Raman Tensor Research Articles

Comparative Raman spectroscopy of magnetic topological material EuCd2X2 (X = P, As)

EuCd2X2 (X = P, As) is a new class of magnetic topological materials discovered recently. The electronic structure and the band topology are intimately coupled with its magnetism, giving rise to interesting properties such as spin fluctuation and colossal magnetoresistance. Phonon excitation can contribute to the quasi-particle response of the topological matters through spin-lattice and electron–phonon coupling. However, the phonon properties of this material family remain unexplored. Here we report a comparative study of Raman-active vibration modes in EuCd2X2 (X = P, As) by means of angle-resolved, temperature-resolved, and magnetic-field-resolved Raman spectroscopy together with the first-principle calculations and Raman tensor analysis. The phonon properties can be tuned by chemical potential and temperature within the material family. All the phonon modes are softened with increased chemical pressure by replacing P with As. Angle-resolved polarized Raman spectroscopy reveals the configuration-sensitive Raman activity and the isotropic intensity response. In addition, the magneto-Raman spectrum indicates the stability of Raman-active vibration modes against the magnetic field at room temperature. Our work sheds light on the phonon dynamics of magnetic topological matters, which are potentially coupled with the topological charge and spin excitation.

Polarized Raman Scattering of In‐Plane Anisotropic Phonon Modes in α‑MoO3

AbstractThe recent discovery of in‐plane hyperbolic phonon polaritons in biaxial polar crystal—α‐MoO3, has aroused a huge research upsurge on anisotropic photonic quasiparticles in van der Waals materials. The physical origin of these highly anisotropic phonon polaritons is attributed to the strong anisotropy of crystal phonons. However, the orientation‐dependent phonon modes have not been fully understood from crystallographic point of view. This work systematically performs in situ angle‐resolved polarized Raman spectroscopy on α‐MoO3 to investigate its anisotropic photo‐phonon interactions. The sample orientation and Raman tensors are unambiguously determined under different polarization configurations. Specifically, the in‐plane anisotropic phonon modes of α‐MoO3 can be well characterized from the highly polarization‐dependent Raman‐active modes with periodic intensity variation. It can be concluded that these findings cannot only offer a better understanding of anisotropic phonon modes in α‐MoO3, but also provide a valuable reference for other anisotropic van der Waals crystals.

Nonlocal nonlinear phononics

Nonlinear phononics relies on the resonant optical excitation of infrared-active lattice vibrations to induce targeted structural deformations in solids. This form of dynamical crystal structure design has been applied to control the functional properties of many complex solids, including magnetic materials, superconductors and ferroelectrics. However, phononics has so far been restricted to protocols in which structural deformations occur within the optically excited volume, sometimes resulting in unwanted heating. Here, we extend nonlinear phononics to propagating polaritons, spatially separating the functional response from the optical drive. We use mid-infrared optical pulses to resonantly drive a phonon at the surface of ferroelectric LiNbO3. Time-resolved stimulated Raman scattering reveals that the ferroelectric polarization is reduced over the entire 50 µm depth of the sample, far beyond the micrometre depth of the evanescent phonon field. We attribute this effect to the anharmonic coupling between the driven mode and a polariton that propagates into the material. For high excitation amplitudes, we reach a regime in which the ferroelectric polarization is reversed, as revealed by a sign change in the Raman tensor coefficients of all the polar modes.

New selection rule of resonant Raman scattering in MoS2 monolayer under circular polarization

