A first principles lattice dynamics and Raman spectra of the ferroelastic rutile to CaCl2 phase transition in SnO2 at high pressure

A first principles calculation of the lattice dynamical properties of rutile SnO₂ has been performed using density functional perturbation theory at ambient and high‐pressure conditions to understand the pressure‐induced phase transition. The calculated zone centre phonon modes at ambient and high pressures have been compared with Raman scattering and infrared measurements. Full phonon dispersion curves and phonon densities of states and Raman intensities at high pressures are calculated and given for the first time in literature. The ferroelastic transition from the rutile to the CaCl₂‐type structure was confirmed. It is clearly illustrated that the first transition is associated with macroscopic shear instability which arises from the strong coupling between elastic constants and softening of Raman active B_1g mode. The observed pressure of phase transition in experimental measurements was reproduced more accurately than in previous calculations, and the difference between observed and calculated transition pressure is only of the order of 2%. The mode Grüneisen parameter is quantitatively as well as qualitatively different from the earlier reported values. Copyright © 2013 John Wiley & Sons, Ltd.     

Soft modes and phonon interactions in studied by neutron scattering

The low frequency lattice dynamics and its relationship to the second order paraelectric-to-ferroelectric transition in Sn₂P₂S₆ is studied. The dispersion branches of the acoustic and lowest lying optical phonons in the a^*-c^* plane have been obtained in the ferroelectric phase, for x-polarized phonons. Close to the phase transition a considerable softening is found for the lowest optical mode (P_x), comparable to the behaviour observed in previous Raman investigations. As found previously in Sn₂P₂Se₆, a strong coupling between the TO(P_x) and TA(u_xz) phonons is observed, although, apparently, not strong enough to lead to an incommensurate phase. The soft TO(P_x) mode at the zone center is observed. The temperature dependence of its frequency and damping shows that the transition is not entirely displacive. At low temperatures an unusual apparent negative LO-TO splitting is observed which is shown to arise from the coupling of the x-polarized soft mode to the nearby z-polarized optical phonon. For comparison, the soft TO(P_x) dispersion in the a^*-b^* plane is measured in both the paraelectric and ferroelectric phases. Consistent frequency changes and LO-TO splitting are observed, revealing a significant interaction between the TA(u_yx) and LA(u_xx) acoustics branches and the TO and LO soft optic branches, respectively. In contrast, the nearby y-polarized optic branch shows almost no temperature dependence. Finally, the influence of piezoelectric effects on the limiting acoustic slopes in the ferroelectric phase is discussed. Received: 11 May 1998 / Revised and Accepted: 15 June 1998     

Speed of sound in an optical lattice

A system of equal mixture of ⁶Li atomic Fermi gas of two hyperfine states loaded into a cubic three‐dimensional optical lattice is studied assuming a negative scattering length (BCS side of the Feshbach resonance). When the interaction is attractive, fermionic atoms can pair and form a superfluid. The dispersion of the phonon‐like mode and the speed of sound in the long‐wavelength limit are obtained by solving the Bethe‐Salpeter equations for the collective modes of the attractive Hubbard Hamiltonian.     

自旋-轨道耦合作用下玻色-爱因斯坦凝聚在量子相变附近的朗道临界速度

各向异性超流体中的朗道临界速度并非简单地由运动方向的元激发能谱决定.在自旋-轨道耦合作用下的双分量玻色-爱因斯坦凝聚中,当系统跨过平面波相与零动量相之间的量子相变时,尽管超流声速连续变化,但垂直于自旋-轨道耦合方向的朗道临界速度会出现跳变,跳变幅度随自旋相互作用强度单调增加.根据线性响应理论,计算了凝聚体中运动杂质在不同速度下的能量耗散率,提出可以通过能量耗散观测临界速度在量子相变处的不连续性.     

Lattice dynamics and baric behavior of phonons in Hg<Subscript>2</Subscript>Cl<Subscript>2</Subscript> crystals at high hydrostatic pressures

A theoretical model based on long-range dispersion corrections of the charge density functional is proposed for model Hg₂Cl₂ calomel crystals, typical representatives of molecular inorganic compounds where the intermolecular interaction is found to play an important role. This model successfully describes the electronic state and the phonon spectrum of the above crystal, predicts the earlier unstudied phase transition at high hydrostatic pressure. Study of the baric behavior of the phonon spectrum with Raman spectroscopy observes the soft mode in the low-symmetry orthorhombic phase with the frequency softening as the pressure rises. Pressures above 9 GPa considerably transform the Raman spectra, indicating a structural phase transition.     

