Off-center Motion Research Articles

Insight into the low-temperature electrical polarization behavior of multiferroic Bi2Fe4O9

Structure, dielectric and pyroelectric properties are investigated for polycrystalline Bi2Fe4O9 ceramics. Antiferromagnetic transition is observed at ∼249 K during the dielectric measurement. Various pyroelectric characterization verifies the current peak at ∼144 K dominantly related to intrinsic ferroelectric transition and the other one because of intrinsic relaxation in the vicinity of ∼280 K, respectively. As confirmed by in-situ Raman measurement under varying temperature and electric field, the ferroelectric polarization at lower temperature is mainly ascribed to structural distortion in Fe1O4 tetrahedron reflected by Fe1–O vibrations at mode of 206 cm−1. The relaxation at higher temperature is originated from the off-center motion of Fe ions due to dipole reorientation shown as the stretching of O atom along c-axis at mode of 554 cm−1. Our study definitely presents the existence of intrinsic ferroelectric order below room temperature, which provides the supplementary reference for subsequent research on Bi2Fe4O9.

Off-center motion of a trapped elastic capsule in a microfluidic channel with a narrow constriction.

Owing to their significance in capsule-related engineering and biomedical applications, a number of studies have considered the dynamics of elastic capsules flowing in constricted microchannels. However, these studies have focused on capsules moving along the channel centerline. In the present study, we numerically investigate the transient motion of an elastic capsule in a microfluidic channel with a rectangular constriction, which is initially trapped at the constriction inlet while off the channel centerline (i.e., on the channel bottom-wall). Under the push of the surrounding flow, the capsule can squeeze into the constriction, but only if the capsule deformability or the constriction size is sufficiently large. We find that the critical capillary number leading to the penetration of the capsule into the constriction is larger for off-centerline capsules compared to centered capsules. The centered capsule is stationary at the steady state when it remains stuck at the constriction; in contrast, the off-centerline capsule is not stationary but exhibits a tank-treading motion, i.e., its overall shape maintains a nonspherical shape with a protrusion into the constriction while its membrane exhibits a continuous rotation. Further, we examine the dependence of the capsule motion type, capsule deformation degree and membrane tension distribution on the capillary number (measuring the effects of flow strength and membrane mechanics) and constriction geometries (including the constriction height and width). Finally, we discuss the mechanism governing the capsule motion by analyzing the hydrodynamic forces acting on the capsule. The shear force acting on the capsule top owing to the fluid flow in the gap between the capsule top and the channel top-wall is the main source inducing the membrane tank-treading rotation.

QCD phase-transition and chemical freezeout in nonzero magnetic field at NICA

Because of relativistic off-center motion of the charged spectators and the local momentum-imbalance experienced by the participants, a huge magnetic field is likely generated in high-energy collisions. The influence of such short-lived magnetic field on the QCD phase-transition(s) shall be analysed. From Polyakov linear-sigma model, we study the chiral phase-transition and the magnetic response and susceptibility in dependence on temperature, density and magnetic field strength. The systematic measurements of the phase-transition characterizing signals, such as the fluctuations, the dynamical correlations and the in-medium modifications of rho-meson, for instance, in different interacting systems and collision centralities are conjectured to reveal an almost complete description for the QCD phase-structure and the chemical freezeout. We limit the discussion to NICA energies.

Quantifying local and cooperative components in the ferroelectric distortion of BaTiO(3): learning from the off-center motion in the MnCl(6)(5-) complex formed in KCl:Mn(+).