• The first-order resonant Raman spectra of monolayer MoS2 under the circularly polarized photoexcitation is re-visited based on the first-principles density functional theory calculation. • The anomalous selection rule for the two-dimensional mode appears under high-energy laser excitation, revealing a certain correlation with valley selectivity of helical optical absorption. • The Raman anomaly can also be understood from the calculated Raman tensor, and supports the pseudo-angular-momentum conservation law. • This study may shed a light on the new understanding of the unconventional phenomenon and help new functional design for applications in helicity related optoelectronics. The first-order resonant Raman spectra of monolayer MoS 2 are calculated under the circularly polarized photoexcitation. The anomalously nonzero Raman intensity of the in-plane E mode under the Z ¯ ( σ + σ + ) Z or Z ¯ ( σ − σ − ) Z geometry, which goes against the conventional selection rule, appears under some circumstances when optical absorption occurs at some special reciprocal points between the zone-center Γ and the zone-edge-center M points. At that moment, the valley selectivity to the circular polarization is lifted. The analysis shows that the anomalous Raman intensity of the E mode for the same circularly polarized incident and scattered light is consistent with the pseudo-angular-momentum conservation law. The calculated E Raman tensor of monolayer MoS 2 is found to vary with laser energy. The two diagonal terms of the Raman tensor change their signs from mutually opposite to the same when the relative intensity of the in-plane E mode to the out-of-plane A 1 ′ mode increases, indicating the increasingly important role played by the Frölich-type electron-phonon interaction over the deformation potential. Our study may shed new light on the understanding of the novel electron-photon process and assist in the design of new type of optoelectronic devices.

Complex Raman Tensor in Helicity-Changing Raman Spectra of Black Phosphorus under Circularly Polarized Light.

In anisotropic two-dimensional materials, complex values of Raman tensors are necessary to explain the abnormal linearly polarized Raman spectra. In this work, we measured the helicity-changing Raman spectra of few-layer black phosphorus (BP) excited by circularly polarized light. We observed that the polarized Raman intensities of the Ag modes show a deflection angle that depends on the sample orientation, thickness, and laser excitation energy. To understand the deflection, we calculated the resonant Raman spectra by first-principles calculations, which give complex Raman tensors as a function of laser excitation energy. In particular, the phase difference between the elements of the complex Raman tensor is relevant to the deflection angle. The calculated results of monolayer BP reproduce the experimental helicity-resolved Raman spectra of few-layer BP satisfactorily.

Mapping blood biochemistry by Raman spectroscopy at the cellular level.

We report how Raman difference imaging provides insight on cellular biochemistry in vivo as a function of sub-cellular dimensions and the cellular environment. We show that this approach offers a sensitive diagnostic to address blood biochemistry at the cellular level. We examine Raman microscopic images of the distribution of the different hemoglobins in both healthy (discocyte) and unhealthy (echinocyte) blood cells and interpret these images using pre-calculated, accurate pre-resonant Raman tensors for scattering intensities specific to hemoglobins. These tensors are developed from theoretical calculations of models of the oxy, deoxy and met forms of heme benchmarked against the experimental visible spectra of the corresponding hemoglobins. The calculations also enable assignments of the electronic transitions responsible for the colour of blood: these are mainly ligand to metal charge transfer transitions.

Raman tensor of zinc-phosphide (Zn3P2): from polarization measurements to simulation of Raman spectra.

Zinc phosphide (Zn3P2) is a II–V compound semiconductor with promising photovoltaic and thermoelectric applications. Its complex structure is susceptible to facile defect formation, which plays a key role in further optimization of the material. Raman spectroscopy can be effectively used for defect characterization. However, the Raman tensor of Zn3P2, which determines the intensity of Raman peaks and anisotropy of inelastic light scattering, is still unknown. In this paper, we use angle-resolved polarization Raman measurements on stoichiometric monocrystalline Zn3P2 thin films to obtain the Raman tensor of Zn3P2. This has allowed determination of the Raman tensor elements characteristic for the A1g, B1g and B2g vibrational modes. These results have been compared with the theoretically obtained Raman tensor elements and simulated Raman spectra from the lattice-dynamics calculations using first-principles force constants. Excellent agreement is found between the experimental and simulated Raman spectra of Zn3P2 for various polarization configurations, providing a platform for future characterization of the defects in this material.

