双层反铁磁体K3Cu2F7 中轨道序驱动的自旋二聚化

基于自旋-轨道-晶格Hamilton量,应用团簇自洽场方法,研究了双层钙钛矿结构材料K₃Cu₂F₇基态的晶格、磁及轨道结构,发现近孤立的双层的对称破缺和Jahn-Teller晶格畸变使得Cu²⁺离子在每层内交替占据 z²-x²〉/ z²-y²〉轨道,进而导致双层的层间表现为强的反铁磁耦合,层内为弱的铁磁耦合.强反铁磁耦合导致层间     

Spin polarization effect for Fe2 molecule

This paper uses the density functional theory （DFT）（B3p86） of Gaussian03 to optimize the structure of Fe2 molecule. The result shows that the ground state for Fe2 molecule is a 9-multiple state, which shows spin polarization effect of Fe2 molecule of transition metal elements for the first time. Meanwhile, we have not found any spin pollution because the wavefunction of the ground state does not mingle with wavefunctions with higher energy states. So, that the ground state for Fe2 molecule is a 9-multiple state is indicative of the spin polarization effect of Fe2 molecule of transition metal elements. That is, there exist 8 parallel spin electrons. The non-conjugated electron is greatest in number. These electrons occupy different spacious tracks, so that the energy of the Fe2 molecule is minimized. It can be concluded that the effect of parallel spin of the Fe2 molecule is laFger than the effect of the conjugated molecule, which is obviously related to the effect of electron d delocalization. In addition, the Murrell Sorbie potential functions with the parameters for the ground state and other states of Fe2 molecule are derived. Dissociation energy De for the ground state of Fe2 molecule is 2.8586ev, equilibrium bond length Re is 0.2124nm, vibration frequency we is 336.38 cm^-1. Its force constants f2, f3, and f4 are 1.8615aJ.nm^-2, -8.6704aJ.nm^-3, 29.1676aj.nm^-4 respectively. The other spectroscopic data for the ground state of Fe2 molecule weXe, Be, αe are 1.5461 cm^-1, 0.1339cm^-1, 7.3428× 10^-4 cm^-1 respectively.     

Spin polarization effect for Mn2 molecule

The density functional theory method （DFT） （b3p86） of Gaussian 03 has been used to optimize the structure of the Mn2 molecule. The result shows that the ground state of the Mn2 molecule is an 11-multiple state, indicating a spin polarization effect in the Mn2 molecule, a transition metal element molecule. Meanwhile, we have not found any spin pollution because the wavefunction of the ground state does not mingle with wavefunctions of higher-energy states. So the ground state for Mn2 molecule being of an 11-multiple state is the indicative of spin polarization effect of the Mn2 molecule among those in the transition metal elements： that is, there are 10 parallel spin electrons in a Mn2 molecule. The number of non-conjugated electrons is the greatest. These electrons occupy different spacious orbitals so that the energy of the Mn2 molecule is minimized. It can be concluded that the effect of parallel spin in the Mn2 molecule is larger than the effect of the conjugated molecule, which is obviously related to the effect of electron d delocalization. In addition, the Murrell-Sorbie potential functions with the parameters for the ground state and other states of the Mn2 molecule are derived. The dissociation energy De for the ground state of the Mn2 molecule is 1.4477 eV, equilibrium bond length Re is 0.2506 nm, vibration frequency ωe is 211.51 cm^-1. Its force constants f2, f3, and f4 are 0.7240 aJ·nm-2, -3.35574 aJ·nm^-3, 11.4813 aJ·nm^-4 respectively. The other spectroscopic data for the ground state of the Mn2 molecule ωeχe, Be, αe are 1.5301 cm^-1, 0.0978 cm^-1, 7.7825×10^-4 cm^-1 respectively.     