The delicate balance between cooperative and local contributions in the ferroelectric distortions of BaTiO3 is explored by means of ab initio calculations. As a salient feature, it is found that a single Ti(4+) ion in BaTiO3 is not allowed to move off-center at ambient pressure, while this is no longer true if the lattice is expanded by only ∼5%, stressing the high sensitivity of the local contribution to chemical and hydrostatic pressures. In order to further understand the effect of local contributions on the phase transition mechanism of ferroelectrics, we have investigated the surprising C3v → C4v → Oh local transformations occurring in the 10-50 K temperature range for the MnCl6(5-) complex formed in KCl:Mn(+) that mimic the behavior of BaTiO3. From Boltzmann analysis of the vibronic levels derived from ab initio calculations and considering decoherence introduced by random strains, the present calculations reproduce the experimental phase sequence and transition temperatures. Furthermore, our calculations show that the off-center instability in KCl:Mn(+) would be suppressed by reducing by only 1% the lattice parameter, a situation that then becomes comparable to that found for BaTiO3 at ambient pressure. The present results thus stress the deep link between the structural phase transitions of ferroelectric materials and local phase transitions displayed by transition-metal impurities in insulators.

Lattice instability and elastic dispersion due to the rattling motion in the type-I clathrate Ba8Ga16Sn30

To investigate the off-center rattling motion and its charge-carrier dependence in type-I clathrate compounds, we carried out ultrasonic measurements on type-I Ba${}_{8}$Ga${}_{16}$Sn${}_{30}$ and a reference compound, K${}_{8}$Ga${}_{8}$Sn${}_{38}$. We found elastic softening of ${C}_{44}$ originating from a lattice instability due to the off-center rattling motion of Ba atom in Ba${}_{8}$Ga${}_{16}$Sn${}_{30}$. Elastic softening below 1 K suggests that the lattice instability remains at very low temperatures. We also found ultrasonic dispersion which has no mode selectivity. No-mode-selective ultrasonic dispersion in Ba${}_{8}$Ga${}_{16}$Sn${}_{30}$ would be caused by a strong electron-phonon coupling. No charge-carrier dependence is observed between $n$-type and $p$-type Ba${}_{8}$Ga${}_{16}$Sn${}_{30}$. The significant softening on the bulk modulus in Ba${}_{8}$Ga${}_{16}$Sn${}_{30}$ contrasts to the continuous hardening in K${}_{8}$Ga${}_{8}$Sn${}_{38}$, indicating the central role of the rattling motion in the softening.

Emergence of Elastic Softening in Sr8Ga16Si30-xGexwith Increasing Ge Concentration

We have carried out an ultrasonic spectroscopy for the single crystals of Sr 8 Ga 16 Si 30- x Ge x with x = 0, 15, 20, 24, and 30 in order to investigate cage-size dependence of elastic moduli. We present here the temperature dependence of transverse modulus C 44 at various ultrasonic frequencies measured by using a pulse-echo type phase comparison technique. The C 44 mode of the sample with x = 30 shows remarkable elastic softening below 100 K. In contrast, no softening is detected in the C 44 mode of the samples with x = 0 and 15. We found clear correlation between the off-center motion of guest atoms and the elastic softening.

Elastic Constants of Filled Skutterudite LaRu4As12

Ultrasonic measurements with frequencies varying between 73 and 160 MHz were performed for the LaRu4As12 single crystal. This As-based filled skutterudite compound is a BCS-type superconductor with Tsc as high as 10.3 K. In order to examine a presence of off-center rattling motion in LaRu4As12, we measured elastic constants CL111 = (C11 + 2C12 + 4C44)/3 and CT111 = (C11 – C12 + 4C44)/3, which are related to longitudinal and transverse sound waves propagating along the [111] direction, respectively. No ultrasonic dispersion was found in the whole temperature range from 1.4 to 300 K.

Ultrasonic investigation of off-center rattling inPr0.55Nd0.45Os4Sb12

Abstract Ultrasonic measurements on a Pr 0.55 Nd 0.45 Os 4 Sb 12 single crystal for temperature down to 20 mK and frequencies up to 245 MHz were performed in order to investigate off-center rattling motion of rare-earth ions. The elastic constant C 11 exhibits double ultrasonic dispersions at ~ 15 and ~ 40 K , which are similar to the features found in NdOs 4 Sb 12 . The estimated activation energy E 1 = 240 K , corresponding to the 40 K-dispersion, possesses an intermediate value between PrOs 4 Sb 12 ( E 1 = 115 K ) and NdOs 4 Sb 12 ( E 1 = 337 K ).

