Central-peak Behavior Research Articles

Structural heterogeneity induced enhancement of physical properties in Sm‐modified K0.5Na0.5NbO3

AbstractDoping of suitable metal ions in ferroelectric oxides modifies the physical properties and can induce additional functionalities. Here, we present a detailed study on the effects of Sm concentration on the structural, dielectric, ferroelectric, and piezoelectric properties of ((K0.5Na0.5)1−3xSmx)NbO3 (KNSN) (0.00 ≤ x ≤ 0.02) ceramics. X‐ray diffraction and Raman spectroscopic analysis indicate that KNSN ceramics exhibit the single‐phase orthorhombic (Amm2) structure for x = 0.00 and the coexistence of orthorhombic and tetragonal (Amm2 + P4mm) structure for the composition range 0.005 ≤ x ≤ 0.02. The tetragonal phase fraction increases with an increase in Sm concentration. We observed dielectric relaxation behavior in KNSN at orthorhombic to tetragonal (TO–T) phase transition temperature, and its origin can be attributed to the structural heterogeneity at the inter‐ferroelectric phase boundary. Increasing Sm concentration leads to the broadening of the ferroelectric phase transition peaks. Further, the structural heterogeneity of the ceramics was seen from the slope of the dielectric constant versus log frequency and central peak behavior of Raman spectra at room temperature (RT). The study reveals that x = 0.005 shows maximum dielectric constant (Ɛr = 583), remanent polarization (2Pr = 57.02 μC/cm2), and piezoelectric coefficient (d33 = 94 pC/N) at RT and is associated with increased local structural heterogeneity due to Sm doping.

Spin dynamics of quantum Ising chain in random correlated magnetic fields

The spin dynamics of one-dimensional quantum Ising chain with random correlated magnetic fields (RCMFs) is studied at the high-temperature limit by the recursion method. Both the spin autocorrelation function and its corresponding spectral density are investigated under the circumstance of bimodal-type and Gaussian-type RCMFs. It is found that the dynamics of the system are highly dependent on the correlated mode and strength between the longitudinal and transverse magnetic fields (i.e., Bxi and Bzi). Due to the cooperation or synergy effect between Bxi and Bzi, crossovers between different dynamical behaviors can be revealed in most of the cases. In general, the dynamics of the system is dominant by the field (Bxi or Bzi) with a larger proportion when the RCMFs are weak. However, when the RCMFs are strong, the system tends to exhibit a disordered behavior, which manifests as a multiple-peak feature in the bimodal-type case or a broaden spectral in the Gaussian-type case. In another perspective, when the proportion of Bzi is small, the central-peak behavior can be enhanced by increasing the proportion of Bxi. Interestingly, when the proportion of Bzi is large, the perturbation of Bxi on Bzi tends to excite new dynamical behavior. Our results indicate that using RCMF to manipulate the spin dynamics of the Ising system may be a new try.

Spin dynamics of an Ising chain with bond impurity in a tilt magnetic field

Spin dynamics of quantum Ising system has been the subject of condensed matter physics in the past few decades. In this work, the bond-impurity effects on dynamics of the one-dimensional quantum Ising model with both transverse (Bzi) and longitudinal magnetic field (LMF, Bxi) was studied in the high-temperature limit by the recurrence relations method. Three cases, i.e., the LMF effect on the dynamics of the pure Ising model without impurity (Bxi≠0), the weak- and strong-bond impurity effect on the dynamics of the transverse Ising model without LMF (the impurity strength Jj≠Ji, Bxi=0), and their combining effect (Jj≠Ji, Bxi≠0), were investigated respectively. It is found that the dynamical behaviors of the system depend on both the impurity and the LMF. In general, the central-peak behavior (collective-mode behavior) will be enhanced (depressed) when increasing Jj or Bxi properly. However, when Jj reaches a critical value Jjc , the spin motion will be frozen, i.e., the bond impurity will act as a switch, which may turn off or turn on the spin motion. In contrast, the LMF can active the motion of the frozen spin. Therefore, the dynamical behavior of the Ising system depends on the combining effects of the impurity and the LMF.

Spin dynamics of random Ising chain in coexisting transverse and longitudinal magnetic fields

The dynamics of the random Ising spin chain in coexisting transverse and longitudinal magnetic fields is studied by the recursion method. Both the spin autocorrelation function and its spectral density are investigated by numerical calculations. It is found that system’s dynamical behaviors depend on the deviation σJ of the random exchange coupling between nearest-neighbor spins and the ratio rlt of the longitudinal and the transverse fields: (i) For rlt=0, the system undergoes two crossovers from N independent spins precessing about the transverse magnetic field to a collective-mode behavior, and then to a central-peak behavior as σJ increases. (ii) For rlt≠0, the system may exhibit a coexistence behavior of a collective-mode one and a central-peak one. When σJ is small (or large enough), system undergoes a crossover from a coexistence behavior (or a disordered behavior) to a central-peak behavior as rlt increases. (iii) Increasing σJ depresses effects of both the transverse and the longitudinal magnetic fields. (iv) Quantum random Ising chain in coexisting magnetic fields may exhibit under-damping and critical-damping characteristics simultaneously. These results indicate that changing the external magnetic fields may control and manipulate the dynamics of the random Ising chain.

