Soft-mode Transition Research Articles

Superconducting dome in ferroelectric-type materials from soft mode instability

We present a minimal theory of superconductivity enhancement in ferroelectric-type materials. Simple expressions for the optical mode responsible for the soft mode transition are assumed. A key role is played by the anharmonic phonon damping which is modulated by an external control parameter (electron doping or mechanical strain) causing the appearance of the soft mode. It is shown that the enhancement in the superconducting critical temperature $T_{c}$ upon approaching the ferroelectric transition from either side is due to the Stokes electron-phonon scattering processes promoted by strong phonon damping effects.

Control Method in Minimum Infinity-Norm Approach for Multicoil Magnetic Manipulation System

A magnetic manipulation system for medical applications is designed with its coils widely distributed over a sufficiently large space such that a patient can lie down, an operator can enjoy the accessibility, and the workspace is sufficiently large. However, this design makes the current references asymmetrical. Moreover, at the corners, some references might exceed the coil current rating, and the magnetic field cannot be synthesized as desired. To address this overcurrent reference problem, this article proposes a magnetic manipulation system controlled with the minimum infinity-norm current reference. In many magnetic manipulation systems, the current reference for a given motion command of the magnetic field is infinite. And the minimum infinity-norm current reference is the most feasible. The proposed control strategy presents an increased maximum synthesizable magnetic field in an arbitrary direction, including the worst case direction, compared with the conventional field of Moore–Penrose inverse control. To verify the effectiveness, the worst case direction of the magnetic field of each method is analytically derived. And, the controllable areas of the eight-coil magnetic manipulation system are compared. This article also proposes a soft mode transition between the two methods for efficiency enhancement. The experimental results show the effectiveness of the proposed control strategy.

Finite-temperature dynamics and the role of disorder in nearly critical Ni(Cl1−xBrx)2·4SC(NH2)2

Inelastic neutron scattering is used to investigate the temperature dependence of spin correlations in the 3-dimensional XY antiferromagnet Ni(Cl$_{1-x}$Br$_x$)$_2$$\cdot$4SC(NH$_2$)$_2$, $ x = 0.14(1)$, tuned close to the chemical-composition-induced soft-mode transition. The local dynamic structure factor shows $\hbar\omega/T$ scaling behavior characteristic of a quantum critical point. The deviation of the measured critical exponent from spin wave theoretical expectations are attributed to disorder. Another effect of disorder is local excitations above the magnon band. Their energy, structure factor and temperature dependence are well explained by simple strong-bond dimers associated with Br-impurity sites.

Order-parameter coupling and strain relaxation behavior of Ti50Pd50−xCrx martensites

A group theoretical model is proposed for linear/quadratic coupling between order parameters which arise from electronic and soft-mode instabilities in doped shape memory alloys, together with coupling to symmetry breaking shear strains. This model is tested by using resonant ultrasound spectroscopy (RUS) to follow the elastic and anelastic anomalies which accompany transitions from B2 to B19, 9R, and incommensurate structures in ${\mathrm{Ti}}_{50}{\mathrm{Pd}}_{50\ensuremath{-}x}{\mathrm{Cr}}_{x}$ alloy samples ($0\ensuremath{\le}x\ensuremath{\le}12$). The pure soft-mode transition gives rise to an incommensurate structure but without any associated changes in the shear modulus, implying that coupling with shear strains is weak. By way of contrast, the observed pattern of softening ahead of and stiffening below the martensitic transition is typical of pseudoproper ferroelastic behavior and confirms that there is strong bilinear coupling of the tetragonal shear strain to the order parameter associated with irrep ${\mathrm{\ensuremath{\Gamma}}}_{3}^{+}$ of the parent space group. The second order parameter has the symmetry properties of ${\mathrm{M}}_{5}^{\ensuremath{-}}$ in TiPd or of a point along the \ensuremath{\Sigma} line of the Brillouin zone for the 9R and incommensurate structures with high Cr contents. Comparison of shear modulus data for Cr-rich samples obtained by RUS at ${10}^{5}\ensuremath{-}{10}^{6}\phantom{\rule{0.16em}{0ex}}\mathrm{Hz}$ with previously reported Young's modulus data obtained for different samples by dynamical mechanical analysis at \ensuremath{\sim}0.1--10 Hz has not revealed the dispersion with frequency that would be expected for a glass transition governed by Vogel-Fulcher dynamics. The two techniques differ in the magnitude of effective applied stress, however, and differences in chemical homogeneity between samples or decomposition during high-temperature measurements might also be a factor.