Peculiar behavior of the ester carbonyl vibrational modes in anisotropic aliphatic and semi-aromatic polyesters

The current work reports on a systematic study related to the vibrational modes of the ester carbonyl group in drawn polyesters. We have observed and try to explain how the presence of aromatic units in the molecular structure substantially affects the respective elements of the Raman tensor in contrast to the dipole moment derivative vector which is only marginally influenced. The work is based on the collection of polarized Raman spectra and FTIR dichroism measurements on the one hand and on DFT calculations on the other. The experimental data were obtained from uniaxially stretched aliphatic and semi-aromatic polyesters. The calculations were applied on relevant oriented oligomers and allowed the extraction: (i) of reliable Raman/FTIR vibrational spectra and (ii) the components of the dipole moment derivative and Raman tensor of the vibrational modes and in particular the ones involving the ester carbonyl group. Experimental data indicate that the intensity of the ester carbonyl band is considerably enhanced in the Raman spectra of semi-aromatic polyesters, which results from a considerable enhancement of the related coupling coefficient. Furthermore, the angles of the principle Raman tensor axis are rotated so that the element of the tensor with the greatest value is oriented towards the direction designated by the segment. The latter explains the peculiar experimentally indicated anisotropy, through the ester carbonyl stretching, for the case of semi-aromatic polyesters, which is totally different with that observed in the aliphatic ones.

Correction to “Symmetric Raman Tensor Contributes to Chiral Vibrational Sum Frequency Generation from Binaphthyl Amphiphile Monolayers on Water: Study of Electronic Resonance Amplitude and Phase Profiles”

Correction to “Symmetric Raman Tensor Contributes to Chiral Vibrational Sum Frequency Generation from Binaphthyl Amphiphile Monolayers on Water: Study of Electronic Resonance Amplitude and Phase Profiles”

Thickness-dependent in-plane anisotropy of GaTe phonons

Gallium Telluride (GaTe), a layered material with monoclinic crystal structure, has recently attracted a lot of attention due to its unique physical properties and potential applications for angle-resolved photonics and electronics, where optical anisotropies are important. Despite a few reports on the in-plane anisotropies of GaTe, a comprehensive understanding of them remained unsatisfactory to date. In this work, we investigated thickness-dependent in-plane anisotropies of the 13 Raman-active modes and one Raman-inactive mode of GaTe by using angle-resolved polarized Raman spectroscopy, under both parallel and perpendicular polarization configurations in the spectral range from 20 to 300 cm−1. Raman modes of GaTe revealed distinctly different thickness-dependent anisotropies in parallel polarization configuration while nearly unchanged for the perpendicular configuration. Especially, three Ag modes at 40.2 ({text{A}}_{text{g}}^{1}), 152.5 ({text{A}}_{text{g}}^{7}), and 283.8 ({text{A}}_{text{g}}^{12}) cm−1 exhibited an evident variation in anisotropic behavior as decreasing thickness down to 9 nm. The observed anisotropies were thoroughly explained by adopting the calculated interference effect and the semiclassical complex Raman tensor analysis.

Tracing microscopic atomic displacements using polarized Raman spectroscopy: a case study on BaTiO3

Here, we demonstrate the power of polarized Raman spectroscopy (PRS) in tracing microscopic atomic displacements in a single crystalline material. Crystalline materials often show extremely small microscopic atomic displacements as a function of temperature, pressure, electric and magnetic field or across phase transition which can be traced by our defined method using routinely available Raman spectrometers and with the knowledge of Raman tensors and phonon deformation potentials. Importantly, the information is directional and provides a vital information about the root cause of polarization in ferroelectrics, multiferroics. In this article, the method is demonstrated by carrying out the temperature and directional dependent PRS study on BaTiO3 single crystal, where the Ti ion displacement across the various phase transitions is well documented. The value of the ferroelectric polarization and its component along different crystallographic axes as well as their temperature variations calculated from the Ti displacement obtained by our defined method matches well with the reported results obtained from other techniques. This method thus can be applied to obtain quantitative information of atomic displacements in a crystalline solid.

