Soft Optic Mode Research Articles

Study of the feature of lattice dynamic and ferroelectric transition in perovskites using molecular-dynamics modeling

Static and dynamic correlation functions of the BaTiO3 crystal are calculated using molecular-dynamics (MD) modeling. Based on time-dependent pair correlation functions, phonon spectra of BaTiO3 are calculated and the central peak of inelastic scattering is studied. It is shown that the phonon frequencies calculated by the MD method are in quite good agreement with those we obtained previously in the quasiharmonic approximation [1, 2]. It is demonstrated that the central peak of inelastic scattering is mainly associated with the soft optical mode and has the same symmetry. The coincidence of symmetries makes it possible to explain both the features in the X-ray scattering and the EXAFS spectroscopy.

Phonon dynamics simulation of TlH2PO4 crystal

AbstractLattice dynamics of TlH2PO4 crystal was simulated within the atomistic semi‐empirical approach in high‐temperature Pbcn and ferroelastic P21/b phases. Phonon dispersion relations, partial density of phonon states, dispersion of mean square displacements and isotropic temperature factors were calculated. Using both the lattice dynamics simulation and phenomenological Landau–Ginzburg analysis it was shown that the ferroelastic phase transition occurs due to the bilinear interaction between the soft B3g optical and transverse acoustic TAYZ phonon modes. The oxygen–hydrogen interactions within the shorter O1H1···O2 hydrogen bonds play the key role at the ferroelastic phase transition.

Soft-mode behavior and incipient ferroelectricity inNa1/2Bi1/2Cu3Ti4O12

The correlation between crystal structure and intrinsic dielectric properties of the unusual cubic perovskite-related family of compounds $A{\text{Cu}}_{3}{\text{Ti}}_{4}{\text{O}}_{12}$, where $A=\text{Ca}$, Cd, ${\text{La}}_{2/3}$, ${\text{Bi}}_{2/3}$, ${\text{Na}}_{1/2}{\text{La}}_{1/2}$, ${\text{Na}}_{1/2}{\text{Bi}}_{1/2}$, etc., (space group $Im\overline{3}$ ) has been a controversial topic for several years, especially for the most studied member of the family ${\text{CaCu}}_{3}{\text{Ti}}_{4}{\text{O}}_{12}$ (CCTO). ${\text{Na}}_{1/2}{\text{Bi}}_{1/2}{\text{Cu}}_{3}{\text{Ti}}_{4}{\text{O}}_{12}$ (NBCTO) is isostructural with CCTO and retains centrosymmetric and cubic symmetry (space group $Im\overline{3}$) down to 4 K. NBCTO ceramics exhibit high intrinsic relative permittivity of $\ensuremath{\sim}145$ at 300 K that rises on cooling and levels off below $\ensuremath{\sim}50\text{ }\text{K}$ with a value of $\ensuremath{\sim}260$ at 10 K without any signature of a structural transition. Such behavior is a typical feature of incipient ferroelectrics such as the perovskite ${\text{CaTiO}}_{3}$. Infrared and terahertz spectroscopy on NBCTO ceramics are presented and reveal a room-temperature soft polar optic mode at $\ensuremath{\sim}34\text{ }{\text{cm}}^{\ensuremath{-}1}$ that softens on cooling and is responsible for the temperature dependence of the relative permittivity. The temperature dependence of the soft-mode frequency obeys the Barrett formula with the onset of quantum fluctuations ${T}_{1}$ occurring near 85 K and a hypothetical Curie temperature ${T}_{0}$ of $\ensuremath{\sim}\ensuremath{-}155\text{ }\text{K}$. A fitted vibrational zero-point energy $({k}_{\text{B}}{T}_{1})/2$ is in good agreement with the measured soft-mode frequency. The crystal structure-intrinsic dielectric properties of NBCTO and possibly all cubic $A{\text{Cu}}_{3}{\text{Ti}}_{4}{\text{O}}_{12}$ phases are, therefore, consistent with that of other untilted/tilted ${\text{TiO}}_{3}$-based centrosymmetric perovskites such as ${\text{CaTiO}}_{3}$ and ${\text{SrTiO}}_{3}$. The ``so-called'' giant permittivity values of $g1000$ reported for CCTO, NBCTO, and related phases from radio-frequency capacitance measurements near room temperature are an extrinsic effect associated with the semiconducting nature of these materials, as opposed to an intrinsic effect associated with their rather unusual perovskite-type crystal structure.