Continuous-time quantum Monte Carlo for fermion-boson lattice models: Improved bosonic estimators and application to the Holstein model

We extend the continuous-time interaction-expansion quantum Monte Carlo method with respect to measuring observables for fermion-boson lattice models. Using generating functionals, we express expectation values involving boson operators, which are not directly accessible because simulations are done in terms of a purely fermionic action, as integrals over fermionic correlation functions. We also demonstrate that certain observables can be inferred directly from the vertex distribution, and present efficient estimators for the total energy and the phonon propagator of the Holstein model. Furthermore, we generalize the covariance estimator of the fidelity susceptibility, an unbiased diagnostic for phase transitions, to the case of retarded interactions. The new estimators are applied to half-filled spinless and spinful Holstein models in one dimension. The observed renormalization of the phonon mode across the Peierls transition in the spinless model suggests a soft-mode transition in the adiabatic regime. The critical point is associated with a minimum in the phonon kinetic energy and a maximum in the fidelity susceptibility.

Beryl-II, a high-pressure phase of beryl: Raman and luminescence spectroscopy to 16.4 GPa

The Raman and Cr3+ and V2+ luminescence spectra of beryl and emerald have been characterized up to 15.0 and 16.4 GPa, respectively. The Raman spectra show that an E1g symmetry mode at 138 cm−1 shifts negatively by −4.57 (±0.55) cm−1/GPa, and an extrapolation of the pressure dependence of this mode indicates that a soft-mode transition should occur near 12 GPa. Such a transition is in accord with prior theoretical results. Dramatic changes in Raman mode intensities and positions occur between 11.2 and 15.0 GPa. These changes are indicative of a phase transition that primarily involves tilting and mild distortion of the Si6O18 rings. New Raman modes are not observed in the high-pressure phase, which indicates that the local bonding environment is not altered dramatically across the transition (e.g., changes in coordination do not occur). Both sharp line and broadband luminescence are observed for both Cr3+ and V2+ in emerald under compression to 16.4 GPa. The R-lines of both Cr3+ and V2+ shift to lower energy (longer wavelength) under compression. Both R-lines of Cr3+ split at ~13.7 GPa, and the V2+ R1 slope changes at this pressure and shifts more rapidly up to ~16.4 GPa. The Cr3+ R-line splitting and FWHM show more complex behavior, but also shift in behavior at ~13.7 GPa. These changes in the pressure dependency of the Cr3+ and V2+ R-lines and the changes in R-line splitting and FWHM at ~13.7 GPa further demonstrate that a phase transition occurs at this pressure, in good agreement with our Raman results. The high-pressure phase of beryl appears to have two Al sites that become more regular under compression. Hysteresis is not observed in our Raman or luminescence spectra on decompression, suggesting that this transition is second order in nature: The occurrence of a second-order transition near this pressure is also in accord with prior theoretical results. We speculate that the high-pressure phase (beryl-II) might be a mildly modulated structure, and/or that extensive twinning occurs across this transition.

Structural investigation of Sr 2LiReO 6. Evidence for a continuous tetragonal–cubic phase transition

The presence of a continuous and reversible Fm 3 ¯ m – I4/ m phase transition in a polycrystalline sample of the ordered double perovskite Sr 2LiReO 6 is described. The transition that occurs near 300 °C is a consequence of in-phase tilting of the BO 6 octahedra. The temperature dependence of both the lattice parameters and the spontaneous strains are consistent with a second order phase transition as would be expected for a soft mode transition.