Self-consistent treatment of superconducting hole systems and anharmonic lattices in oxides

An extention of Hirsch's Hamiltonian describing the hole system is proposed by including a coupling to the anharmonic lattice and a modulation of the hopping interaction due to lattice displacements. The model is discussed within the variational Bogoliubov's approach, assuming a BCS-like trial Hamiltonian for the hole-like subsystem and a self-consistent phonon approximation for the lattice. The model allows in general to discuss an interplay between superconductivity and ferroelectricity. The results for the critical temperature and the isotope effect coefficient in the superconducting paraelectric phase in one dimension are presented. In particular, the strong influence of the phonon softening on the superconducting transition is widely discussed.     

Bose−Einstein condensates with tunable spin−orbit coupling in the two-dimensional harmonic potential: The ground-state phases,stability phase diagram and collapse dynamics

We study the ground-state phases, the stability phase diagram and collapse dynamics of Bose−Einstein condensates (BECs) with tunable spin−orbit (SO) coupling in the two-dimensional harmonic potential by variational analysis and numerical simulation. Here we propose the theory that the collapse stability and collapse dynamics of BECs in the external trapping potential can be manipulated by the periodic driving of Raman coupling (RC), which can be realized experimentally. Through the high-frequency approximation, an effective time-independent Floquet Hamiltonian with two-body interaction in the harmonic potential is obtained, which results in a tunable SO coupling and a new effective two-body interaction that can be manipulated by the periodic driving strength. Using the variational method, the phase transition boundary and collapse boundary of the system are obtained analytically, where the phase transition between the spin-nonpolarized phase with zero momentum (zero momentum phase) and spin-polarized phase with non-zero momentum (plane wave phase) can be manipulated by the external driving and sensitive to the strong external trapping potential. Particularly, it is revealed that the collapsed BECs can be stabilized by periodic driving of RC, and the mechanism of collapse stability manipulated by periodic driving of RC is clearly revealed. In addition, we find that the collapse velocity and collapse time of the system can be manipulated by periodic driving strength, which also depends on the RC, SO coupling strength and external trapping potential. Finally, the variational approximation is confirmed by numerical simulation of Gross−Pitaevskii equation. Our results show that the periodic driving of RC provides a platform for manipulating the ground-state phases, collapse stability and collapse dynamics of the SO coupled BECs in an external harmonic potential, which can be realized easily in current experiments.     

Effect of optical phonon‐magnon interaction on the magnon softening at finite temperature

A magnon‐phonon interaction model is set up in a two‐dimensional ferromagnetic compound square‐lattice system. Using the Matsubara Green function theory we calculated the magnon dispersion curves on the main symmetric line in Brillouin zone, compared the influences of the magnetic ion optical phonon with non‐magnetic ion optical phonon on the magnetic excitation of the system and discussed the influences of various parameters on the magnon softening. The lower Debye temperature of ferromagnetic materials is, the more likely the magnon softening occurs. It turned out that the optical phonon‐magnon coupling plays an important role on the magnon softening, the longitudinal optical phonon contributes the most to the magnon softening and magnon damping. It is also found that the contribution of the non‐magnetic ion to the magnon softening and magnon damping is more significant than that of magnetic ion when the mass of the magnetic ion is less than that of the non‐magnetic ion, or the mass of magnetic ion and the non‐magnetic ion are equal.     

Raman scattering study of the phase sequence in A2BX4 halides

Raman spectra of Cs₂ZnI₄ single crystal have been measured in different scattering orientations covering the successive phase transitions down to 68 K. Two second order anomalies at around ice temperature (270 K) and at ～ 92 K are observed. The anomaly around ice temperature exhibits the features of a normal-incommensurate transition evidenced by softening of a low-lying lattice phonon whose frequency decreases as the transition temperature is approached from below whereas the latter one appears to arise from usual structural distortions.     

First-Principles Prediction of High-Pressure Phase of CaC6

The lattice dynamics of rhombohedral GaG6 is studied as a function orpressure to probe Its high pressure phase with low superconducting transition temperature using the density functional liner-response theory. The pressureinduced phase transition in CaC6 is attributable to the softening transverse acoustic （TA） phonon mode at the zone boundary X （0.5, 0.0, 0.5） point. The high pressure phase is then explored by performing fully structural optimization in the supercell which accommodates the atomic displacements corresponding to the eigenvectors of the unstable mode of TA（X）. The high-pressure phase is predicted to be a monoclinic unit cell with space group P21/m.     