Spin polarization effect of Ni2 molecule

The density functional theory （DFT） method （b3p86） of Gaussian 03 is used to optimize the structure of the Ni2 molecule. The result shows that the ground state for the Ni2 molecule is a 5-multiple state, symbolizing a spin polarization effect existing in the Ni2 molecule, a transition metal molecule, but no spin pollution is found because the wavefunction of the ground state does not mingle with wavefunctions of higher-energy states. So the ground state for Ni2 molecule, which is a 5-multiple state, is indicative of spin polarization effect of the Ni2 molecule, that is, there exist 4 parallel spin electrons in Ni2 molecule. The number of non-conjugated electrons is greatest. These electrons occupy different spatial orbitals so that the energy of the Ni2 molecule is minimized. It can be concluded that the effect of parallel spin in the Ni2 molecule is larger than that of the conjugated molecule, which is obviously related to the effect of electron d delocalization. In addition, the Murrell-Sorbie potential functions with the parameters of the ground state and other states of the Ni2 molecule are derived. The dissociation energy De for the ground state of the Ni2 molecule is 1.835 eV, equilibrium bond length Re is 0.2243 nm, vibration frequency we is 262.35 cm^-1. Its force constants f2, f3 and f4 are 1.1901 aJ.nm^-2, -5.8723 aJ.nm^-3, and 21.2505 aJ.nm^-4 respectively. The other spectroscopic data for the ground state of the Ni2 molecule ωeχe, Be and αe are 1.6315cm 2, 0.1141 cm^-1, and 8.0145× 10^-4 cm^-1 respectively.     

Spin-Hamiltonian theory of orbital near-degenerate state in tetragonal field

In this paper, a Spin-Hamiltonian theory of orbital near-degenerate state in tetragonal field is presented. For orbital doublet ²E, which is an orbital degenerate state in the cubic field and is a near-degenerate state in the tetragonal field, we obtain the cubic invariant form and the tetragonal invariant form of the Spin-Hamiltonian. In case of near-degeneracy (tetragonal splitting is very small) two additional g-factors are introduced to investigate Zeeman-splitting for tetragonal field. The two additional g-factors g_2z and g_2xy describe the magnetic interest between A_1g and B_1g states for a parallel magnetic field with z-axis and a perpendicular magnetic field with z-axis, respectively. The theory is based on the time-reversal invariant and the point-group symmetry invariant. The theoretical method can also be used for other orbital degenerate states ^2S+1Γ including and Γ=T₁ or T₂ and can be used for other point-group symmetry.     

The Ground State Spectroscopic Parameters and Equilibrium Structure of PD3

Infrared spectra of PD₃ have been measured in the 20-320 cm⁻¹ range and in the region of the ν₂/ν₄ and ν₁/ν₃ fundamental bands near 750 and 1690 cm⁻¹, respectively, with a resolution of ca. 0.0025 cm⁻¹. Furthermore, submillimeter-wave spectra covering the J=4-3, 13-12, and 14-13 clusters in the vibrational ground state were recorded. The observed ΔJ=+1 rotational lines were augmented by about 5500 ground state combination differences formed from transitions belonging to the fundamental bands. Of these, 1300 involved perturbation-allowed lines with ΔK≠0. These data and observations taken from the literature were appropriately weighted and fitted to 14 ground state molecular constants. The A and B reductions of the rotational Hamiltonian were found to be equivalent. Improved effective ground state and equilibrium structures were determined for both PH₃ and PD₃; the equilibrium structures, r_e (PH)=141.1607(83) pm and α_e (HPH)=93.4184(95)° and r_e (PD)=141.1785(57) pm and α_e (DPD)=93.4252(68)°, are in good agreement.     

Magnetic resonance in quantum spin chains

The present understanding of quantum spin chains is reviewed from the magnetic resonance point of view. This includes both the ideal one-dimensional properties in the spin sector as well as the complex interplay with orbital, charge, and lattice degrees of freedom which govern the ground state. In copper-phosphates we observe an extremely extended paramagnetic regime governed by strong antiferromagnetic correlations with record values of the ratio k_BT_N/J < 6×10⁻⁴, which compares the ordering temperature of a Néel state to the magnitude of the exchange J between neighbouring spins. A detailed quantitative discussion of NMR and ESR relaxation within this paramagnetic regime elucidates the relevant exchange interactions in typical bonding geometries of most common quantum-spin-chain systems like KCuF₃, CuGeO₃, Na_xV₂O₅, and LiCuVO₄. Concerning the ground state, paramount topics of modern solid-state physics arise among these examples as there are multiferroicity, charge order, metal-insulator transition, and spin dimerization as well as phase separation.     