Ladder Lattice Model of Soft Optical Phonon

A linear lattice model for demonstrating a soft optical mode at a zone center is proposed. The unit cell consists of only two atoms. If the optical mode is sufficiently soft, anticrossing takes place between the optical and acoustic phonon branches. By using the generalized Langevin's equation method, the spectral function is calculated analytically. The intensity of the optical mode disappears at approximately the anticrossing wave number. In general, the spectral line shape of the optical mode is asymmetric because of the interaction between the two branches.

High-pressure ferroelastic phase transition in aluminosilicate hollandite

We used x-ray synchrotron powder diffraction, Raman spectroscopy, and first-principles calculations to characterize the high-pressure ferroelastic $I4/m$ to $I2/m$ transition of ${\text{K}}_{0.8}{\text{Na}}_{0.2}{\text{AlSi}}_{3}{\text{O}}_{8}$ hollandite, a structural prototype of materials used in various applications ranging from immobilization of radioactive wastes to ionic conductors. The transition is second-order in character with an equilibrium transition pressure renormalized by coupling of the soft mode with the spontaneous strain. The variations in the lattice strains and of the frequency of the soft optic mode with pressure have been used to develop a Landau free-energy expansion to describe the elastic constant variations in ${\text{K}}_{0.8}{\text{Na}}_{0.2}{\text{AlSi}}_{3}{\text{O}}_{8}$ across the transition.

The soft optic mode in ferroelasticRb4LiH3(SO4)4

Raman scattering measurements were performed on the ferroelastic compoundRb4LiH3(SO4)4 to determine the nature of the structural transition observed atTc = 134 K. A double-grating spectrometer was used to obtain the Raman active B modes ofRb4LiH3(SO4)4. Back-scattering measurements, as a function of temperature, reveal that the 31 cm−1 mode shows softening consistent with that of an order parameter. Asa result, our investigation indicates that the structural transition inRb4LiH3(SO4)4 should be cataloged as a pseudo-proper ferroelastic transition rather than a properferroelastic one.

Investigation of specific features of the lattice dynamics and the ferroelectric transition in perovskite crystals

The specific features of diffuse X-ray scattering in BaTiO3, KNbO3, and PbTiP3 perovskite crystals have been investigated. The former two perovskite compounds in cubic, tetragonal, and orthorhombic phases exhibit anomalous sheets due to diffuse X-ray scattering, whereas no similar sheets are observed in the case of diffuse X-ray scattering in PbTiO3. For these compounds, the phonon spectra are calculated in the quasi-harmonic approximation within the polarizable-shell model, and the mechanism of stabilization of the soft mode above the temperature of the phase transition to the ferroelectric state is considered. It is demonstrated that, in the cubic phase of BaTiO3 and KNbO3 crystals, there exist quasi-one-dimensional “soft” modes of vibrations of ions in M-O-M-O- chains, where M = Ti or Nb. In PbTiO3, this feature of the soft mode has not been revealed. The pair correlation functions of simultaneous atomic displacements in BaTiO3, KNbO3, and PbTiO3 are determined and used to calculate the intensity of diffuse X-ray scattering. The results obtained are in good agreement with experimental data. This is a strong argument in support of the hypothesis that the specific features of diffuse scattering are associated with the existence of quasi-one-dimensional correlations of atomic displacements in the soft optical mode and that the ferroelectric transition in perovskites is a displacive ferroelectric phase transition. The possible influence of the specific features revealed in the phonon spectra of the perovskite crystals on the processes of nuclear magnetic resonance and X-ray absorption (extended X-ray absorption fine structure spectra) is briefly discussed.

(Sr,Mn)TiO3—a magnetoelectrically coupled multiglass

Extending the framework for multiferroic materials, in which long-rangeelectric and magnetic orderings coexist, we present a novel ‘multiglass’concept, where two different glassy states occur simultaneously. It applies toSr0.98Mn0.02TiO3 ceramics,where the Mn2+ dopant ions are at the origin of both polar and spin glasses.Spin freezing is initiated at the dipolar glass temperature,Tg≈38 K. BelowTg, bothglass phases are independently verified by memory and rejuvenation effects. Strong biquadratic interactionof the Mn2+ spins with the optic soft mode of the incipient ferroelectric host crystalSrTiO3 explains the high spin glass temperature and comparably strong higher ordermagnetoelectric coupling between the polar and magnetic degrees of freedom.

