TLAH)。实验装置是由传统的微波电子回旋共振化学气相沉积系统改造而成为热丝辅助微波电子回旋共振化学气相沉积系统。为了对这一退火方法进行比较，对样品还进行了热退火、热退火同时进行光诱导退火。同时，为了定量地分析光电导衰退，我们假设光电导衰退遵循扩展指数规律：1/σph=1/σs-(1/σs-1/σ0)exp[-(t/τ)β]，这里扩展指数参数β 和时间常数 τ 可从与 lnt 的线性关系中截距和斜率得到, 式中光电导饱和值σs可以通过在对数坐标系中表示的光电导和光照时间关系进行高斯拟合得到。实验结果显示：TLAH 方法可以提高氢化非晶硅薄膜的稳定性、改善其微结构和光电特性，同时还发现，光学带隙明显减小、荧光光谱显著地朝着低能方向移动。     

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.     

Anisotropic properties of TaS2

The anisotropic properties of 1T- and 2H-TaS2 axe investigated by the density functional theory within the framework of full-potential linearized augmented plane wave method. The band structures of 1T- and 2H-TaS2 exhibit anisotropic properties and the calculated electronic specific-heat coefficient γ of 2H-TaS2 accords well with the existing experimental value. The anisotropic frequency-dependent dielectric functions including the effect of the Drude term are analysed, where the ε^xx（ω） spectra corresponding to the electric field E perpendicular to the z axis show excellent agreement with the measured results except for the ε1^xx（ω） of 1T-TaS2 below the energy level of 2.6 eV which is due to the lack of the enough CDW information for reference in our calculation. Furthermore, based on the values of optical effective mass ratio P of 1T and 2H phases it is found that the anisotropy in 2H-TaS2 is stronger than that in 1T-TaS2.     

On the definition of a diffusion constant in a nonequilibrium system

A diffusion constant for electrons in a current-carrying semiconductor can be unambiguously defined in nearly uniform systems. For frequency-dependent density gradients it is $$D_{\alpha \beta } (\omega ) \equiv \int\limits_0^\infty {dt e^{i\omega t} \overline {\Delta \upsilon _\alpha (t)\Delta \upsilon _\beta (0),} } $$ where \(\overline {\Delta \upsilon _\alpha (t)\Delta \upsilon _\beta (0)} \) is the velocity correlation function with respect to the steady state in a bias field. This result has been elucidated in the relaxation approximation by different approaches to the diffusion problem. Essential for its derivation is a statistical independence assumption of space and velocities, and in order to get a classical diffusion law of Fick's type certain velocities have to be distributed according to the steady state in a bias field. Diffusion constant and noise temperature are discussed for a few band structures in the relaxation approximation.     

Appearance of metallic features in small tungsten clusters

The structures and properties of W_n (n=2--14) clusters were studied by using the density functional theory (DFT) at LSDA level. The most stable structures of W_n (n=2--14) clusters with global minimum were determined. The average binding energy (E_b), the first and second difference of total energy (\itδ E, \itδ₂E), the vertical detachment energy (VDE), and the HOMO-LUMO gap versus the size were also discussed. The abrupt decrease of VDE and HOMO-LUMO gap at size n=8 and 10 implied that tungsten clusters of W₈ and W₁₀ appeared to have metallic features. These changes were also accompanied by the delocalization of electron charge density and the strong hybridization between 5d and 6s orbits in W₈ and W_10 clusters. Our results are in good agreement with the available experimental data.     

Impacts of dark energy on constraining neutrino mass after Planck 2018

Considering the mass splittings of three active neutrinos, we investigate how the properties of dark energy affect the cosmological constraints on the total neutrino mass $\sum {m}_{\nu }$ using the latest cosmological observations. In this paper, several typical dark energy models, including ΛCDM, wCDM, CPL, and HDE models, are discussed. In the analysis, we also consider the effects from the neutrino mass hierarchies, i.e. the degenerate hierarchy (DH), the normal hierarchy (NH), and the inverted hierarchy (IH). We employ the current cosmological observations to do the analysis, including the Planck 2018 temperature and polarization power spectra, the baryon acoustic oscillations (BAO), the type Ia supernovae (SNe), and the Hubble constant H₀ measurement. In the ΛCDM+$\sum {m}_{\nu }$ model, we obtain the upper limits of the neutrino mass $\sum {m}_{\nu }\lt 0.123\,\mathrm{eV}$ (DH), $\sum {m}_{\nu }\lt 0.156\,\mathrm{eV}$ (NH), and $\sum {m}_{\nu }\lt 0.185\,\mathrm{eV}$ (IH) at the 95% C.L., using the Planck+BAO+SNe data combination. For the wCDM+$\sum {m}_{\nu }$ model and the CPL+$\sum {m}_{\nu }$ model, larger upper limits of $\sum {m}_{\nu }$ are obtained compared to those of the ΛCDM+$\sum {m}_{\nu }$ model. The most stringent constraint on the neutrino mass, $\sum {m}_{\nu }\lt 0.080\,\mathrm{eV}$ (DH), is derived in the HDE+$\sum {m}_{\nu }$ model. In addition, we find that the inclusion of the local measurement of the Hubble constant in the data combination leads to tighter constraints on the total neutrino mass in all these dark energy models.