3D phonon dispersion surface of incommensurate phases of alpha-U metal

The experimental data on incommensurate phase versus temperature, as they have been obtained by high resolution inelastic neutron scattering, are compared to theoretical models. In the experiments reported we have set out to examine the phonon dispersion surface to verify that the charge-density wave (CDW) state is present continuously at temperature even above TCDW. The position of the phonon minimum (qmin = qCDW), as well as the detailed shape of the dispersion surface of phonon modes over an extended areas in the (E, q) space, is important in view of the debate on the origin of the CDW at the Peierls transition (2nd_order phase) and gives rise to a further modulation of the structure. This work confirms that the CDW state has precursor effects before the phase transition, there is a strong coupling between phonon and electronic states and that a 'soft-mode transition' occurs at TCDW. This result is compared to theories discussing the origin of the CDW state.

Soft modes near the buckling transition of icosahedral shells

Icosahedral shells undergo a buckling transition as the ratio of Young's modulus to bending stiffness increases. Strong bending stiffness favors smooth, nearly spherical shapes, while weak bending stiffness leads to a sharply faceted icosahedral shape. Based on the phonon spectrum of a simplified mass-and-spring model of the shell, we interpret the transition from smooth to faceted as a soft-mode transition. In contrast to the case of a disclinated planar network where the transition is sharply defined, the mean curvature of the sphere smooths the transition. We define elastic susceptibilities as the response to forces applied at vertices, edges, and faces of an icosahedron. At the soft-mode transition the vertex susceptibility is the largest, but as the shell becomes more faceted the edge and face susceptibilities greatly exceed the vertex susceptibility. Limiting behaviors of the susceptibilities are analyzed and related to the ridge-scaling behavior of elastic sheets. Our results apply to virus capsids, liposomes with crystalline order, and other shell-like structures with icosahedral symmetry.

The Soft Mode Transition Induced by Magnetic Field and Pressure in TlCuCl3and Related Dimer Compounds

TlCuCl 3 is an example of a quantum spin liquid of S = 1/2 Cu 2+ dimers. Strong inter-dimer superexchange interactions give rise to a three-dimensional dispersion of the triplet magnon. The minimum excitation energy determines the spin gap which is significantly smaller than the dimer coupling. It can be closed by an applied hydrostatic pressure of the order of 1 kbar or by a magnetic field of 5.6 T, offering a unique opportunity to study the evolution of the magnon modes through the pressure- and field-induced quantum phase transitions.

Origin of anomalous line shape of the lowest-frequencyA1(TO)phonon inPbTiO3

The origin of the anomalous line shape of the ${A}_{1}(1\mathrm{T}\mathrm{O})$ soft mode in ${\mathrm{PbTiO}}_{3}$-based single crystals was investigated by polarized Raman-scattering method over a wide range of temperature between 100 and 700 K. Detailed scattering data indicated that the previously proposed anharmonicity model could not properly explain the anomalous behavior of the lowest-frequency subpeak of the ${A}_{1}(1\mathrm{T}\mathrm{O})$ mode that was primarily responsible for the phonon softening of the undoped ${\mathrm{PbTiO}}_{3}.$ Further Raman studies of Ba-doped ${\mathrm{PbTiO}}_{3}$ crystals showed that the Ba-impurity peak that dominated the soft-mode transition also had the ${A}_{1}$ symmetry of the ${\mathrm{PbTiO}}_{3}$ host lattice. A careful comparison of these two distinct peaks having the same ${A}_{1}$ symmetry indicates that the observed anomalous line shape of the ${A}_{1}(1\mathrm{T}\mathrm{O})$ mode is caused not only by the lattice anharmonicity but also by some lattice defects. Particularly, the lowest-frequency subpeak of the ${A}_{1}(1\mathrm{T}\mathrm{O})$ mode is not directly related to the anharmonicity but originates from the existence of thermodynamically unavoidable lattice defects in ${\mathrm{PbTiO}}_{3}.$

