Temperature- and x-dependent Raman scattering studies of the charge density wave (CDW) amplitude modes in CuxTiSe2 show that the amplitude mode frequency omega_o exhibits identical power-law scaling with the reduced temperature, T/T_CDW, and the reduced Cu content, x/x_c, i.e., omega_o ~ (1 - p)^0.15 for p = T/T_CDW or x/x_c, suggesting that mode softening is independent of the control parameter used to approach the CDW transition. We provide evidence that x-dependent mode softening in CuxTiSe2 is caused by the reduction of the electron-phonon coupling constant lambda due to expansion of the lattice, and that x-dependent `quantum' (T ~ 0) mode softening reveals a quantum critical point within the superconductor phase of CuxTiSe2.
1T-TiSe2 is one of the most studied charge density wave (CDW) systems, not only because of its peculiar properties related to the CDW transition, but also due to its status as a promising candidate of exciton insulator signaled by the proposed plasmon softening at the CDW wave vector. Using high-resolution electron energy loss spectroscopy, we report a systematic study of the temperature-dependent plasmon behaviors of 1T-TiSe2. We unambiguously resolve the plasmon from phonon modes, revealing the existence of Landau damping to the plasmon at finite momentums, which does not support the plasmon…
We report a Raman scattering study of low-temperature, pressure-induced melting of the CDW phase of 1T-TiSe2. Our Raman scattering measurements reveal that the collapse of the CDW state occurs in three stages: (i) For P<5 kbar, the pressure dependence of the CDW amplitude mode energies and intensities are indicative of a ``crystalline'' CDW regime; (ii) for 5 < P < 25 kbar, there is a decrease in the CDW amplitude mode energies and intensities with increasing pressure that suggests a regime in which the CDW softens, and may decouple from the lattice; and (iii) for P>25 kbar, the absence of amp…
TiSe2 is a member of transition metal dichalcogenide family of layered van-der-Waals materials that exhibits some distinctive electronic and optical properties. Here, we perform Raman spectroscopy studies on single crystal TiSe2 to investigate photon-induced defects associated with formation of selenium vacancies. Two additional Eg phonon peaks are observed in the laser-irradiated regions, consistent with Raman spectra of selenium deficient TiSe2. Temperature dependent studies of the threshold laser intensity necessary to form selenium vacancies show that there is a linear dependence. We extra…
The evolution of the charge carrier concentrations and mobilities are examined across the charge-density-wave (CDW) transition in TiSe2. Combined quantum oscillation and magnetotransport measurements show that a small electron pocket dominates the electronic properties at low temperatures whilst an electron and hole pocket contribute at room temperature. At the CDW transition, an abrupt Fermi surface reconstruction and a minimum in the electron and hole mobilities are extracted from two-band and Kohler analysis of magnetotransport measurements. The minimum in the mobilities is associated with …
We report high-resolution inelastic x-ray measurements of the soft phonon mode in the charge-density-wave compound TiSe$_2$. We observe a complete softening of a transverse optic phonon at the L point, i.e. q = (0.5, 0, 0.5), at T ~ T_{CDW}. Renormalized phonon energies are observed over a large wavevector range $(0.3, 0, 0.5) \le \mathbf{q} \le (0.5, 0, 0.5)$. Detailed ab-initio calculations for the electronic and lattice dynamical properties of TiSe2 are in quantitative agreement with experimental frequencies for the phonon branch involving the soft mode. The observed broad range of renormal…
We have employed high resolution angle resolved photoemission spectroscopy (ARPES) measurements to investigate many-body renormalizations of the single-particle excitations in $1T$-TiSe$_2$. The energy distribution curves of the ARPES data reveal intrinsic peak-dip-hump feature, while the electronic dispersion derived from the momentum distribution curves of the data highlights, for the first time, multiple kink structures. These are canonical signatures of a coupling between the electronic degrees of freedom and some Bosonic mode in the system. We demonstrate this using a model calculation of…
