Zone-center Phonon Modes Research Articles

Hydrostatic pressure induced structural instability and dielectric property of cubic BaZrO3

Using the first-principle calculations, we investigate in detail the structure instability resulting from softening of the polar zone-center phonon mode [ferroelectric (FE) instability] and nonpolar zone-boundary mode [antiferrodistortive (AFD) instability] in cubic BaZrO3 (BZO) under hydrostatic pressure P from −20 to 90 GPa. The hydrostatic pressure enhances the AFD instability, while it suppresses and then enhances the FE instability. A sequence of FE→cubic→AFD→AFD/FE phase transitions with increasing P is predicted. A careful examination of the pressure dependence of full phonon dispersions and interatomic force constants in real space reveals the microscopic key interactions in driving the transitions. With increasing pressure P, the drastically evolving short-range forces suppress the FE instability induced by the long-range dipole-dipole forces under low pressure, and enhance both the AFD and FE instability under high pressure. We investigate the dielectric properties of cubic BZO under hydrostatic pressure. The dielectric constant as a function of pressure shows a minimum contributed from the TO1 mode with the lowest frequency. We argue that this pressure dependence of the dielectric constant mainly originates from fluctuations of the SR forces.

Response to “Comment on ‘Electronic structure and zone-center phonon modes in multiferroic bulk BiFeO3’ ” [J. Appl. Phys. 105, 036108 (2009)

We agree with the comment made by Hermet et al. on our recent paper [J. Appl. Phys. 103, 083712 (2008)] regarding the zone-center phonon modes in multiferroic bulk BiFeO3. In this reply we show that our correctly assigned modes are in agreement with their results.

Comment on “Electronic structure and zone-center phonon modes in multiferroic bulk BiFeO3” [J. Appl. Phys. 103, 083712 (2008)

In a recent paper, Tütüncü and Srivastava [J. Appl. Phys. 103, 083712 (2008)] report the electronic structure and the assignment of the zone-center phonon modes of the R3c phase of BiFeO3 using the density functional theory. In the present comment, we point out some physical inaccuracies in their mode assignment. We review their interpretation and analyze which conclusions are actually justified.

SrTiO3andBaTiO3revisited using the projector augmented wave method: Performance of hybrid and semilocal functionals

The structural, electronic, and phonon properties of the cubic and tetragonal phase of ${\text{SrTiO}}_{3}$ and ${\text{BaTiO}}_{3}$ are studied from ab initio. The calculations are performed in the projector augmented wave density-functional theory framework using the local density approximation, gradient corrected functionals, and hybrid functional as implemented in the Vienna ab initio simulation package. Due to the large variation of theoretical predictions for the frequency of the ${\ensuremath{\Gamma}}_{15}$ (TO1) zone-center phonon mode $(94i\ensuremath{-}64\text{ }{\text{cm}}^{\ensuremath{-}1})$ special attention is accorded to this particular mode and its volume dependence.

Structural stability and lattice dynamics ofSiO2cristobalite

Among the phases of ${\text{SiO}}_{2}$ are $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ cristobalites, which have a long and somewhat controversial history of proposed structural assignments and phase-transition mechanisms. Recently, Zhang and Scott found new indications that the higher-temperature $\ensuremath{\beta}$ phase has space group $I\overline{4}2d$ and, by assuming a group-subgroup relationship between phases, they argued that the lower-temperature $\ensuremath{\alpha}$ phase should have lower symmetry than that of the widely accepted $P{4}_{1}{2}_{1}2$ space group. With this motivation, we use first-principles calculations to investigate the energy, structure, and local stability of $P{4}_{1}{2}_{1}2$ and $I\overline{4}2d$ structures. We also compute the frequencies of the zone-center phonon modes in both structures, as well as certain zone-boundary modes in the $I\overline{4}2d$ structure, and compare with experiment. We then argue that the various $P{4}_{1}{2}_{1}2$ and $I\overline{4}2d$ enantiomorphs can be grouped into three clusters, each of which is identified with a three-dimensional manifold of structures of $P{2}_{1}{2}_{1}{2}_{1}$ symmetry in which the $P{4}_{1}{2}_{1}2$ and $I\overline{4}2d$ appear as higher-symmetry special cases. We find that there are relatively high energy barriers between manifolds, but low barriers within a manifold. Exploring the energy landscape within one of these manifolds, we find a minimal-energy path connecting $P{4}_{1}{2}_{1}2$ and $I\overline{4}2d$ structures with a surprisingly low barrier of $\ensuremath{\sim}5\text{ }\text{meV}$ per formula unit. Possible implications for the phase-transition mechanism are discussed.