Direct observation of melted Mott state evidenced from Raman scattering in 1T-TaS_2 single crystal

The evolution of electron correlation and charge density wave(CDW)in 1T-TaS_2 single crystal has been investigated by temperature-dependent Raman scattering,which undergoes two obvious peaks of A_(1g) modes about 70.8 cm~(-1) and 78.7 cm~(-1) at 80 K,respectively.The former peak at 70.8 cm~(-1) is accordant with the lower Hubbard band,resulting in the electron-correlation-driven Mott transition.Strikingly,the latter peak at 78.7 cm~(-1) shifts toward low energy with increasing the temperature,demonstrating the occurrence of nearly commensurate CDW phase(melted Mott phase).In this case,phonon transmission could be strongly coupled to commensurate CDW lattice via Coulomb interaction,which likely induces appearance of hexagonal domains suspended in an interdomain phase,composing the melted Mott phase characterized by a shallow electron pocket.Combining electronic structure,atomic structure,transport properties with Raman scattering,these findings provide a novel dimension in understanding the relationship between electronic correlation,charge order,and phonon dynamics.     

Behaviour of electrical resistivity and elastic constants at the phase transition in Ge0.08Sn0.92Te

Electrical resistivity and ultrasonic wave velocity measurements made through the phase transition in Ge_0.08Sn_0.92Te crystals provide further evidence that the acoustic anomaly is due to interaction between the softening optic phonon mode and the acoustic modes at the zone centre.     

金刚石氮-空位色心的原子自旋声子耦合机理

金刚石氮-空位色心结构因在量子精密测量领域的高灵敏度优势而备受关注.本文引入耦合声子场对氮-空位色心原子自旋进行共振调控,以提高氮-空位色心的自旋跃迁效率.首先,基于波函数和晶格的点阵位移矢量关系,分析了声子与晶格能量交互作用,研究了基于声子共振调控的氮-空位色心的自旋跃迁机理,建立了基于应变诱导的能量转移声子-自旋交互耦合激发模型.其次,基于氮-空位色心晶格振动理论,引入满足布洛赫定理的系数矩阵,建立了不同轴向氮-空位色心第一布里渊区特征区域的声子谱模型.同时,基于德拜模型,考虑热膨胀效应,解析该声子共振系统的声子热平衡性质,并对其比热模型进行研究.最后,基于分子动力学仿真软件CASTEP和密度泛函理论进行第一性原理研究,构建了声子模式下不同轴向氮-空位色心的结构优化模型,并分析了其结构特性、声子特性和热力学特性.研究结果表明,系统声子模式的演化依赖于氮-空位的占位,声子模式强化伴随着热力学熵的降低.含氮-空位色心金刚石的共价键较纯净无缺陷金刚石更弱,热力学性质更不稳定.含氮-空位色心金刚石的声子主共振频段处于THz量级,次共振频率约为[800,1200]MHz.根据次共振频段设计叉指宽度为1.5μm的声表面波共振机构,其中心频率约为930 MHz.在该声子共振调控参数条件下,声子共振调控方法可有效增大氮-空位色心的自旋跃迁概率,实现氮-空位色心原子自旋操控效率的提高.     

多层交替介质中电子-SO声子的耦合函数和色散关系

本文根据Wendler,潘金声提出的双层介电系统的电子-声子相互作用理论,推导了具有对称结构的多层交替介质的电子与SO声子的耦合函数和SO声子的色散关系,并以GaAs-Ga1-xAlxAs介质为例做了数值计算.     

N型4H-SiC低温拉曼光谱特性

利用拉曼散射技术对N型4H-SiC单晶材料进行了30～300 K温度范围的光谱测量。实验结果表明,随着温度的升高,N型4H-SiC单晶材料的拉曼峰峰位向低波数方向移动,峰宽逐渐增宽。分析认为,晶格振动随着温度的升高而随之加剧,其振动恢复力会逐渐减小,使振动频率降低;原子相对运动会随温度的升高而加剧,使得原子之间及晶胞之间的相互作用减弱,致使声学模和光学模皆出现红移现象。随着温度的升高,峰宽逐渐增宽。这是由于随着温度的升高声子数逐渐增加,增加的声子进一步增加了散射概率,从而降低了声子的平均寿命,而声子的平均寿命与峰宽成反比,因此随着温度的升高峰宽逐渐增宽。声子模强度随温度升高呈现不同规律,E₂(LA),E₂(TA),E₁(TA)和A₁(LA)声子模随着温度升高强度单调增加,而E₂(TO),E₁(TO)和A₁(LO)声子模强度出现了先增后减的明显变化,在138 K强度出现极大值。分析认为造成原因是由于当温度高于138 K时,高能量的声子分裂成多个具有更低能量的声子所致。     