Hearing the zero locus of a magnetic field

We investigate the ground state of a two-dimensional quantum particle in a magnetic field where the field vanishes nondegenerately along a closed curve. We show that the ground state concentrates on this curve ase/h tends to infinity, wheree is the charge, and that the ground state energy grows like (e/h)^2/3. These statements are true for any energy level, the level being fixed as the charge tends to infinity. If the magnitude of the gradient of the magnetic field is a constantb ₀ along its zero locus, then we get the precise asymptotics(e/h) ^2/3 (b ₀) ^2/3 E _* +O(1) for every energy level. The constantE _* .5698 is the infimum of the ground state energiesE() of the anharmonic oscillator family .     

硅中空穴与核的超精细作用及p型硅的核磁弛豫

本文把半导体中载流子和它的原子核的超精细作用(包括非接触项)表达为作用在有效质量波函数上的“准接触作用”。具体对硅中Si²⁹核和价带空穴的这个作用可表达为{S₁(J_xμ_nx+J_yμ_ny+J_zμ_nz)+S₂(J_x³μ_nx+J_y³μ_ny+J_z³μ_nz)}δ(r-r_n),参量S₁、S₂是联系着价带顶的波函数的一些积分;一般地S₂≈0。用它来处理了p型硅中Si²⁹核的核自旋弛豫,得到弛豫时间的表达式;从弛豫时间的实验值估计了S₁的值;还从价带自旋轨道分裂值估计了同一参量。     

Jahn-Teller effect and the orbital ground state of Cu2+ ions in Eu2CuO4 and La2CuO4 crystals

Local ion displacements and their anharmonicity in Eu₂CuO₄ and La₂CuO₄ crystals are studied by high-precision x-ray diffractometry. A symmetry analysis and the temperature behavior of the probability density function of Cu²⁺ ions reveal a degenerate ground orbital state in the Eu₂CuO₄ crystal (tetragonal doublet d _xz, d _yz). The pattern and anharmonicity of the local displacements are found to be determined not only by lattice vibrations but by 2D antiferromagnetic spin fluctuations in the CuO₂ sheet as well. By contrast, in the La₂CuO₄ crystal the orbital ground state of the Cu²⁺ ion is a singlet (d _z 2). The pattern of Eu³⁺ local displacements and their effect on the properties of the Cu subsystem in the Eu₂CuO₄ crystal are also studied. Fiz. Tverd. Tela (St. Petersburg) 39, 1600–1608 (September 1997)     

UH和UH2分子的结构与势能函数

用相对论有效原子实势(RECP)和密度泛函(B3LYP/SDD)方法研究了UH,UH₂基态和低激发态的结构和势能函数,导出了分子的光谱数据.结果表明,UH和UH₂的基电子状态分别为X⁴Π和X³A₂,离解能分别为2.886eV和5.249eV,UH₂具有C2v对称性,得到了UH和UH₂的几个不同的低激发态的结构与光谱数据.应用多体项展式理论以及数字拟合方法 关键词： UH 2')" href="#">UH₂ 势能函数 分子结构     

Structure and stability of various states of the EuC and EuC2 molecules

B3LYP level density functional theory （DFT） and multiconfiguration self-consistent-field （MCSCF） level ab initio method calculations have been performed on the basis of relativistic effective core potentials to investigate the nature of EuC and EuC2 molecules. The computed results indicate that the ground states of EuC and EuC2 are ^12∑^＋ and SA2, respectively. Dissociation potential energy curves of the low-lying electronic states of EuC have been calculated using the MCSCF method, and the same level calculation on EuC2 indicates that the dissociation energy of EuC2 of ground state compares well with the available experimental data. The bond characteristic is also discussed using Mulliken populations.     

Quantum glass transition in a periodic long-range Josephson array

We show that the ground state of a periodic long-range Josephson array frustrated by a magnetic field is a glass for sufficiently large Josephson energies despite the absence of quenched disorder. Like superconductors, this glass state has non-zero phase stiffness and Meissner response; for lower Josephson energies the glass “melts” and the ground state loses its phase stiffness and becomes insulating. We find the critical scaling behavior near this quantum phase transition: the excitation gap vanishes as (J−J _c )², and the frequency-dependent magnetic susceptibility behaves as . Zh. éksp. Teor. Fiz. 116, 1450–1461 (October 1999) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Deformation in the light Br isotopes

The nuclear ground state spins of the odd-A Br nuclides^{75, 77, 79}Br with Z=35 are all 3/2⁻. Nilsson orbital calculations show that the 35^th proton occupies the f_5/2 [301]3/2⁻ orbital for ε<0.20 and the p_3/2 [312]3/2⁻ orbital at larger deformations. The magnetic moments of these two states differ by a factor of two, giving clear evidence for the magnitude of the ground state deformation. Low Temperature Nuclear Orientation measurements made in Oxford and Bonn on^{76, 77g}BrFe prepared at ISOLDE, and on line at the SERC Daresbury Laboratory on^{72, 74m, 75}BrFe, have yielded the magnetic moments of these isotopes, using a two non-zero field model with magnetic hyperfine fields of +81.38(6) T and 26(2) T. The spin of the⁷³Br ground state is also deduced. An interpretation of the ground state configurations of these isotopes is given.     