Effects of dimensionality and excitation energy on the Raman tensors of triclinic ReSe2

AbstractIn this work, we present measurements of angle‐resolved polarized Raman spectra of single‐layer (1L) and bulk ReSe2 recorded with excitation energies of 1.92 eV (647.1 nm) and 2.34 eV (530.8 nm). The Raman tensors for all modes were obtained by fitting simultaneously the angular dependence of the parallel (I‖) and crossed (I⊥) polarized intensities. We observed that the tensor elements are, in general, complex numbers, and their magnitudes and phases depend on both the dimensionality of the sample (1L or bulk) and the excitation energy. Results are discussed by considering the intrinsic contribution of a single layer to the tensor elements and the macroscopic contribution coming from the stacking of several layers. We show that the different behaviour of angle‐resolved polarized Raman spectra for different excitation energies is due to the resonant Raman effect, which affects both the real and imaginary parts of the Raman tensor elements. Our work highlights the importance of understanding the fundamental physics of low symmetry 2D materials that can be used to fabricate devices sensitive to the direction of light polarization or electrical current.

Raman tensor determination of transparent uniaxial crystals and their thin films—a-plane GaN as exemplary case

The classical Raman tensor approach does not work for optically anisotropic materials in general. For the transparency regime, this can be circumvented by using an effective Raman tensor that considers the material's birefringence. In the specific case of an uniaxial crystal with in-plane orientation of principal axis, this effective Raman tensor is similar to the classical one, except for an additional phase factor for each tensor element. This phase is dependent on the sample thickness, which is demonstrated here experimentally via polarization resolved Raman scattering of a-plane GaN thin films. The experimental observations coincide very well with our model predictions.

Raman tensor of graphite: Symmetry of G, D and D′ phonons

自石墨的拉曼光谱在1970年被首次记录以来, 其拉曼特征峰G、D和D′峰)背后的物理起源一直是人们争论的焦点. 目前, 人们普遍认为G峰对应于拉曼活性E2g2模式, D和D′峰则是与缺陷有关的无序诱发峰. 然而, 到目前为止, 这些石墨拉曼峰所对应的声子对称性, 还缺乏细致的研究与直接的实验证据. 在这里, 我们利用角分辨偏振拉曼光谱对这些重要方面进行了阐述. 结果表明, D、D′峰的实验拉曼强度与G峰的偏振角关系相似. 结合拉曼张量分析和双共振机制, 我们进一步了解了D′和D峰的声子对称性. 我们的工作为石墨声子对称性提供了可靠的实验证据和合理的解释.

Polarized Raman Spectroscopy for Determining Crystallographic Orientation of Low-Dimensional Materials.

Raman spectroscopy is a fast and nondestructive characterization technique, which has been widely used for the characterization of the composition and structure information of various materials. The symmetry-dependent Raman tensor allows the detection of crystallographic orientation of materials by using polarization information. In this Perspective, we discuss polarized Raman spectroscopy as a powerful tool for determination of the crystallographic orientation of various materials. First, we introduce the basic principles of polarized Raman spectroscopy and the corresponding experimental setups; the determination of crystallographic orientation of two-dimensional (2D) materials with in-plane isotropy and in-plane anisotropy using linearly polarized Raman scattering are then discussed. Furthermore, we discuss that using circularly polarized Raman spectroscopy, the azimuthal angle of materials in three dimensions (3D) can be characterized. In the final section, we show that the orientation distribution of nanomaterial assemblies can be measured using polarized Raman spectroscopy by introducing the orientation distribution function.

Effect of thickness and stacking order on Raman spectrum of layered CrCl3

Layer- and stacking-dependent physical properties discovered in van der Waals materials have attracted a lot of attention recently. In this work, we have investigated the Raman spectrum of layered magnetic CrCl3 with different atomic thickness and stacking order from first principles. Our study indicates Raman shift of R and C2/m phase is near degenerate except that the first and fourth Raman resonant modes exhibit a marked peak difference about 3 cm−1, which can be understood by stacking-dependent vibrational eigenvectors. Moreover, we also find that both frequency and intensity of Raman modes of few-layer CrCl3 increase with the number of layers simultaneously. Furthermore, the Raman tensor and polarization-dependent Raman intensity are also evaluated in details, which are found to be in good agreement with available experiments. Our results proposed several distinctive signals to identify layer number and stacking order of layered CrCl3, which will provide an important reference to further experimental study.