Electronic structure and lattice dynamics of Li2Ni(WO4)2

We combined spectroscopic ellipsometry and Raman scattering measurements to explore the electronic structure and lattice dynamics in Li₂Ni(WO₄)₂. The optical absorption spectrum of Li₂Ni(WO₄)₂ measured at room temperature presents a direct optical band gap at 2.25 eV and two bands near 5.2 and 6.0 eV, which are attributed to charge-transfer transitions from oxygen 2p states to nickel 3d or tungsten 5p states. The Raman scattering spectrum of Li₂Ni(WO₄)₂ measured at room temperature presents seventeen phonon modes at approximately 112, 143, 193, 222, 267, 283, 312, 352, 387, 418, 451, 476, 554, 617, 754, 792, and 914 cm⁻¹. When the temperature is decreased to 20 K, the frequency, linewidth, and normalized intensity of all phonon modes exhibited almost no temperature dependence. Upon cooling across 13 K, which is the antiferromagnetic phase transition temperature, the oxygen octahedra stretching mode at 914 cm⁻¹ exhibited a softening and an increase in intensity, thus suggesting a coupling between the magnetic and lattice degrees of freedom. The spin-phonon coupling constant was estimated to be 0.94 mRy/Ų, indicating a weak spin-phonon interaction in Li₂Ni(WO₄)₂.     

Peierls-Fröhlich instability and Kohn anomaly

A mathematical basis is given to the Peierls-Fröhlich instability and the Kohn anomaly. The techniques and ideas are based on the recently developed mathematical theory of quantum fluctuations and response theory. We prove that there exists a unique resonant one-mode interaction between electrons and phonons which is responsible for the Peierls-Fröhlich instability and the phase transition in the Mattis-Langer model. We prove also that the softening of this phonon mode at the critical temperature (Kohn anomaly) is a consequence of the critical slowing down of the dynamics of the lattice distortion fluctuations. It is the result of the linear dependence of two fluctuation operators corresponding to the frozen charge density wave and the distortion order parameter.     

Spin-phonon coupling in highly correlated transition-metal monoxides

We report on the optical response of the highly correlated transition-metal monoxides MnO, FeO, CoO and NiO in the far-infrared regime. The main focus is put on spin-phonon coupling effects, which are found to significantly influence the lattice dynamics in the magnetically ordered phase. Measurements have been performed in the ordered and paramagnetic state for temperatures up to 550 K. A clear splitting of the cubic mode accompanying the transition into long range magnetic order can be identified in MnO, CoO and NiO. In the case of FeO it is argued that an anisotropic phonon response seems to be very likely, though it could not be observed directly. The results are compared to recent experimental and theoretical studies in frustrated magnets, which predict the splitting of zone center phonon modes induced by a non-cubic spin-density distribution.     

Experimental Observation of Phase Transition in Sb203 under High Pressure

The in situ high-pressure behavior of the semiconductor antimony trioxide(Sb_2O_s) is investigated by the Raman spectroscopy techniques and angle-dispersive synchrotron x-ray powder diffraction in a diamond anvil cell up to31.5 and 30.7 GPa,respectively.New peaks observed in the external lattice mode range in the Raman spectra at 13.5 GPa suggest that the structural phase transition occurs.The group mode(140 cm~(-1)) in Sb_2O_3 exhibits anomalous pressure dependence;that is,the frequency decreases gradually with the increasing pressure.High pressure synchrotron x-ray diffraction measurements at room temperature reveal that the transition from the orthorhombic structure to high-pressure new phase occurs at about 14.2 GPa,corresponding to the softening of the group optic mode(140 cm~(-1)).     

Size dependence of surface optical mode and electron–phonon coupling in ZnO nanocombs

ZnO nanocombs with different sizes are synthesized by simple thermal evaporation methods. Scanning electron microscopy and transmission election microscopy testify the growth of single crystal ZnO nanocombs along [0 0 0 2] direction. The temperature-dependent Raman spectra show that the intensity of surface optical (SO) modes in ZnO nanocombs obviously increases with declining measure temperatures. With the decrease of diameters, the frequency of SO modes shows a blue shift due to the passivation of surface states. The resonant Raman scattering shows that the strength of electron–phonon coupling increases with decreasing size. Calculated on size-dependent electron–phonon interaction energy agrees well with measured values for a large size range. The origin of electron–phonon coupling in ZnO nanocombs is also discussed.