Relaxations as Key to the Magnetocapacitive Effects in the Perovskite Manganites

We present a detailed dielectric study of the relaxation effects that occur in several perovskite rare-earth manganites, including the multiferroics TbMnO(3) and DyMnO(3). We demonstrate that the strong magnetocapacitive effects, observed for electrical fields E parallel c, are nearly completely governed by magnetic-state induced changes of the relaxation parameters. The multiferroic materials, which undergo a transition into a spiral magnetic state, show qualitatively different relaxation behavior than those compounds transferring into an A-type antiferromagnetic state. We ascribe the relaxations in both cases to the off-center motion of the manganese ions, which in the multiferroic systems also leads to the ferroelectric ordering.

Ultrasonic Investigation of Off-Center Rattling in Filled Skutterudite Compound NdOs4Sb12

The off-center rattling of Nd rare-earth ions in the filled skutterudite compound NdOs 4 Sb 12 has been investigated by ultrasonic measurement. The longitudinal C 11 mode for frequencies between 34 and 253 MHz shows a marked frequency dependence in elastic constant and ultrasonic attenuations at two different temperatures centered at around 45 and 15 K. The relaxational frequency dependence of ultrasonic dispersion reveals a thermally activated Γ 23 -type off-center motion of Nd-ions, involving local charge fluctuations with Γ 23 symmetry in the (OsSb 3 ) 4 cage. An attempt time τ 0,(1) =7.5×10 -12 s and an activation energy E 1 =337 K were obtained from fits to the dispersion at around 45 K. The presence of another dispersion at lower temperatures of around 15 K implies that the rattling in NdOs 4 Sb 12 has an additional low-energy excitation characterized by a lower activation energy E 2 ∼67 K with an attempt time τ 0,(2) =5.1×10 -11 s.

Ultrasonic study of rattling and tunneling in clathrate compounds [formula omitted] (R=La, Ce; X=Si, Ge)

We have carried out an ultrasonic measurement to investigate an off-center motion of a rare-earth ion in clathrate compounds R 3 Pd 20 Si 6 and R 3 Pd 20 Ge 6 . In R 3 Pd 20 Ge 6 , an elastic constant C 44 shows an ultrasonic dispersion around 10–30 K. This is caused by thermally activated rattling of the rare-earth ion over an anharmonic potential in the cage. In addition, the C 44 of La 3 Pd 20 Ge 6 exhibits a remarkable softening proportional to 1 / T below 3 K down to 20 mK. This result indicates the tunneling state of the rare-earth ion through the potential barrier. On the other hand, the C 44 of La 3 Pd 20 Si 6 and Ce 3 Pd 20 Si 6 shows no ultrasonic dispersion indicating the absence of the rattling.

Quadrupolar susceptibility of [formula omitted

Elastic constants of filled-skutterudite NdOs 4 Sb 12 single crystals have been investigated by means of ultrasonic measurements. Transverse C 44 and longitudinal C 11 modes show Curie-type softening, which is proportional to the reciprocal temperature from 10 K down to 0.9 K . This softening can be explained in terms of the quadrupolar susceptibility modified by crystalline electric field with a Γ 8 quartet ground state in O h symmetry. The C 11 mode also shows a broad shoulder and a small dip around 45 and 13 K , respectively. A Debye-type frequency dependence of the anomalies in the longitudinal C 11 mode resembles an ultrasonic dispersion in PrOs 4 Sb 12 , which is expected to be due to the “rattling” effect, a thermally activated off-center motion of the rare-earth atom in the Sb-cage.