The complex coupling between charge carriers and phonons is responsible for diverse phenomena in condensed matter. We apply ultrafast electron diffuse scattering to unravel electron-phonon coupling phenomena in 1T-TiSe$_2$ in both momentum and time. We are able to distinguish effects due to the real part of the many-body bare electronic susceptibility, $\Re\left[χ_0(\mathbf{q})\right]$, from those due to the electron-phonon coupling vertex, $g_{\mathbf{q}}$, by following the response of semi-metallic (normal phase) 1T-TiSe$_2$ to the selective photo-doping of carriers into the electron pocket …
Exciton condensation indicating the spontaneous formation of electron-hole pair can cause the phase transition from a semimetal to an excitonic insulator by gap opening at the Fermi surface. While the idea of this excitonic insulator has been proposed for decades, current theoretical approaches can only provide qualitative descriptions, and a quantitative predicting tool is still missing. To shed insight on this problem, we developed an $ab~initio$ method based on the finite-temperature density functional theory and many-body perturbation theory to compute the exciton condensation critical beh…
Polarized Raman scattering measurements have been performed on Na0.5CoO2 single crystal from 8 to 305 K. Both the A1g and E1g phonon modes show a softening below Tc1 ~ 83 K. Additionally, the A1g phonon mode, which is forbidden in the scattering geometry of cross polarization for the triangular CoO2 layers, appears below Tc1. In contrast, the metal-insulator transition at Tc2 ~ 46 K has only secondary effect on the Raman spectra. The phonon softening and the ``forbidden'' Raman intensity follow closely magnetic order parameter and the gap function at the Fermi surface, indicating that the dist…
We investigate the microscopic mechanisms of the charge-density-wave (CDW) formation in a monolayer TiSe$_2$ using a realistic multiorbital $d$-$p$ model with electron-phonon coupling and intersite Coulomb (excitonic) interactions. First, we estimate the tight-binding bands of Ti $3d$ and Se $4p$ orbitals in the monolayer TiSe$_2$ on the basis of the first-principles band structure calculations. We thereby show orbital textures of the undistorted band structure near the Fermi level. Next, we derive the electron-phonon coupling using the tight-binding approximation and show that the softening o…
Temperature-dependent Raman spectra of TbMnO$_3$ from 5 K to 300 K in the spectral range of 200 to 1525 cm$^{-1}$ show five first-order Raman allowed modes and two high frequency modes. The intensity ratio of the high frequency Raman band to the corresponding first order Raman mode is nearly constant and high ($\sim$ 0.6) at all temperatures, suggesting a orbiton-phonon mixed nature of the high frequency mode. One of the first order phonon modes shows anomalous softening below T$_N$ ($\sim$ 46 K), suggesting a strong spin-phonon coupling.
Giant softening by 30 cm$^{-1}$ of the 490- and 620-cm$^{-1}$ modes is observed by Raman scattering measurements below the Curie temperature of single crystalline LaMnO$_{3+δ}$ ($0.085\leq δ\leq0.125$). A pseudogap-like electronic continuum and a Fano antiresonance at 144 cm$^{-1}$ appear below the charge ordering temperature. This gives evidence for the presence of an orbital fluctuating state and the formation of a hole stripe, respectively. This is further corroborated by a unstructured broadening and shifting of multiphonon features with increasing doping $δ$. Our study suggests the signif…
We report high pressure Raman experiments of Black phosphorus up to 24 GPa. The line widths of first order Raman modes A$^1_g$, B$_{2g}$ and A$^2_g$ of the orthorhombic phase show a minimum at 1.1 GPa. Our first-principles density functional analysis reveals that this is associated with the anomalies in electron-phonon coupling at the semiconductor to topological insulator transition through inversion of valence and conduction bands marking a change from trivial to nontrivial electronic topology. The frequencies of B$_{2g}$ and A$^2_g$ modes become anomalous in the rhombohedral phase at 7.4 GP…