Charge disproportionation and collinear magnetic order in the frustrated triangular antiferromagnetAgNiO2

We report a high-resolution neutron diffraction study of the crystal and magnetic structure of the orbitally degenerate frustrated metallic magnet ${\text{AgNiO}}_{2}$. At high temperatures the structure is hexagonal with a single crystallographic Ni site, low-spin ${\text{Ni}}^{3+}$ with spin 1/2 and twofold orbital degeneracy, arranged in an antiferromagnetic triangular lattice with frustrated spin and orbital order. A structural transition occurs upon cooling below 365 K to a tripled hexagonal unit cell containing three crystallographically distinct Ni sites with expanded and contracted ${\text{NiO}}_{6}$ octahedra, naturally explained by spontaneous charge order on the Ni triangular layers. No Jahn-Teller distortions occur, suggesting that charge order occurs in order to lift the orbital degeneracy. Symmetry analysis of the inferred Ni charge order pattern and the observed oxygen displacement pattern suggests that the transition could be mediated by charge fluctuations at the Ni sites coupled to a soft oxygen optical phonon breathing mode. At low temperatures the electron-rich Ni sublattice (assigned to a valence close to ${\text{Ni}}^{2+}$ with $S=1$) orders magnetically into a collinear stripe structure of ferromagnetic rows ordered antiferromagnetically in the triangular planes. We discuss the stability of this uncommon spin order pattern in the context of an easy-axis triangular antiferromagnet with additional weak second-neighbor interactions and interlayer couplings.

Raman scattering study of ca-modified lead titanate

The paraelectric to ferroelectric phase transitions were studied by Raman scattering in Ca-doped lead titanate ceramics. The soft optic modes responsible for the ferroelectric phase transitions were clearly observed. The A(1)(1TO) mode, which softens toward T(c), contains four subpeaks. The frequencies of these subpeaks depend to a great extent on the Ca content and the temperature. These behaviors are discussed on the basis of the anharmonicity of lattice vibrations.

Quantum paraelectric behavior of pyrochlorePb1.83Mg0.29Nb1.71O6.39

Pb{sub 1.83}Mg{sub 0.29}Nb{sub 1.71}O{sub 6.39} crystallizing in a cubic pyrochlore structure exhibits a typical feature of quantum paraelectrics--its permittivity continuously increases on cooling and levels off below {approx}30 K without any signature of a structural phase transition. Broadband dielectric spectra do not show any dielectric dispersion in the real part of permittivity up to 8.8 GHz. Terahertz and infrared spectra reveal a soft polar optic mode, which is responsible for the temperature dependence of the permittivity. The leveling off of the permittivity at low temperatures obeys the Barrett formula, and the fitted vibrational zero-point energy (1/2)k{sub B}T{sub 1} corresponds to the measured soft-mode frequency. The number of observed infrared phonons exceeds that predicted from the factor-group analysis, which indicates that the structure is at least locally noncubic.

Heat capacity and high-resolution Brillouin scattering studies of phase transitions inK2MgWO2(PO4)2: Observation of the coupled soft optic and acoustic mode

High-resolution micro-Brillouin scattering and heat capacity studies of phase transitions in ferroelectric ${\mathrm{K}}_{2}\mathrm{Mg}\mathrm{W}{\mathrm{O}}_{2}{(\mathrm{P}{\mathrm{O}}_{4})}_{2}$ were performed in the temperature range $300\char21{}810\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Strong anomalies in Brillouin shift and attenuation were observed near 633, 519, and $434\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ upon cooling for the sound waves corresponding to the ${c}_{11}$ and ${c}_{33}$ elastic constants. The analysis of these anomalies and heat capacity results revealed that they correspond to second-order, typical first-order, and nearly second-order phase transitions, respectively. The highest temperature phase transition was shown to have mainly an order-disorder nature whereas the two remaining transitions may have both order-disorder and displacive nature. The obtained results revealed also very strong coupling between the ${c}_{44}$ acoustic mode and the soft optic mode of $E$ symmetry. The coupled mode model was employed to fit the experimental data. It was shown that the relaxation time of the order parameter exhibits slowing down indicating that the phase transition at $519\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ is induced by instability of the $E$-symmetry soft mode. The possible microscopic origin of the soft mode is proposed.