Ab initio determination of Raman spectra of Mg2SiO4 and Ca2MgSi2O7 showing mixed modes related to LO/TO splitting

AbstractDensity functional theory was used to calculate the nonresonance Raman spectra of forsterite (Mg2SiO4) and åkermanite (Ca2MgSi2O7). The Raman tensors are determined from electric polarizibility using finite difference scheme. The Raman reduced spectra (wavenumbers and intensities) are calculated for several typical polarized light scattering geometries for single crystal and polycrystals, demonstrating good agreement with existing published data. In åkermanite, special attention is paid to B2 and E symmetry phonon modes, which exhibit simultaneous infrared and Raman activities, labeled as mixed representations, and are involved in the longitudinal optic (LO)/transverse optic (TO) splitting. Close to zone‐center point, the phonon dispersion curves of mixed modes are analyzed in details, showing for example that mixed modes repulse each other.

Anisotropic Generation and Detection of Coherent Ag Phonons in Black Phosphorus.

Black phosphorus (BP) has attracted great attention due to its layer-tuned direct bandgap, in-plane anisotropic properties, and novel optoelectronic applications. In this work, the anisotropic characteristics of BP crystal in terms of the Raman tensor and birefringence are studied by investigating polarization dependence in both the generation and detection of Ag mode coherent phonons. While the generated coherent phonons exhibit the typical linear dichroism of BP crystal, the detection process is found here to be influenced by anisotropic multiple thin film interference, showing wavelength and sample thickness sensitive behaviors. We additionally find that the Ag1 and Ag2 optical phonons decay into lower frequency acoustic phonons through the temperature-dependent anharmonic process.

A Raman probe of phonons and electron\u2013phonon interactions in the Weyl semimetal NbIrTe4

There is tremendous interest in measuring the strong electron–phonon interactions seen in topological Weyl semimetals. The semimetal NbIrTe4 has been proposed to be a Type-II Weyl semimetal with 8 pairs of opposite Chirality Weyl nodes which are very close to the Fermi energy. We show using polarized angular-resolved micro-Raman scattering at two excitation energies that we can extract the phonon mode dependence of the Raman tensor elements from the shape of the scattering efficiency versus angle. This van der Waals semimetal with broken inversion symmetry and 24 atoms per unit cell has 69 possible phonon modes of which we measure 19 modes with frequencies and symmetries consistent with Density Functional Theory calculations. We show that these tensor elements vary substantially in a small energy range which reflects a strong variation of the electron–phonon coupling for these modes.

The correlation between experimental polarized Raman spectra and their density functional theory prediction in the LCAO framework: The R3c LiNbO3 crystal as a test case

AbstractIn this study, the polarized Raman spectra of the R3c LiNbO3 crystal are used as a benchmark test for density functional theory (DFT) full periodic boundary conditions linear combination of atomic orbitals (LCAO) calculation of the Raman tensors, according to the implementation in the CRYSTAL software. The theoretical approach used proved to provide excellent results regarding wavenumbers and relative intensities predictions for the transverse optical modes of both A1 and E symmetry, considerably improving over previously reported data based on the plane waves approach. Overall, the present investigation demonstrates that the LCAO approach, as implemented in the CRYSTAL software, gives excellent results regarding the calculation of Raman tensors and polarized Raman spectra. The possibility to put in correspondence the individual Raman tensors components and bands intensities in the different back‐scattering experimental configurations revealed that the computed Raman tensors are very accurate, not only considering their average values (tensors invariant in the combination suitable for the description of Raman scattering of isotropic materials) but also when the tensors individual components are considered. Based on the present results, a reassignment of the E (TO) modes of the R3c LiNbO3 crystal is proposed, in particular for the 2 E and 9 E modes, which have been a matter of discussion in the recent years.