Pressure-induced metallization and resonant Raman scattering in Zn1−xMnxTe

Pressure-induced resonant Raman scattering is adopted to analyze the zone-center optical phonon modes and crystal characteristics of Zn1−xMnxTe (0≦x≦0.26) thin films. The pressure (Pt) at which the semiconducting undergoes a transition to the metallic phase declines as a function of Mn concentration (x) according to the formula Pt(x)=15.7−25.4x+19.0x2 (GPa). Pressure-dependent longitudinal and transverse optical phonon frequencies and the calculated mode Grüneisen parameters were adopted to investigate the influence of Mn2+ ions on the iconicity. The experimental results indicate that the manganese ions tend to increase the iconicity of ZnTe under ambient conditions, whereas an external hydrostatic pressure tends to reduce the iconicity and the bond length of Zn1−xMnxTe.

Electronic structure and zone-center phonon modes in multiferroic bulk BiFeO3

We present ab initio investigations of the electronic structure and zone-center phonon modes in bulk BiFeO3 with rhombohedral R3c symmetry. The electronic structure has been studied using the plane wave pseudopotential method, with electron-electron interaction treated within the local spin density approximation (LSDA), a spin-polarized generalized gradient approximation (σGGA), and the LSDA+U and σGGA+U schemes. It is found that with a reasonable choice of a rotationally invariant value of U both the LSDA+U and σGGA+U schemes produce electronic band gaps in the range of values derived from optical spectroscopy. The computed electronic structure results are utilized to determine the zone-center phonon modes by applying a linear response technique. We provide a clearer analysis of the energy values and polarization characteristics of the Raman active modes than is presently available from theoretical and experimental studies.

First-principles study of the cubic perovskitesBiMO3(M=Al, Ga, In, and Sc)

We systematically investigated the structure, electronic properties, zone-center phonon modes, and structure instability of four cubic perovskite $\mathrm{Bi}M{\mathrm{O}}_{3}$ compounds, with three of the $M$ ions being IIIB metals (Al, Ga, and In) and one IIIA transition-metal Sc, using first-principles density-functional calculations. Optimized lattice parameters, bulk moduli, band structures, densities of states, as well as charge density distributions are calculated and compared with the available theoretical data. Our results are in good agreement with those previously reported in the literature. All the $\mathrm{Bi}M{\mathrm{O}}_{3}$ oxides considered in the present work are semiconductors with an indirect band gap between the occupied $\mathrm{O}\phantom{\rule{0.2em}{0ex}}2p$ and unoccupied $\mathrm{Bi}\phantom{\rule{0.2em}{0ex}}6p$ states varying between 0.17 and $1.57\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. Their electronic properties are determined mainly by Bi--O bonding, which, in turn, depends on the $M--\mathrm{O}$ bonding. Ferroelectric properties of these oxides come from the $6{s}^{2}$ lone pair on the $A$-site Bi ion and is similarly affected by the $M$ ions through their influence on the Bi--O bonding, as suggested by our calculations of density of state, Born effective charge, and soft modes. The existence of soft modes and eight [111] minima suggests that the phase transition in $\mathrm{Bi}\mathrm{Al}{\mathrm{O}}_{3}$ has a mixed displacive and order-disorder character. There is evidence that ferroelectricity is absent in $\mathrm{Bi}\mathrm{Ga}{\mathrm{O}}_{3}$. Our investigation suggests that the $\mathrm{Bi}M{\mathrm{O}}_{3}$ oxides or their modified versions are promising ferroelectric, piezoelectric, multiferroic, and photocatalytic materials.

Temperature dependence of the A1(LO) and E2 (high) phonons in hexagonal InN nanowires

The frequencies and dampings of the zone-center optical phonon modes of A1(LO) (longitudinal-optical) and E2 (high) in wurtzite InN nanowires have been investigated by micro-Raman scattering in the temperature range from 80 to 300 K. Our results reveal that the phonon frequencies decrease and the linewidths broaden with increasing temperature. The obtained experimental data of the frequencies and linewidths at various temperatures can be well described by an empirical model which takes into account the contribution of the thermal expansion of lattice and symmetric decay of phonons into two and three identical phonons with lower energy. The results show that decay into two phonons is the probable channel for the A1(LO) mode and three-phonon decay dominates the E2 (high) mode.