ELECTRICAL RESISTIVITY AND MAGNETO-RESISTANCE OF La0.7Sr0.3-xAgxMnO3 PELLETS BETWEEN 10 AND 450 K

The temperature dependence of the electrical resistivity and magneto-resistance in silver substituted La 0.7 Sr 1-x Ag x MnO 3 pellets prepared by a simple pyrophoric method has been investigated between 10 and 450 K for H=0 and 0.8T. Ag substitution enhances the conductivity of this system. Curie temperature (T C ) also increases sharply from ~303 K (x=0.05) to ~363 K (x=0.25). Above the metal-insulator transition temperature (T MI ), the electrical resistivity is well represented by usual adiabatic polaronic transport, while in the ferromagnetic region at low temperatures, the resistivity data shows an excellent agreement to an expression containing the residual resistivity, two-magnon scattering term and the term associated with small-polaron metallic conduction, which involves a relaxation time due to a soft optical phonon mode. Based on a scenario that the doped manganites consist of phase separated ferromagnetic metallic and paramagnetic insulating regions, all the features of the temperature variation of the resistivity between ~50 K and 300 K could be described very well. All the Ag doped samples reveal resistivity minimum, which is strongly field dependent (H=0.8 T ). These minimum results have been analyzed and the observed field dependent minimum is found to be in excellent agreement to those calculated from the model based on charge carrier tunneling between antiferro-magnetically coupled grains. Field dependence of magnetoresistance at various temperatures below T c is accounted fairly well by a phenomenological model based on spin polarized tunneling at the grain boundaries. The contributions from the intrinsic part arising from DE mechanism, as well as the part originating from intergranular spin polarized tunneling are also estimated.

Dielectric response of soft mode in ferroelectric SrTiO3

The authors report far-infrared dielectric properties of powder form ferroelectric SrTiO3. Terahertz time-domain spectroscopy (TDS) measurement reveals that the low-frequency dielectric response of SrTiO3 is a consequence of the lowest transverse optical (TO) soft mode TO1 at 2.70THz (90.0cm−1), which is directly verified by Raman spectroscopy. This result provides a better understanding of the relation of low-frequency dielectric function with the optical phonon soft mode for ferroelectric materials. Combining terahertz TDS with Raman spectra, the overall low-frequency optical phonon response of SrTiO3 is presented in an extended spectral range from 6.7to1000.0cm−1.

Composition dependence of the diffuse scattering in the relaxor ferroelectric compound(1−x)Pb(Mg1∕3Nb2∕3)O3−xPbTiO3(0≤x≤0.40)

We have used neutron diffraction to characterize the diffuse scattering in five single crystals of the relaxor ferroelectric $(1\ensuremath{-}x)\mathrm{Pb}({\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}){\mathrm{O}}_{3}\ensuremath{-}x{\mathrm{PbTiO}}_{3}$ $(\mathrm{PMN}\text{\ensuremath{-}}x\mathrm{PT})$ with $x=0$, 10, 20, 30, and 40%. The addition of ferroelectric ${\mathrm{PbTiO}}_{3}$ modifies the well-known ``butterfly'' and ``ellipsoidal'' diffuse scattering patterns observed in pure PMN $(x=0)$, which are believed to be associated with the presence of randomly oriented polar nanoregions. In particular, the anisotropy of the diffuse scattering diminishes as the PT content increases. The spatial correlation length $\ensuremath{\xi}$ along the $[1\overline{1}0]$ direction derived from the width of the diffuse scattering at room temperature increases from $12.6\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ for PMN to $350\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ for PMN-20%PT. In addition, the diffuse scattering intensity at $q=0$ grows and reaches a maximum value around the morphotropic phase boundary (MPB), which suggests that it is proportional to the dielectric susceptibility. Beyond $x=30%$, a concentration very close to the MPB, no diffuse scattering is observed below ${T}_{C}$, and well-defined critical behavior appears near ${T}_{C}$. By contrast, the diffuse scattering for $x\ensuremath{\le}20$% persists down to low temperatures, where the system retains an average cubic structure $({T}_{C}=0)$. Finally, the anisotropic soft transverse optic (TO) modes observed in PMN are found to be isotropic for PMN-30%PT, which strongly suggests a connection between the anisotropic diffuse scattering and the TO modes.

Thermoelectric power of potassium doped lanthanum manganites at low temperatures

The temperature-dependent resistivity and thermoelectric power of monovalent (K) doped La 1− x K x MnO 3 polycrystalline pellets ( x=0.05, 0.10 and 0.15) between 50 and 300 K are reported. K substitution enhances the conductivity of this system. Curie temperature ( T C) also increases from 260 to 309 K with increasing K content. In the paramagnetic region ( T> T C), the electrical resistivity is well represented by adiabatic polaron hopping, while in the ferromagnetic region ( T< T C), the resistivity data show a nearly perfect fit for all the samples to an expression containing, the residual resistivity, spin-wave and two-magnon scattering and the term associated with small-polaron metallic conduction, which involves a relaxation time due to a soft optical phonon mode. Small polaron hopping mechanism is found to fit well to the thermoelectric power (S) data for T> T C whereas at low temperatures ( T< T C) in ferromagnetic region ( S FM), S FM is well explained with the spin-wave fluctuation and electron–magnon scattering. Both, resistivity and thermopower data over the entire temperature range (50–300 K) are also examined in light of a two-phase model based on an effective medium approximation.