Dipole ordering effects and reentrant dipolar glass state inKTaO3:Li,Nb

Dielectric permittivity and Raman-scattering studies reveal unconventional dipole ordering and structural effects that arise in the incipient ferroelectric ${\mathrm{KTaO}}_{3}$ due to the simultaneous presence of off-center ${\mathrm{Li}}^{+}$ and ${\mathrm{Nb}}^{5+}$ ions. A soft-mode-driven transition into a ferroelectric phase accompanied by the formation of a dipole glass in the ${\mathrm{Li}}^{+}$ subsystem was identified at 39 K in a sample of composition ${\mathrm{K}}_{0.9986}{\mathrm{Li}}_{0.0014}{\mathrm{Ta}}_{0.988}{\mathrm{Nb}}_{0.012}{\mathrm{O}}_{3}.$ A second soft-mode transition was found at 30 K, whereas a transition into a phase identified as a ``reentrant dipolar glasslike state'' was observed at 15 K. Such a sequence of phases, diordered--long range ordered--reentrant glass, already known for disordered ferromagnets, is here reported for a highly polarizable matrix with soft modes.

Pressure-induced transformations in deep mantle and core minerals

AbstractRecent experimental and theoretical studies provide new insight into the variety of high-pressure transformations in minerals that comprise the Earth’s deep mantle and core. Representative examples of reconstructive, displacive, electronic and magnetic transformations studied by new diamond-anvil cell techniques are examined. Despite reports for various transitions in (Mg,Fe)SiO3-perovskite, the stability field of the orthorhombic phase expands relative to magnesiowüstite + SiO2 with increasing pressure and temperature. The partitioning of Fe and Mg between Mg-rich silicate perovskite magnesiowüstite depends strongly on pressure, temperature, bulk Fe/Mg ratio, and ferric iron content. The soft-mode transition in SiO2 from the rutile- to CaCl2-type structure, originally documented by X-ray powder diffraction, Raman scattering, and first-principles theory has been explored in detail by single crystal diffraction, and transitions to higher-pressure forms have been examined. The effect of H on the transformations of various nominally anhydrous phases and transitions in dense hydrous Mg-silicates are also examined. New studies of the phase diagram of FeO include the transition to rhombohedral and higher-pressure NiAs polymorphs, and provide prototypical examples of coupled structural, electronic, and magnetic transitions. High-spin/low-spin transitions in FeO have been examined by high-resolution X-ray emission spectroscopy to 150 GPa, and the results are compared with similar studies of Fe2O3 and FeS. Finally, laser-heating studies to above 150 GPa and 2500K show that (hcp) ε-Fe has a large P-T stability field. Radial XRD measurements carried out at room temperature to 220 GPa have constrained the elasticity, rheology and sound velocities of ε-Fe at core pressures.

Bioferroelectricity in models of voltage-dependent ion channels

Ion channels are glycoprotein components of biomembranes that switch specific ionic currents on and off. It is here argued that, in the nonconducting phase, these macromolecules are ferroelectric liquid crystals, containing S4 and other segments that share the properties of chirality and tilt with SmC* phases. In the ion-conducting phase they are modeled as metalloproteins, with their structure coordinated by the permeant ions, which are dehydrated by enzymatic action as they enter the channel. Permeant ions may replace structural protons in an ion-exchange reaction. The conformational transition from closed to open phase is postulated to be a soft mode transition, in which the tilt angles of the S4 segments decrease to zero. It is also likely to involve the flexoelectric effect. Experimental data support these models.