Micro-Raman spectroscopy has been used to study lattice dynamics associated with the ferroelectric domains of a BiFeO$_3$ single crystal at low temperature. The phonon assignment shows a large frequency splitting between the transverse and longitudinal components of the A$_1$ phonon mode related to the Bi-O bonds in contrast with thin films where the splitting is negligible. Applying an external electric field induces frequency shifts of the low energy modes related to the Bi-O bonds. These softenings are due to a tensile stress via the piezoelectric effect. We give estimates of the phonon def…
We investigated the temperature-dependence of the Raman spectra of a nine-layer BaRuO$_3$ single crystal and a four-layer BaRuO$_3$ epitaxial film, which show pseudogap formations in their metallic states. From the polarized and depolarized spectra, the observed phonon modes are assigned properly according to the predictions of group theory analysis. In both compounds, with decreasing temperature, while $A_{1g}$ modes show a strong hardening, $E_g$ (or $E_{2g}$) modes experience a softening or no significant shift. Their different temperature-dependent behaviors could be related to a direct Ru…
The temperature dependence of phonon excitations and the presence of spin phonon coupling in polycrystalline Pr2NiMnO6 samples were studied using micro-Raman spectroscopy and magnetometry. Magnetic properties show a single ferromagnetic-to-paramagnetic transition at 228 K and a saturation magnetization close to 4.95 \muB/f.u.. Three distinct Raman modes at 657, 642, and 511 cm-1 are observed. The phonon excitations show a clear hardening due to anharmonicity from 300 K down to 10 K. Further, temperature dependence of the 657 cm-1 mode shows only a small softening. This reflects the presence of…
We study the polarization-dependent electronic Raman response of untwinned YBa$_2$Cu$_3$O$_{7-δ}$ superconductors employing a tight-binding band structure with anisotropic hopping matrix parameters and a superconducting gap with a mixing of $d$- and s-wave symmetry. Using general arguments we find screening terms in the $B^{\}_{1g}$ scattering channel which are required by gauge invariance. As a result, we obtain a small but measurable softening of the pair-breaking peak, whose position has been attributed for a long time to twice the superconducting gap maximum. Furthermore, we predict superc…
Raman spectroscopy is employed to probe directly the soft rotation and tilting modes, which are two primary order parameters predicted in the hybrid improper ferroelectric material Ca$_3$Mn$_2$O$_7$. We observe a giant softening of the 107-cm$^{-1}$ octahedron tilting mode by 26~cm$^{-1}$, on heating through the structural transition from a ferroelectric to paraelectric orthorhombic phase. This is contrasted by a small softening of the 150-cm$^{-1}$ rotational mode by 6~cm$^{-1}$. In the intermediate phase, the competing soft modes with different symmetries coexist, bringing about many-faceted…
We report a Raman study of the effect of temperature on the self-energies of optical phonons in a number of transition metals with hexagonal-close-packed structure. Anisotropic softening of phonon energies and narrowing of phonon linewidths with increasing temperature are observed. These effects are reproduced in the calculations of phonon spectral functions based on \textit{ab initio} electronic structures and with carrier scattering by phonons taken into account. The combined observations and results of simulations indicate a relation between observed anomalies and the renormalization of the…
In the orbitally ordered, quasi-one dimensional Heisenberg antiferromagnet KCuF3 the low-energy Eg and B1g phonon modes show an anomalous softening (25% and 13%) between room temperature and the characteristic temperature T_S = 50 K. In this temperature range a freezing-in of F ion dynamic displacements is proposed to occur. In addition, the Eg mode at about 260 cm-1 clearly splits below T_S. The width of the phonon lines above T_S follows an activated behavior with an activation energy of about 50 K. Our observations clearly evidence a reduction of the structural symmetry below T_S and indica…
