Soft Mode Frequency Research Articles

Thermodynamic and dielectric properties of hexagonal barium titanate near the phase transitions

The critical behavior of the thermodynamic quantities is studied for the two phase transitions near the transition temperatures (74 K and 222 K) in the hexagonal (h) BaTiO3. A linear relationship has been established between the variations of the frequency shifts and of the dielectric constant by using the literature data in h-BaTiO3. Temperature and pressure dependence of the mode Grüneisen parameters ( γp and γT ) are also described by a power-law formula as the other thermodynamic parameters near Tpt in h-BaTiO3. Our results show that they explain the observed behavior adequately, in particular soft-mode frequency, dielectric constant, thermal expansion, the excess specific heat and the entropy near Tpt in h-BaTiO3. Temperature dependence of the isobaric mode Grüneisen parameter ( γp ), enthalpy and the Gibbs free energy, which we have evaluated, can be compared with experiments in h-BaTiO3.

Study of Ferroelectric Phase Transition in Triglycine Fluoberyllate Crystal

Triglycine fluoberyllate (TGFB) is an important member of hydrogen bonded order disorder type ferroelectrics, resembling other ferroelectrics which belongs to its group it experiences phase transition at certain temperature. In current theoretical work by utilizing Green’s function (double time thermal dependent) and modified pseudospin two-sublattice mode model we are analyzing ferroelectric behavior of TGFB crystal. For this purpose we are evaluating expressions for shift ( Δ ) , width ( Γ ) , soft mode frequency ( Ω ̂ ) , dielectric constant ( ε ) and loss tangent ( tan δ ) , after that by utilizing model values for TGFB crystal thermal dependence of Ω ̂ , ε and tan δ have been calculated. Comparison illustrates that theoretical results obtained by us are in good harmony with experimental results.

Terahertz ferroelectric soft mode in weakly doped SrTiO3: M thin films (M=Mn, Ni, Fe, Co)

Systematic study of the terahertz soft-mode in SrTiO3: M thin (150 nm) films doped (2 at%) with transition metals M = Mn, Fe, Ni, Co is performed at frequencies 7–1000 cm−1 and temperatures 5–300 K. The soft mode dielectric strength and frequency follow the Barrett-like temperature behaviours with unusually high quantum temperatures and large in magnitude negative Curie temperatures, indicating strong destabilization of the ferroelectric state due to a combined effect of quantum fluctuations, dead layers at the boundaries of crystallites, misfit strains within crystallites and disorder induced by doping. Dopant-dependent variation in the asymmetry of the Fano resonance describing coupling of the TO2 phonon and continuum states of polarization fluctuations is observed suggesting presence of polar nanoregions in the films. Clear correlation between the asymmetry parameter and the Barrett quantum temperature is observed that highlights the complex character of the local structure-dielectric properties relationships in the films.

Nature of Dielectric Relaxation in SrTiO<sub>3</sub>:Mn Single Crystals

Dielectric spectra of SrTiO3and SrTiO3:Mn single crystals have been studied in the frequency range of 10‒3000 cm–1and in the temperature range of 5–297 K using time-domain terahertz spectroscopy and Fourier-transform infrared spectroscopy. A comparative analysis of the experimental results made it possible to detect a significant broadening of the absorption lines corresponding to the Slater and Last phonon modes, while the parameters of the Axe mode when replacing Ti with Mn (2 at %) stay invariant. This effect is associated with an enhance in structural disorder in the cation subsystem (B-sublattice) of the SrTiO3crystal. It has been established that doping with Mn ions reduces the antiferrodistortive phase transition temperature by about 20 K, but hardly affects the character of the temperature dependence of the parameters of a ferroelectric soft mode at temperatures of about 60–297K. It has been found that an additional excitation with the frequency below the frequency of the ferroelectric soft mode should be taken into account for an appropriate model description of the dispersion of the permittivity of SrTiO3:Mn in the terahertz frequency range. The results obtained in this work indicate that dielectric relaxation in the SrTiO3:Mn crystal is due to thermally activated hops of Mn atoms between displaced (noncentral) crystallographic sites; i.e., the mechanism of radiofrequency relaxation in SrTiO3:Mn is hopping rather than polaronic, which is also actively discussed in the literature.