Vibrationally reduced magnetic interactions in Cu and the magnetic ordering in a magnetic field

The nuclear ordering temperatures in Cu is in the n-K range. Yet, the zero-point vibrational motion of the atoms is found to have the effect of reducing the calculated Ruderman-Kittel interaction significantly for all interactions J n beyond the nearest-neighbor interaction J 1. Using J 1 and J 2 = − J 1/10 and a spin wave calculation of the soft-mode transition from the ferromagnetically polarized state it is found that in Cu the antiferromagnetic state changes from a type-I (001) state for fields in the [100] and [110] direction to an incommensurate ( t + δ, t- δ, 0) state with t ≈ 2 3 and a small δ, for fields in a region around the [111] direction. In this region the ordering has not yet been solved experimentally. It is a result of the close competition between the dipole and Ruderman-Kittel forces in Cu.

Soft-mode transition in the ferroelastic crystal K2Hg(CN)4.

Inelastic neutron scattering techniques have been used to investigate the structural transition from the paraelastic to the ferroelastic phase in ${\mathrm{K}}_{2}$Hg(CN${)}_{4}$. Several low-frequency phonon branches were measured along the high-symmetry directions and found to be almost independent of temperature. However, a particular low-lying branch along [111] was found to show a strong temperature dependence. The structure factor for this mode shows it to be a longitudinal, librational mode whose eigenvector specifies antiphase rotation of adjacent rigid cyanotetrahedra. This is in agreement with the change in the crystal structure observed at the transition by diffraction measurements. The frequency of this branch at the zone-boundary L point tended to zero at \ensuremath{\approxeq}101 K, thus showing the paraelastic to ferroelastic transition in this cyanospinel is a soft-mode transition.

Raman scattering studies of ferroelectric transitions induced by lithium and niobium in KTaO3

Abstract The low temperature phases produced by Nb and Li in K1-x Lix Ta1-y NbyO3 have been studied using Raman scattering and optical depolarization for x≲0.06 and y≲0.06. When x=0 and 0.008<y0.06, the low temperature phase has been shown to be rhombohedral and the phase transition is predominantly a soft mode transition. This behavior contrasts with the order-disorder transition to a tetragonal phase seen when y=O and 0.01≲x≲0.06. The unique feature of K1-x Lix TaO3 is that small ferroelectric domains lead to Raman spectra with no evidence of the anisotropy of the mixed mode phonon energy expected in a polar lattice. K1-xLixTaO3 cannot be poled after the temperature is reduced below Tc, but it is poled if the sample is cooled with an applied electric field along a cubic axis. In poled samples, the anisotropy of the energy of the mixed mode can be demonstrated directly in the Raman spectra by changing the experimental geometry so that the scattered phonons have different components of k along the polar a...

Thermodynamic properties of Rb 2ZnCl 4 associated with three phase transitions

Transitions were observed by heat capacity measurements at 74.6 K, 195.2 K, and 303 K. They are a soft mode transition ( ΔH t = 30 J mol −1, ΔS t = 0.42 J K −1 mol −1), a first-order commensurate-incommensurate transition ( ΔH t = 6.2 J mol −1 ΔS t = 0.032 J K −1 mol −1), and a second-order incommensurate-normal transition, respectively.

Self pulsing in second harmonic generation

We consider nonlinear optical processes in a cavity maintained far from thermal equilibrium by external pumping. In second harmonic generation we predict a hard mode instability at a critical pump strength indicating the existence of undamped spiking similar to that in strongly pumped lasers. In subharmonic generation above the soft mode transition noted by Graham we predict the appearance of sidebands in the subharmonic spectrum.

Suppression of antiferroelectricity in TiSe2 by excess carriers

Analysis of the optical reflectivity spectra of TiSe2 at room temperature shows that the lattice polarizabilitye t * as well as the electronic polarizability ɛ∞ are unusually large. This suggests to us that the phase transition atT 0=200 K is a phonon-driven antiferroelectric transition. The properties of such a soft-mode transition in a semi-metal are investigated. It is found that excess carriers suppress the transition and that the excess resistivity at the transition varies as |T−T 0|−1.