The spin dynamics of the random transverse Ising chain with a double-Gaussian disorder

The dynamical properties of one-dimensional random transverse Ising model (RTIM) with a double-Gaussian disorder is investigated by the recursion method. Based on the first twelve recurrences derived analytically, the spin autocorrelation function (SAF) and associated spectral density at high temperature were obtained numerically. Our results indicate that when the standard deviation σJ (or σB) of the exchange couplings Ji (or the random transverse fields Bi) is small, no long-time tail appears in the SAF. The spin system undergoes a crossover from a central-peak behavior to a collective-mode behavior, which is the dynamical characteristics of RTIM with the bimodal disorder. However, when σJ (or σB) is large enough, the system exhibits similar dynamics behaviors to those of the RTIM with the Gaussian disorder, i.e., the system exhibits an enhanced central-peak behavior for large σJ or a disordered behavior for large σB. In this instance, SAFs exhibit a similar long-time tail, i.e., C(t) ∼ t−2 for large t. Similar properties are obtained when Ji (or Bi) satisfy the double-exponential distribution or the double-uniform distribution. Besides, when both the standard deviations and the mean values of the exchange couplings are small, the effects of the Gaussian random bonds may drive the system undergo two crossovers from a triplet state to a doublet state, and then to a collective-mode state.

The dynamics of one-dimensional random quantum XY system with Dzyaloshinskii—Moriya interaction

In this paper, the effects of random variables on the dynamics of the s = 1/2 XY model with the Dzyaloshinskii-Moriya interaction are studied. By means of the recurrence relation method in the high-temperature limit, we calculate the spin autocorrelation functions as well as the corresponding spectral densities for the cases that the exchange couplings between spins or external magnetic fields satisfy the double-Gaussian distribution. It is found that when the standard deviation of random exchange coupling δJ (or the standard deviation of random external field δB) is small, the dynamics of the system undergoes a crossover from a collective-mode behavior to a central-peak one. However, when δJ(or δB) is large, the crossover vanishes, and the system shows a central-peak behavior or the most disordered one. We also analyze the cases in which the exchange couplings or the external fields satisfy the bimodal and the Gaussian distributions. Our results show that for all the cases considered, the dynamics of the above system is similar to that of the one-dimensional random XY model.

Effects of random external fields on the dynamics of the one-dimensional Blume-Capel model

The dynamical properties of quantum spin systems have received a great deal of theoretical and experimental attention in the past decades. Only recently, has much attention been paid to the random quantum spin systems. In this paper the effect of random external field on the dynamics of one-dimensional Blume-Capel model with s = 1 in the high-temperature limit is investigated by using the recurrence relations method. The spin autocorrelation function as well as the corresponding spectral density of the system is calculated in the presence of the field that satisfies two types of distributions. When the single-ion anisotropy takes 0, for the bimodal distribution, the dynamics of the system behaves as a crossover from a central peak behavior to a collective mode one. For the Gaussian distribution, when the standard deviation is small, the dynamical behavior of the system also exhibits a crossover; when the standard deviation is large enough, the system only shows a disordered behavior. We also discuss the effect of the single-ion anisotropy on the dynamical property of the system, and find that the collective-mode behavior becomes weaker as the single-ion anisotropy exists.

Crossover of the dynamical behavior in two-dimensional random transverse Ising model

The dynamics of the two-dimensional spin-$\frac{1}{2}$ random transverse Ising model is studied by means of the recurrence relations method. Both the autocorrelation functions and the corresponding spectral densities are calculated in the cases that the exchange couplings or fields satisfy three typical distributions, respectively. For the cases of Gaussian and double-Gaussian distribution, when the standard deviation of the random variable is small, the dynamics of the system undergoes a crossover from a central-peak behavior to a collective-mode one, the result is similar to that of the bimodal distribution. While the standard deviation is large enough, the crossover disappears and the dynamics of the system shows a central-peak behavior or a disordered behavior.