Hyperfine structure and isotope shifts in the 5d6s2 a2D3/2--5d6s(a3D)6p z4F5/2 ° transition of Hf II

The hyperfine structure and isotope shifts of the transition between the 5d6s² a²D_3/2 ground state and the 5d6s(a³D)6p z⁴F_5/2 ^° excited state of singly ionized hafnium at \lambda=340 nm have been investigated by laser spectroscopy using a radio-frequency quadrupole ion trap. The magnetic dipole coupling constant A and electric quadrupole coupling constant B of the two atomic levels for both stable isotopes ¹⁷⁷Hf and ¹⁷⁹Hf are determined. The changes of mean square nuclear charge radii \delta[ r²] of the stable Hf isotopes and the radioactive isotope ¹⁷²Hf (T_1/2=1.87a) have been extracted from the data. This revised version was published online in August 2006 with corrections to the Cover Date.     

Incommensurate magnetic structure and crystal field in ErNi2B2C Studied by 166Er Mössbauer spectroscopy and specific heat measurements

¹⁶⁶Er Mössbauer absorption spectra have been recorded in the superconductor ErNi₂B₂C (T _c = 10 K), in zero field and in the temperature range 1.4 K–40 K. The spectra in the magnetically ordered phase (T _N ? 5.5 K) are characteristic of an incommensurate magnetic structure with a maximum Er³⁺ moment of 8.2 μB. We show that the magnetic transition is first order, with a small temperature range where magnetically ordered and paramagnetic domains coexist. The analysis of the magnetic and quadrupolar hyperfine interactions below and above T _N suggests that the Er³⁺ ground doublet is close to |J = 15/2; J _z = ± 1/2 > and shows that there is a low lying (? 10 K) excited doublet. The measured Er³⁺ electronic relaxation rate 1/T₁ shows an anomaly at 10 K (T _c suggesting that the conduction electrons that are exchange coupled to the 4f spin take part in the formation of the superconducting state. We also present specific heat data for Er _x Y_{1 ? x} Ni₂B₂C and Er_0.2Lu_0.8Ni₂B₂C which also evidence a low lying doublet and from which we propose a modified (improved) Er³⁺ crystal field level scheme (0, 9, 62, 71, 73, 181, 212 and 216 K) where the energies of the higher levels are consistent with published neutron scattering data.     

Exact results of an alternating-bond mixed spin-1/2 and spin-1 Ising chain with both longitudinal and transverse single-ion anisotropies

The alternating-bond mixed spin-1/2 and spin-1 Ising chain with both longitudinal and transverse single-ion anisotropies are solved exactly by means of a mapping of the spin-1/2 transverse Ising chain and the Jordan-Wigner transformation. The ground state quantities are strongly dependent on the model Hamiltonian parameters J₁, J₂, D_x and D_z. We obtain the quasi-particles' spectra Λ_k, the dimerization gap Δ_d, the minimal energy Δ₀ for exciting a fermion quasi-particle, the minimal energy gap Δ_h for exciting a hole and the ground state energy E_g. The phase diagram of the ground state is also given. The results show that the alternating bond just quantitatively changes the ground state properties; no matter the nearest-neighbor exchange interactions J₁ and J₂ are equal or not, when D_z≥0 for any finite value of D_x, there is no quantum critical point and the ground state is always in a spin ordered phase.     

Magnetism and electronic properties of BiFeO3 under lower pressure

Ab initio calculations show an antiferromagnetic-ferromagnetic phase transition around 9-10 GPa and a magnetic anomaly at 12 GPa in BiFeO₃. The magnetic phase transition also involves a structural and insulator-metal transition. The G-type AFM configuration under pressure leads to an increase of the y component and a decrease of the z component of the magnetization, which is caused by the splitting of the d_z² orbital from doubly degenerate e_g states. Our results agree with the recent experimental results.