Phase Transition Behavior in Antiferroelectric Copper Formate Tetrahydrate Crystal

Antiferroelectric properties of copper formate tetrahydrate (CFT) crystal having phase transition temperature at were investigated theoretically. CFT have a layer-type structure in which layers of are sandwiched between the layers of copper formate in the lattice plane. By considering modified two sublattice pseudospin lattice coupled mode model Hamiltonian and double-time temperature-dependent Green function method for antiferroelectric copper formate tetrahydrate (CFT) crystal, the phase transition properties of crystal have been studied. Expressions are derived for soft mode frequency, dielectric constant and loss tangent for considered crystal. Model values are fitted in the derived expressions and the dependence of the above properties on temperature have been calculated. Theoretically obtained results are compared with experimental data and show similarities between them. Dielectric constant as a function of temperature shows a behaviour of the first-order transition with a large discontinuity at the transition point. These properties can be employed in a wide range of applications including memory devices, solar cells, biosensors and photovoltaic devices.

Resonant Excitation of the Ferroelectric Soft Mode by a Narrow-Band THz Pulse.

This study investigates the impact of narrow-band terahertz pulses on the ferroelectric order parameter in Ba0.8Sr0.2TiO3 films on various substrates. THz radiation in the range of 1-2 THz with the pulse width of about 0.15 THz was separated from a broadband pulse with the interference technique. The 375 nm thick BST film on a MgO (001) substrate exhibits enhanced THz-induced second harmonic generation when excited by THz pulses with a central frequency of 1.6 THz, due to the resonant excitation of the soft phonon mode. Conversely, the BST film on a Si (001) substrate shows no enhancement, due to its polycrystalline state. The 800 nm thick BST film on a MgO (111) substrate demonstrates the maximum of a second harmonic generation signal when excited by THz pulses at 1.8 THz, which is close to the soft mode frequency for the (111) orientation. Notably, the frequency spectrum of the BST/MgO (111) film reveals peaks at both the fundamental and doubled frequencies, and their intensities depend, respectively, linearly and quadratically on the THz pulse electric field strength.

Impact of quartic anharmonicity on lattice thermal transport in EuTiO3: A comparative theoretical and experimental investigation

We investigate the role of the quartic anharmonicity in the lattice dynamics and thermal transport of the cubic EuTiO3 by combining ab initio self-consistent phonon theory with compressive sensing techniques and experimental thermal conductivity determination measurement. The antiferromagnetic G-type magnetic structure is used to mimic the para-magnetic EuTiO3. We find that the strong quartic anharmonicity of oxygen atoms plays an important role in the phonon quasiparticles free from imaginary frequencies in EuTiO3 and causes the hardening of vibrational frequencies of soft modes. Based on these results, the lattice thermal transport properties are predicted through the Boltzmann transport equation within the relaxation time approximation. The hardened modes thereby affect calculated lattice thermal conductivity significantly, resulting in an improved agreement with experimental results, including the deviation from κL ∝ T−1 at high temperatures. The calculated thermal conductivity of 8.2 W/mK at 300 K matched the experimental value of 6.1 W/mK. When considering the boundary scattering, the calculated thermal conductivity is reduced to 6.9 W/mK at 300 K, which agrees better with the experiment.