We have used a combination of ultrafast coherent phonon spectroscopy, ultrafast thermometry, and time-dependent Landau theory to study the inversion symmetry breaking phase transition at $T_c = 200$ K in the strongly spin-orbit coupled correlated metal Cd$_2$Re$_2$O$_7$. We establish that the structural distortion at $T_c$ is a secondary effect through the absence of any softening of its associated phonon mode, which supports a purely electronically driven mechanism. However, the phonon lifetime exhibits an anomalously strong temperature dependence that decreases linearly to zero near $T_c$. W…
We perform Raman spectroscopy studies on $α$-RuCl$_3$ at room temperature to explore its phase transitions of magnetism and chemical bonding under pressures. The Raman measurements resolve two critical pressures, about $p_1=1.1$~GPa and $p_2=1.7$~GPa, involving very different intertwining behaviors between the structural and magnetic excitations. With increasing pressures, a stacking order phase transition of $α$-RuCl$_3$ layers develops at $p_1=1.1$~GPa, indicated by the new Raman phonon modes and the modest Raman magnetic susceptibility adjustment. The abnormal softening and splitting of the…
Monoclinic semi-metallic Mo$_8$O$_{23}$ belongs to a multifunctional series of compounds showing multiple ordering phenomena that have not achieved much attention till now. Previous X-rays studies of this compound have revealed an incommensurate ordering transition at $T_{\mathrm{IC}}\sim350$ K, followed by a structural transition to commensurate order at $T_{\mathrm{IC-C}}=285$ K. In addition, an enigmatic resistance maximum is observed at $T_{\mathrm{el}}\sim150$ K, whose origin has so far proved elusive. Aiming to disentangle these multiple orders we use the polarized transient optical spec…
In this paper, we present the spin-phonon coupling and dielectric response of nano-crystalline Pr$_2$CoMnO$_6$ employing Raman and dielectric spectroscopic study. Pr$_2$CoMnO$_6$ is a manganite compound , it undergoes a paramagnetic to ferromagnetic (PM-FM) phase transition around $T_c$ $\sim$172 K. Temperature-dependent Raman scattering experiment is carried out across $T_c$ to study the spin-phonon behavior in this material. The results from Raman study reveal an obvious softening of the phonon mode involving stretching vibrations of the (Co/Mn)O$_6$ octahedra in ferromagnetic temperature re…
Electronic structure near Fermi level of Pr2CoFeO6 (at 300 K) was investigated by X-ray photoemission spectroscopy (XPS) technique. All three cations, i.e., Pr, Co and Fe were found to be trivalent in nature. XPS analysis also suggested the system to be insulating in nature. Moreover, Raman spectroscopy study indicated the random distribution of the B-site ions (Co/Fe) triggered by same charge states. In temperature-dependent Raman study, the relative heights of the two observed phonon modes exhibited anomalous behaviour near magnetic transition temperature TN~270 K, thus indicating towards in…
We report temperature-dependent Raman scattering and X-ray diffraction studies of pyrochlore iridates, (Eu$_{1-x}$Bi$_x$)$_2$Ir$_2$O$_7$, for x=0, 0.02, 0.035, 0.05 and 0.1. The temperature variation in Raman experiments spans from 4 K to 300 K, covering the metal-insulator phase transition accompanied by paramagnetic to all-in/all-out (AIAO) spin ordering (T$_N$). These systems also show a Weyl semi-metal (WSM) phase at low temperatures (below ~50 K). We show that the Ir-O-Ir bond bending mode, A$_{1g}$ (510 cm$^{-1}$), shows anomalous softening in the magnetically ordered AIAO state, arising…
Dynamical Response of the Kitaev Spin Liquid under Third-Nearest-Neighbor Heisenberg Interaction
School of Physical Science and Technology, Lanzhou University（兰州大学物理科学与技术学院）；Lanzhou Center for Theoretical Physics, Key Laboratory of Quantum Theory and Applications of MoE, Key Laboratory of Theoretical Physics of Gansu Province, Gansu Provincial Research Center for Basic Disciplines of Quantum Physics, Lanzhou University（兰州大学理论物理中心，教育部量子理论与应用重点实验室，甘肃省理论物理重点实验室，甘肃省量子物理基础学科研究中心）；School of Physics, Hangzhou Normal University（杭州师范大学物理学院）
Hidden phonon-assisted charge density wave transition in BaFe2Al9 revealed by ultrafast optical spectroscopy
Beijing Normal University（北京师范大学）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Institute of Metal Research, Chinese Academy of Sciences（中国科学院金属研究所）