Atomistic study of lattice structure of BiScO 3

The total energies and lattice structures of one paraelectric and two ferroelectric phases of BiScO 3 (BSO) were obtained through first principles calculations at zero temperature. The structural instability and phase transition of this material with 5-atom per unit cell was revealed by the simultaneous existence of zone-center and zone-boundary soft phonon modes in phonon dispersion relations. Based on the first principles calculations, a simple rigid-ion pair potential model was developed by fitting of total energy. This atomistic model reproduced the crucial ferroelectric properties of BSO and enabled the molecular dynamics (MD) simulations to be performed for the investigation of BSO on the ground state at non-zero temperature. A monoclinic phase was discovered for BSO, which is consistent with experimental results.

Effect of pressure on the Raman modes of antimony

The effect of pressure on the zone-center optical phonon modes of antimony in the $A7$ structure has been investigated by Raman spectroscopy. The ${A}_{g}$ and ${E}_{g}$ frequencies exhibit a pronounced softening with increasing pressure, the effect being related to a gradual suppression of the Peierls-like distortion of the $A7$ phase relative to a cubic primitive lattice. Also, both Raman modes broaden significantly under pressure. Spectra taken at low temperature indicate that the broadening is at least partly caused by phonon-phonon interactions. We also report results of ab initio frozen-phonon calculations of the ${A}_{g}$ and ${E}_{g}$ mode frequencies. The presence of strong anharmonicity is clearly apparent in calculated total energy versus atom displacement relations. Pronounced nonlinearities in the force versus displacement relations are observed. Structural instabilities of the Sb $A7$ phase are briefly addressed in the Appendix.

First-principles study of the electronic and vibrational properties ofLiNbO2

In the layered transition metal oxide LiNbO$_2$ the Nb$^{3+}$ ($4d^2$) ion is trigonal-prismatically coordinated with O ions, with the resulting crystal field leading to a single band system for low energy properties. A tight-binding representation shows that intraplanar second neighbor hopping $t_2 = 100$ meV dominates the first neighbor interaction ($t_1 = 64$ meV). The first and third neighbor couplings are strongly modified by oxygen displacements of the symmetric Raman-active vibrational mode, and electron-phonon coupling to this motion may provide the coupling mechanism for superconductivity in Li-deficient samples (where $T_c = 5$ K). We calculate all zone-center phonon modes, identify infrared (IR) and Raman active modes, and report LO-TO splitting of the IR modes. The Born effective charges for the metal ions are found to have considerable anisotropy reflecting the degree to which the ions participate in interlayer coupling and covalent bonding. Insight into the microscopic origin of the valence band density, composed of Nb $d_{z^2}$ states with some mixing of O $2p$ states, is obtained from examining Wannier functions for these bands.

Acoustic Phonon Emission from a Weakly Coupled Superlattice under Vertical Electron Transport: Observation of Phonon Resonance

We report measurements of acoustic phonon emission from a weakly coupled AlAs/GaAs superlattice (SL) under vertical electron transport. The phonons were detected using superconducting bolometers. A peak (resonance) was observed in emission parallel to the SL growth axis when the electrical energy drop per SL period matched the energy of the first SL mini-Brillouin zone-center phonon mode. This peak was mirrored by an increase of the differential conductance of the SL. These results are evidence for stimulated emission of terahertz phonons as previously predicted theoretically and suggest that such a SL may form the basis of a SASER (sound amplification by stimulated emission of radiation) device.

The intrinsic lifetime of low-frequency zone-centre phonon modes in silicon nanowires and carbon nanotubes

Estimates of the intrinsic lifetime of low-frequency zone-centre phonon modes in silicon nanowires and carbon nanotubes have been presented from the application of Fermi’s golden rule formula based upon an elastic continuum model for cubic anharmonicity. In particular, results have been presented for the lowest non-zero mode in both nanostructures, and also the breathing mode in the nanotube. Except for the ultrathin nanowire, the lifetime increases with size and decreases with an increase in temperature. Typically, these modes have a lifetime of the order of nanoseconds, almost a thousand times larger than the lifetimes of optical phonon modes in the corresponding bulk materials. Also, at room temperature the lifetime of the lowest non-zero mode is nearly an order of magnitude larger in the (20,20) nanotube than in the nanowire of similar thickness (width 2.2 nm).