Dielectric properties and lattice dynamics of Ca-dopedK0.95Li0.05TaO3

Relaxor behavior and lattice dynamics have been studied for a single crystal of K$_{1-x}$Li$_x$TaO$_3$ $(x=0.05)$, where a small amount of a Ca impurity ($\sim 15$~ppm) was incorporated. The dielectric measurements revealed Debye-like relaxations with Arrhenius activation energies of 80 and 240 meV that are assigned to Li$^+$ dipoles and the Li$^+$-Li$^+$ dipolar pairs, respectively. In the neutron scattering results, diffuse scattering ridges appear around the nuclear Bragg peaks below $\sim 150$ K and phonon line broadening features start to appear at even higher temperatures suggesting that polar nano-regions (PNR's) start to form at these temperatures. These results are supported by the dielectric data that reveal relaxor behavior starting at $\sim 200$ K on cooling. From analyses of the diffuse intensities, the displacements include a uniform phase shift of all of the atoms in addition to the atomic displacements corresponding to a polarization vector of the transverse optic soft ferroelectric mode, a finding that is analogous to that in the prototypical relaxor material Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_3$.

SO phonon scattering rates at the Si-HfO2 interface in Si MOSFETs

Silicon MOSFETs with high κ gate stacks offer a significant reduction in gate leakage current, but the presence of soft surface optic phonon modes degrades the mobility. A progressively more complex set of models for SO phonon scattering at the Si-HfO2 interface is presented based upon dynamic screening models. Landau damping of the electron-phonon-plasmon coupling is examined by simple approximations. A novel approach to determining the re-normalised phonon spectrum based on Padé approximants is outlined as a route to obtaining practical scattering rate for Monte Carlo simulation.

Lattice instability at phase transitions near the Lifshitz point in proper monoclinicferroelectrics

The temperature dependence of acoustic properties of theSn2P2(SexS1−x)6 uniaxial ferroelectric in the vicinity of the Lifshitz point (LP) was investigated byBrillouin spectroscopy and analysed in the Landau–Khalatnikov approximation. Ananomalous decrease of the longitudinal hypersound velocity in the paraelectricphase caused by fluctuation effects and crystal structure defects has been foundnear the LP. Besides this, a small softening of the transverse acoustic phonons isobserved, which is due to their linear interaction with the soft optic mode found forincommensurate phase transitions in proper ferroelectrics. The lattice instability analysis ofSn2P2S6 and Sn2P2Se6 crystals and their solid solutions in a polarizable ion model shows that a possible reason forthe absence of a soft acoustic mode is nonorthogonality of the spontaneous polarizationvector and modulation wavevector which both lie in the monoclinic symmetry plane.

Damped soft phonons and diffuse scattering in40%Pb(Mg1∕3Nb2∕3)O3−60%PbTiO3

Using neutron elastic and inelastic scattering and high-energy x-ray diffraction, we present a comparison of 40% Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$-60% PbTiO$_{3}$ (PMN-60PT) with pure Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$ (PMN) and PbTiO$_{3}$ (PT). We measure the structural properties of PMN-60PT to be identical to pure PT, however, the lattice dynamics are exactly that previously found in relaxors PMN and PZN. PMN-60PT displays a well-defined macroscopic structural transition from a cubic to tetragonal unit cell at 550 K. The diffuse scattering is shown to be weak indicating that the structural distortion is long-range in PMN-60PT and short-range polar correlations (polar nanoregions) are not present. Even though polar nanoregions are absent, the soft optic mode is short-lived for wavevectors near the zone-centre. Therefore, PMN-60PT displays the same waterfall effect as prototypical relaxors PMN and PZN. We conclude that it is random fields resulting from the intrinsic chemical disorder which is the reason for the broad transverse optic mode observed in PMN and PMN-60PT near the zone centre and not due to the formation of short-ranged polar correlations. Through our comparison of PMN, PMN-60PT, and pure PT, we interpret the dynamic and static properties of the PMN-xPT system in terms of a random field model in which the cubic anisotropy term dominates with increasing doping of PbTiO$_{3}$.