Structural-Stability Study of AntiperovskiteNa3OClforNa-Rich Solid Electrolyte

The structural phase transition of the high-symmetry cubic phase of antiperovskite $\mathrm{Na}$${}_{3}$$\mathrm{O}\mathrm{Cl}$ is investigated by computing the phonon band structures of 14 different polymorphs with distinct types of $\mathrm{O}\mathrm{Na}$${}_{6}$ octahedral tilting. The resulting $P$-$T$ phase diagram shows that, at high temperature and low pressure, the high-symmetry cubic structure with $Pm\overline{3}m$ symmetry is the most stable phase. At low temperature and high pressure, on the other hand, the monoclinic structure with $P{2}_{1}/m$ symmetry becomes the most stable phase. In between those two, there is a region in the phase diagram where the orthorhombic structure with $Bmmb$ symmetry is the most stable phase. To improve upon the quasiharmonic results, we do additional calculations in the framework of the self-consistent phonon (SCP) theory, including lattice anharmonicity by using cubic and quartic interatomic force constants (IFCs). This is particularly important for the high-symmetry cubic phase. We find that by decreasing the temperature, the frequency of the soft phonon at the $M$ and $R$ symmetry points gradually shifts to lower values. From these results, we can infer that a phase transition occurs around 166--195 K upon soft-mode condensation. Due to the proximity of the soft-mode frequencies at both symmetry points $R$ and $M$, we expect a cubic-to-orthorhombic phase transition to be realized via simultaneous condensation of the two octahedral tilting modes.

Lattice dynamics and phase transitions peculiarities of Ba[formula omitted]Sr[formula omitted]TiO[formula omitted] solid solutions with high Sr content

In this study, the lattice dynamics and phase transition peculiarities of BaxSr1−xTiO3 solid solution samples with x =1,0.5 and 0.3 are investigated by the Raman spectroscopy in a wide temperature range. The compositional and temperature dependences of soft mode frequencies were obtained. In contrast to ceramics with x =1 and 0.5, the soft E(TO) mode frequency in a solid solution with x =0.3 exhibits temperature dependence similar to the classical behavior of the soft mode for displacement-type transitions. From the analysis of the activation energy of titanium ion jumps, it was found that with increasing strontium concentration, the mechanism of these jumps changes from thermal over the potential barrier to tunneling under the barrier. This, in turn, leads to a significant increase in the lifetime of the rhombohedral distorted state of the crystal lattice and suppression of the ferroelectric transition by the Slater mechanism.

Thermal dependence of soft mode frequency, dielectric constant, and tangent loss in lead hydrogen phosphate (LHP) crystal

Ferroelectric materials have promising uses in modulators, infrared detectors, data storage devices, and other circuits. The ferroelectric properties in LHP crystallites are investigated theoretically in the study that followed, with some modifications, including the incorporation of fourth and third-orderphonon anharmonic connections, indirect connections, four-body connections, and electric field terms. We will take into account the PLCM model Hamiltonian. Calculations of soft mode frequency, loss tangent, and dielectric constant for said LHP crystal have been computed by using Green's function methodology. The analysis has been done mathematically by putting numerous model values into theoretical expressions that have been established, as well as thermal perturbations of soft mode frequency, Tangent loss (dielectric loss) and dielectric constant have been established. The findings of this study for the LHP crystal are quite well consistent with Negran et al studies of experimental data.

Phase transition dielectric properties in order–disorder antiferroelectric NH[formula omitted](H[formula omitted]PO[formula omitted]) (ADP) crystal

A modified four sublattice pseudospin lattice coupled model Hamiltonian by adding extra spin–lattice interaction, direct spin–spin interaction has been used to study dielectric properties for ammonium dihydrogen phosphate (ADP) crystal. Using the double-time temperature-dependent Green’s function method, the expressions for soft mode frequency, dielectric permittivity and loss tangent have been derived. By fitting the model values of various physical parameters, the thermal variations of the above quantities are calculated and compared with the experimental results. Our theoretical obtained results are in good agreement with experimental data.

Terahertz time-domain spectroscopic ellipsometry of metallic strontium titanate

The coexistence of the polar instability and metallic conduction has attracted much attention. Ferroelectric soft optic modes and carrier electrons were investigated in A- and B-site heterovalent doped strontium titanate SrTiO3 crystals by the terahertz time-domain spectroscopic ellipsometry. The observed real and imaginary parts of a complex dielectric constant were fitted by the damped harmonic oscillator model for the ferroelectric soft optic mode and the Drude-Smith model for carrier electrons. The observed soft mode frequency increases as the La and Nb content increases. It is found that the square of the ferroelectric soft mode frequency linearly changes to the carrier electron concentration. This fact indicates that the carrier electrons suppress the ferroelectric instability and the ferroelectric soft mode frequency increases as the carrier concentration increases.