First-principles studies of ground-state and dynamical properties of MgS, MgSe, and MgTe in the rocksalt, zinc blende, wurtzite, and nickel arsenide phases

An ab initio pseudopotential method is used to investigate the structural and electronic properties of MgS, MgSe, and MgTe in the rocksalt, zinc blende, wurtzite, and nickel arsenide phases. It is found that rocksalt is the most stable phase for MgS and MgSe, while nickel arsenide is the most stable phase for MgTe. Differences in the density of states for the upper valence bands and lower conduction bands between these competing phases are pointed out. The lattice dynamics of these semiconductors has been studied by employing a linear response approach based on the density functional theory. Differences in the phonon spectra and density of states both in the acoustic and optical ranges between the competing phases are investigated. The calculated zone-center phonon modes for the rocksalt and zinc blende phases of MgS are in good agreement with experimental observations.

Electronic Structure and Ferroelectric Behavior of Lanthanum Substituted Bismuth Titanate

The effect of substituting La for Bi atoms in Bi 4 Ti 3 O 12 is investigated from first-principles calculations using the full-potential linearized augmented plane wave (LAPW) method. A comparative study of the electronic structure and lattice-dynamics properties of Bi 4 Ti 3 O 12 and La 2 Bi 2 Ti 3 O 12 shows the role of covalent bonding in the ferroelectric instabilities. The displacement patterns displayed by unstable zone-center phonon modes and a detailed analysis of the orbital contribution to the valence band illustrate the importance of Bi (La)-O interactions for the ferroelectric behavior of the doped material.

Electronic and structural properties of SnO under pressure

Pressure-induced changes in the electronic and structural properties of tin monoxide are examined by means of ab initio density-functional calculations. Also, the pressure shifts of the ${A}_{1g}$ and ${E}_{g}$ zone-center phonon modes are derived. The results are compared to recent experimental high-pressure data as well as to previous calculations for ambient conditions. In agreement with earlier findings we observe that the Sn-$5s$ lone pair is not inert but hybridizes with the O-$p$ states. Differences in that respect between SnO and PbO are shown to be a ``relativistic dehybridization effect'' caused by the large mass-velocity downshift of the Pb-$6s$ states. SnO is a small-gap (indirect) semiconductor at ambient pressure, but an insulator-metal transition occurs as pressure is applied. The transition is estimated to occur around 5 GPa. The gap depends sensitively on the distance between the layers $d{E}_{\text{gap}}∕d\phantom{\rule{0.2em}{0ex}}\mathrm{ln}(c∕a)\ensuremath{\approx}21\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$.

Strain-induced shifts of the zone-center phonons of III-Nitrides

In this work, by using the density-functional theory within the local density approximation, plane wave expansions and the pseudopotential method, we present our preliminary results for the strain-induced shifts of the zone center phonon modes and of the effective charges on the III-Nitrides. Our results are in good agreement with the experiment as well as with other calculations, whenever a comparison is possible.

Lattice dielectric response ofCdCu3Ti4O12andCaCu3Ti4O12from first principles

Structural, vibrational, and lattice dielectric properties of CdCu{3}Ti{4}O{12} are studied using density-functional theory within the local spin-density approximation, and the results are compared with those computed previously for CaCu{3}Ti{4}O{12}. Replacing Ca with Cd is found to leave many calculated quantities largely unaltered, although significant differences do emerge in zone-center optical phonon frequencies and mode effective charges. The computed phonon frequencies of CdCu{3}Ti{4}O{12} are found to be in excellent agreement with experiment, and the computed lattice contribution to the intrinsic static dielectric constant (~60) also agrees exceptionally well with a recent optical absorption experiment. These results provide further support for a picture in which the lattice dielectric response is essentially conventional, suggesting an extrinsic origin for the anomalous low-frequency dielectric response recently observed in both materials.

Lattice dynamics and elastic properties of corundum by the self-consistent atomic deformation method

We apply a recently developed density-functional method based on localized densities to study electronic, structural, elastic, optical, and vibrational properties of $\ensuremath{\alpha}\ensuremath{-}{\mathrm{Al}}_{2}{\mathrm{O}}_{3}.$ Although our approach is generally less accurate than conventional band-structure methods, calculation of polarization, and related properties is greatly simplified and our results are in reasonably good agreement with experiment and other theoretical calculations. We also assign the symmetry of zone center and other high-symmetry phonon modes and calculate the variation of the zone-center mode frequencies as a function of wave vector direction.