Effects of next-nearest-neighbor interactions on the dynamics of random quantum Ising model

The dynamics of one-dimensional random quantum Ising model with both nearest-neighbor and next-nearest-neighbor （NNN） interactions is investigated in the high temperature limit by the method of recurrence relations. Spin autocorrelations and the corresponding spectral densities of the system are calculated. Supposing that the exchange couplings （or the transverse fields） satisfy the double-Gaussian distribution, the effects of this distribution on the dynamics of the system is studied. The results show that the dynamics of the system undergoes a crossover from a collective-mode behavior to a central-peak one when the standard deviations σJ（or σB）of the random variables are small and there is no crossover when σJ（or σB）are large. Meanwhile, the effects of NNN interactions on the dynamics of the system are studied. It is found that the central-peak behavior becomes more obvious and the collective-mode behavior becomes weaker as Ki increase, especially when Ki>Ji/2（Ji and Ki are exchange couplings of the NN and NNN interactions, respectively）. However, the effects are small when the NNN interactions are weak （KiJi/2）.

Dynamics of the one-dimensional random transverse Ising model with next-nearest-neighbor interactions

The dynamics of the one-dimensional random transverse Ising model with both nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions is studied in the high-temperature limit by the method of recurrence relations. Both the time-dependent transverse correlation function and the corresponding spectral density are calculated for two typical disordered states. We find that for the case of bimodal disorder the dynamics of the system undergoes a crossover from a collective-mode behavior to a central-peak one and for the case of Gaussian disorder the dynamics is complex. For both cases, it is found that the central-peak behavior becomes more obvious and the collective-mode behavior becomes weaker as K i increase, especially when K i > J i / 2 ( J i and K i are the exchange couplings of the NN and NNN interactions, respectively). However, the effects are small when the NNN interactions are weak ( K i < J i / 2 ).

Effects of double-Gaussian disorder on the dynamics of the quantumXYchain

We investigate the dynamics of the random one-dimensional spin-1/2 quantum isotropic $XY$ model in high-temperature limit by the recurrence relations method. Both the time-dependent transverse autocorrelation function and the corresponding spectral density are calculated for the cases that the exchange couplings between spins or transverse fields satisfy the double-Gaussian distribution. It is found that when the value of ${\ensuremath{\sigma}}_{J}$ (standard deviation of random exchange coupling) or ${\ensuremath{\sigma}}_{B}$ (standard deviation of random external magnetic field) is small, the dynamics of the system undergoes a crossover between a central-peak behavior and a collective-mode one. However, when ${\ensuremath{\sigma}}_{J}$ or ${\ensuremath{\sigma}}_{B}$ is large enough, the crossover vanishes, and the system shows the most disordered behavior or a central-peak behavior. We also investigate the cases that the couplings or fields satisfy the bimodal distribution and Gaussian distribution, which are the two special cases of double-Gaussian distribution, and find that the dynamics of the system is similar to that of the one-dimensional transverse Ising system.

Effects of Gaussian disorder on the dynamics of the random transverse Ising model

The effects of Gaussian disorder on the dynamics of the one-dimensional spin-1/2 random transverse Ising model are studied in the high-temperature limit by the recursion method. Both spin autocorrelation functions and the corresponding spectral densities are calculated for three types of disordered cases. It is found that when the standard deviation ${\ensuremath{\sigma}}_{J}$ of the exchange coupling (or the standard deviation ${\ensuremath{\sigma}}_{B}$ of the random transverse field) is small, the dynamics of the system undergoes two crossovers in sequence as the mean value of the exchange coupling (or the random transverse field) varies: from a central-peak behavior to a collective-mode one, and then to the precession of free spins in an external transverse magnetic field. However, when ${\ensuremath{\sigma}}_{J}$ or ${\ensuremath{\sigma}}_{B}$ are large enough, there is no crossover, i.e., the dynamics of the system shows a central-peak behavior and a disordered behavior, respectively.

Dynamics of the random one-dimensional transverse Ising model

We study the dynamics of the spin-1/2 random transverse Ising model in the high-temperature limit by means of the method of recurrence relations. We analyze two types of disorder: a disorder on the transverse field, and a disorder on the exchange coupling. We find that the dynamics undergoes a crossover from a central peak behavior onto a collective mode behavior as a function of the disorder. @S0163-1829~99!04937-1#

Central peak in light scattering from the relaxor ferroelectricPbMg1/3Nb2/3O3

A model relaxor ferroelectric ${\mathrm{PbMg}}_{1/3}{\mathrm{Nb}}_{2/3}{\mathrm{O}}_{3}$ (PMN) in single-crystal form has been studied by Raman scattering with special attention to the low-frequency spectra in the vicinity of both the diffuse ferroelectric transition (\ensuremath{\sim}270 K) and the electric-field-induced ferroelectric transition (\ensuremath{\sim}200 K). In addition to the hard-mode features without any pronounced change, a broad central component has been observed and analyzed. This component exhibits some distinct characteristics of a relaxation mode and shows an increase in the intensity and a slow down in the relaxation times in the vicinity of both the transitions mentioned above. No usual soft mode has been found, in agreement with other studies. The central component is only a distinctive dynamic characteristic of the evolution of relaxor ferroelectrics to a ferroelectric state. The central peak activity at about 200 K is connected with the polarization fluctuations whereas the main anomaly in the central-peak behavior in the range of the diffuse transition is caused by the complex fluctuations. We postulate a competition in this range between the development of a ferroelectric state and another nonpolar phase. We emphasize an obvious correlation between the central peak dynamics and other properties, such as acoustic phonon anomalies and modified dielectric response in PMN and some other related relaxor ferroelectrics.