Very recently we revealed a large family of triangular lattice quantum spin liquid candidates named rare-earth chalcogenides, which features a high-symmetry structure without structural/charge disorders and spin impurities, and may serve as an ideal platform exploring spin liquid physics. The knowledge of crystalline electric-field (CEF) excitations is an essential step to explore the fundamental magnetism of rare-earth spin systems. Here we employed inelastic neutron scattering (INS) and Raman scattering (RS) to carry out a comprehensive CFE investigation on $NaYbSe_{2}$, a promising represen…
We report on Raman scattering measurements of the A-site ordered YBaMn2O6 in the wide temperature range of 10-650K. Upon cooling almost all phonon modes show pronounced temperature dependencies of frequency, linewidth, and scattering intensity. This suggests that the octahedra tilting, Mn-O bond angles and lengths vary with temperature in a concerted way. The remarkable feature is that the high-temperature metallic and the charge and orbital ordered (CO-OO) states coexist down to T_N=195K. In the antiferromagnetic state zone-folded modes are induced by the CO-OO superstructure and the phonon m…
Spin Reorientation Driven Renormalization of Spin-Phonon Coupling in Fe$_4$GeTe$_2$
S. N. Bose National Centre for Basic Sciences（S.N. 玻色基础科学国家中心）；Uppsala University（乌普萨拉大学）；Bose Institute（玻色研究所）；Indian Institute of Technology Madras（马德拉斯印度理工学院）；Saha Institute of Nuclear Physics（萨哈核物理研究所）
We measured the temperature dependent infrared reflectivity spectra of MnF2 between 4 K and room temperature. We show that the phonon spectrum undergoes a strong renormalization at TN. The ab-initio calculation we performed on this compound accurately predict the magnitude and the direction of the phonon parameters changes across the antiferromagnetic transition, showing that they are mainly induced by the magnetic order. In this material, we found that the dielectric constant is mostly from phonon origin. The large change in the lattice parameters with temperature seen by X-ray diffraction as…
Structural phase transitions described by Mexican hat potentials should in principle exhibit aspects of Higgs and Goldstone physics. Here, we investigate the relationship between the phonons that soften at such structural phase transitions and the Higgs- and Goldstone-boson analogues associated with the crystallographic Mexican hat potential. We show that, with the exception of systems containing only one atom type, the usual Higgs and Goldstone modes are represented by a combination of several phonon modes, with the lowest energy phonons of the relevant symmetry having substantial contributio…
Effect of an internal chemical pressure on structural, optical, magnetic and electrical properties in Bi0.9RE0.1FeO3 Ceramics (RE =Gd3+,Tb3+,Dy3+)has been studied extensively. Some of the highlights are as follows; 1. Coexistence of orthorhombic Bragg reflections along with the R3c phase.(Structural Phase separation revealed from XRD and Raman spectroscopy) 2. Selective softening of phonon mode corresponding to oxygen motion suggests a significant destabilization in the FeO6 octahedra. 3. Three Charge transfer transitions (Fe1 3d\rightarrow Fe2 3d, Op \rightarrow Fed,Op \rightarrow Bip) and a …
The charge-density wave (CDW) phase is often accompanied by the condensation of a soft acoustic phonon mode, giving rise to lattice distortion and charge density modulation. This picture was challenged for the recently discovered kagome metal CsV$_3$Sb$_5$, based on the evidence of absence of soft phonons. Here we report the observation of Raman-active CDW amplitude modes in this material, which are collective excitations typically thought to emerge out of frozen soft phonons. The amplitude modes strongly hybridize with other superlattice modes, imparting them with clear temperature-dependent …
Interplay of Charge and Magnetic Orders in SmNiC$_2$ Mediated by Electron-Phonon Interaction
Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院量子材料与技术研究所）；Karlsruhe Nano Micro Facility (KNMFi), Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院卡尔斯鲁厄纳米显微设施）；ESRF – The European Synchrotron（欧洲同步辐射装置）