Dielectric properties of ammonium iron sulphate-dodecahydrate alum crystal

The statistical Green function theory and extended two sublattice pseudospin coupled-mode model Hamiltonian. The modified model summing with phonon anharmonic couplings, extra spin-lattice couplings, direct spin-spin coupling together with an applied electric field has been used to explain the dielectric properties of ammonium iron alum crystal. The expressions for energy shift, linewidth, ferroelectric soft mode frequency, dielectric permittivity, and dielectric loss tangent are derived. By fitted the model values of different parameters in the above theoretical expressions. The temperature dependence of soft mode frequency, dielectric permittivity, and dielectric loss properties have been numerically calculated. Our theoretical obtained results compared well agreement with experimental results reported by others.

Dielectric properties of ferroelectric methylammonium aluminium sulphate alum (MASD) crystal

By considering two sublattice pseudospin lattice coupled mode model Hamiltonian has been modified to include the extra spin–lattice interactions, the direct spin–spin coupling interaction, an applied electric field and the phonon anharmonic interactions for MASD alum. By using double-time thermal-dependent Green function method and modified Hamiltonian formulation, the expressions for soft mode frequency, dielectric constant and dielectric tangent loss properties have been derived and evaluated. Fitting the model values of various physical parameters in theoretical obtained expressions, the thermal variations of the above quantities have been calculated. Theoretical results compare well with experimental data of others on MASD alum.

Insight into Pyroelectricity and Phase Transitions in Ferroelectrics from Nonequilibrium Approach: The Case of PbTiO3

AbstractComputational methodology is proposed to simulate time dependent temperature variations via thermostat approach. The methodology is applied to study pyroelectricity under nonequilibrium conditions in prototypical ferroelectric PbTiO3. It is found that at room temperature the nonequilibrium effects in pyroelectricity begin manifesting above 1.0 THz and originate from the overlap with the intrinsic soft mode frequency. Therefore, the proposed computational methodology can be used to predict equilibrium pyroelectric response by choosing a frequency of temperature variation below the intrinsic polar mode frequencies for the material. Probing the dynamics of ferroelectric phase transition with the proposed methodology revealed that it takes about a nanosecond for the computational supercell to undergo phase transition. It is concluded that computational techniques capable of simulating picoseconds can be used to compute pyroelectric response from nonequilibrium dynamical approach while those that can reach nanoseconds are suitable for simulating phase transitions in ferroelectrics.

Dielectric properties of hydrogen-bonded cesium dihydrogen phosphate-type ferroelectric crystals

Cesium dihydrogen phosphate crystal belongs to the potassium dihydrogen phosphate family of ferroelectrics. It is ferroelectric below 154 K. It shows a large isotope effect like other members of this family. We have modified two-sublattice pseudospin lattice coupled-mode model Hamiltonian by adding phonon anharmonic interactions, extra-spin lattice interactions, and direct spin-spin coupling as well as an electric field. By using modified model Hamiltonian, double-time thermal Green function method and following the Zubarev and Kubo formalism, we have derived theoretically expressions for soft mode frequency, dielectric constant, and loss tangent for cesium dihydrogen phosphate (CDP)-type ferroelectric crystals. By fitting model values of physical parameters, we have calculated thermal variations of normal mode frequency, dielectric constant, and dielectric tangent loss for CDP-crystal. We have compared our theoretical results with the experimental results of others. Our theoretical obtainedresults agree well with the experimental results of others.

Underdamped longitudinal soft modes in ionic crystallites-lattice and charge motions observed by ultrafast x-ray diffraction.