Soft mode behavior in a one-dimensional model ferroelectric

Abstract We use a moment-expansion method for the spectral functions to show that a one-dimensional molecular field model of a ferroelectric crystal has a soft zone-center mode of vibration. The frequency of the mode goes towards zero at the transition point but the mode becomes overdamped very close to the transition. Within the limitations of the moment-expansion method, we see no central peak behavior.

Order-disorder and central peak behavior in SrTiO3

Abstract Recent detailed Electron Paramagnetic Resonance (EPR) studies will be presented which gave insight into the central peak phenomenon concerning its width and intensity. The studies were conducted with the Fe3+ - Vo center in a monodomain single crystal of SrTiO3, for Tc ≤ T < 295 K.1 From the angular dependence of the observed width, an upper limit of 6 MHz is placed upon the characteristic frequency of the local rotation fluctuations between Tc < T < Tc + 11K. The characteristic collective-mode relaxation rate, i.e., the “central-peak” width, should be about an order of magnitude narrower. A comparison of its narrow width with existing computer simulations2 above Tc indicates that the width of the c.p. has extrinsic origin, i.e., is impurity dominated.

Nonequilibrium thermodynamics and quasielastic light scattering from crystals

A methodology is proposed whereby a systematic analysis may be carried out of the spectrum of light scattered quasielastically by crystals. It involves: (i) determination of the equations satisfied by the crystal's thermodynamic variables, taking into account irreversible processes of energy dissipation, (ii) solution of such equations for the chosen scattering vector and the relevant crystalline symmetry, and (iii) determination of the spectrum by means of the Onsager hypothesis relating the solutions obtained and the correlation functions involving the same variables. The methodology was applied to K${\mathrm{H}}_{2}$P${\mathrm{O}}_{4}$ and to the superionic conductor Rb${\mathrm{Ag}}_{4}$${\mathrm{I}}_{5}$. The degrees of freedom associated with the diffusing silver ions in Rb${\mathrm{Ag}}_{4}$${\mathrm{I}}_{5}$ were assumed to be characterized by an internal (strain-independent) temperature and taken into account by means of a relaxing internal specific heat, the relaxation time being related to the hopping frequency. As the temperature is lowered, the ionic conductivity decreases, with a consequent decrease in the relaxation frequency and thus an increase in the Rayleigh intensity, typical of central-peak behavior, is predicted.

Neutron-scattering study of SrTiO3under [111] uniaxial stress

The anitferrodistortive phase transitions in uniaxially [111]-stressed SrTi${\mathrm{O}}_{3}$ were investigated by means of elastic and inelastic neutron scattering. From elastic intensity measurements at the ($\frac{3}{2},\frac{1}{2},\frac{\overline{5}}{2}$) and ($\frac{1}{2},\frac{\overline{3}}{2},\frac{5}{2}$) cubic $R$ points, the ${P}_{[111]}\ensuremath{-}T$ phase diagram was obtained in agreement with an earlier EPR determination. In the cubic phase, the effect of stress is to split the triply degenerate ${R}_{25}$ mode into a singlet ($A$) mode, corresponding to octahedra rotations around the stress axis, and a doublet ($E$) mode. Condensation of the $A$ component leads to the stress-induced trigonal phase. The dynamic responses from each of the two components were measured separately in the stressed cubic phase, by means of inelastic scattering at the above-mentioned $R$ points. The experimental line shapes are analyzed in terms of the usual damped oscillator central-peak model. The resulting best-fit values for the $A$- and $E$-mode quasiharmonic frequencies ${\ensuremath{\omega}}_{\ensuremath{\infty}}^{2}$ and central-peak strengths ${\ensuremath{\delta}}^{2}$ are obtained as a function of temperature and compared to the corresponding zero-stress values. In the mean-field range and in the presence of [111] stress the frequencies agree with the prediction of the Landau model and known stress coupling constants. At zero stress, the central-peak behavior is found to be sample dependent. For $Tg{T}_{c}$, this latter result is discussed in the light of recent theories on the coupling of soft modes with slowly relaxing defects.