Soft modes in crystals are lattice vibrations with frequencies that decrease and eventually vanish as the temperature approaches a critical point, e.g., a structural change due to a phase transition. In ionic para- or ferroelectric materials, the frequency decrease is connected with a diverging electric susceptibility and, for infrared active modes, a strong increase in oscillator strength. The traditional picture describes soft modes as overdamped transverse optical phonons of a hybrid vibrational-electronic character. In this context, potassium dihydrogen phosphate (KH2PO4, KDP) has been studied for decades as a prototypical material with, however, inconclusive results regarding the soft modes in its para- and ferroelectric phase. There are conflicting assignments of soft-mode frequencies and damping parameters. We report the first observation of a longitudinal underdamped soft mode in paraelectric KDP. Upon impulsive femtosecond Raman excitation of coherent low-frequency phonons in the electronic ground state of KDP crystallites, transient powder diffraction patterns are recorded with femtosecond hard x-ray pulses. Electron density maps derived from the x-ray data reveal oscillatory charge relocations over interatomic distances, much larger than the sub-picometer nuclear displacements, a direct hallmark of soft-mode behavior. The strongly underdamped character of the soft mode manifests in charge oscillations persisting for more than 10 ps. The soft-mode frequency decreases from 0.55 THz at T = 295 K to 0.39 THz at T = 175 K. An analysis of the Raman excitation conditions in crystallites and the weak damping demonstrate a longitudinal character. Our results extend soft-mode physics well beyond the traditional picture and pave the way for an atomic-level characterization of soft modes.

First order ferroelectric phase transition phenomenon in alkali-phosphate crystal by using Green’s function approach

In this paper, first order phase transition phenomenon in CsH2AsO4 crystal has been theoretically investigated. With the help of a simple PLCM modified model presently Hamiltonian, with the consideration of four body interaction SizSjzSkzSlz, cubic, and quartic phonon anharmonic interactions, and another all possible interactions are added into it. The contribution of pseudo spin parameter <Sz> and <Sx> are also introduced here which accounts for the spontaneous polarisation. It is shown that soft mode frequency, and phase transition phenomenon such as, permittivity, loss tangent, and Cochran’s mode frequency in the vicinity of Curie’s temperature at about 145.5K due to anharmonicity within the crystal. Observed the obtained theoretical consequences of above parameters are in well resembles with the experimental results of earlier authors.

Quantum paraelectric phase of SrTiO3 from first principles

We demonstrate how the quantum paraelectric ground state of ${\mathrm{SrTiO}}_{3}$ can be accessed via a microscopic ab initio approach based on density functional theory. At low temperature the quantum fluctuations are strong enough to stabilize the paraelectric phase even though a classical description would predict a ferroelectric phase. We find that accounting for quantum fluctuations of the lattice and for the strong coupling between the ferroelectric soft mode and lattice elongation is necessary to achieve quantitative agreement with experimental frequency of the ferroelectric soft mode. The temperature dependent properties in ${\mathrm{SrTiO}}_{3}$ are also well captured by the present microscopic framework.

Lattice instability of B-site substituted SrTiO3 crystals studied by terahertz time-domain spectroscopic ellipsometry

The B-site substituted quantum paraelectric strontium titanate, SrTiO3 (STO), crystals with the perovskite structure were studied regarding their dielectric properties in the terahertz frequency range. When Ti4+ ions at the B-site are substituted by heterovalent Nb5+ ions, free electrons are introduced and the conductivity increases. The complex dielectric constants were accurately determined by the terahertz time-domain spectroscopic ellipsometry. The dielectric spectra were analyzed by the damped harmonic oscillator model for a ferroelectric soft mode and the Drude-Smith model for free electrons. The soft mode frequency and the plasma frequency increased with the increasing Nb content. The square of the plasma frequency is proportional to the concentration of free electrons. It was found that the change in the ferroelectric soft mode frequency is approximately proportional to the concentration of free electrons. This fact suggests that the increase in the free electrons by donor-doping suppresses the ferroelectric instability.