Quadrupole fluctuation and off-center rattling motion in heavy fermion superconductor PrOs 4Sb 12

We have made ultrasonic measurements on a filled skutterudite PrOs 4Sb 12 showing a heavy Fermion superconductivity at T C = 1.85 K . The elastic constants ( C 11 - C 12 ) / 2 and C 44 of PrOs 4Sb 12 exhibit low-temperature softenings below 20 K down to T C , indicating a quadrupole fluctuation of Pr 3 + ion. A minimum of ( C 11 - C 12 ) / 2 in magnetic fields along the [1 1 0] direction around 8 T shows a level crossing of one of a excited Γ 4 ( 2 ) triplet to a ground state Γ 1 singlet. An ultrasonic dispersion in ( C 11 - C 12 ) / 2 around 30 K suggests a thermally activated off-center rattling of Pr ion in a cage of Sb-icosahedron. The observed relaxation time shows the Arrhenius-type temperature dependence τ = τ 0 exp ( E / k B T ) with an attempt time τ 0 = 8.8 × 10 - 11 s and an activation energy E = 168 K . The charge fluctuation of the off-center motion and the quadrupole fluctuation of the 4f electron may participate in the formation of the heavy fermion and the superconductivity in PrOs 4Sb 12.

Cu2+impurities in fluorite-type crystals: Mechanisms favoring an off-center motion

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">Cu</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>impurities in fluorite-type crystals: Mechanisms favoring an off-center motion

Quadrupolar effect and rattling motion in the heavy-fermion superconductorPrOs4Sb12

The elastic properties of a filled skutterudite PrOs_4Sb_{12} with a heavy Fermion superconductivity at T_C=1.85 K have been investigated. The elastic softening of (C_{11}-C_{12})/2 and C_{44} with lowering temperature down to T_C indicates that the quadrupolar fluctuation due to the CEF state plays a role for the Cooper paring in superconducting phase of PrOs_4Sb_{12}. A Debye-type dispersion in the elastic constants around 30 K revealed a thermally activated Gamma_{23} rattling due to the off-center Pr-atom motion obeying tau=tau_{0}exp(E/k_{B}T) with an attempt time tau_0=8.8*10^{-11} sec and an activation energy E=168 K. It is remarkable that the charge fluctuation of the off-center motion with Gamma_{23} symmetry may mix with the quadrupolar fluctuation and enhance the elastic softening of (C_{11}-C_{12})/2 just above T_C.

Big off-center displacements of ions in insulators: The Jahn-Teller ionNi+inCaF2

The big off-center displacement along directions observed for Ni + in CaF 2 is explored through density functional theory (DFT) calculations on a NiF 8 Ca 1 7 + 12 cluster, placing the Ni + ion at different (0,0,z) points. For supporting the results additional calculations on clusters with a total of 51, 99, and 107 atoms have also been carried out. In a first step calculations have been performed for the (xy) 5 / 3 (xz) 5 / 3 (yz) 5 / 3 configuration where the three xy,xz, and yz antibonding crystal-field levels (degenerated in cubal geometry) are forced to have the same electronic occupancy. While the energy minimum for this configuration of NiF 8 Ca 1 7 + 12 appears at z = 0, it is found, however, at z 0 =1.07 A when the unpaired electron is fully located on the b 2 orbital transforming like xy. The z 0 values obtained for clusters with 51 (z 0 = 1.13 A), 99 (z 0 =1.17 A) and 107 (z 0 = 1.17 A) atoms outline the small dependence of the phenomenon on cluster size. This big off-center motion, which concurs with electron paramagnetic resonance data, is shown to arise mainly from a delicate balance between an electrostatic barrier, avoiding the impurity displacement and the energy gained through bonding on passing from eightfold to fourfold coordination. Following this analysis an increase of the lattice parameter and a diminution of ligand electronegativity both favor the off-center motion of d 9 ions in lattices with fluorite structure. First DFT calculations by means of a 21-atom cluster lead in fact to an off-center motion for Ag 2 + and Cu 2 + in SrCl 2 , while both ions would be on center in CaF 2 , these results being in agreement with experimental findings. At variance with the normal situation for on-center 3d impurities the energy minimum for the crystal-field excited state corresponding to the xy → x 2 -y 2 transition is found at z=0, thus involving a huge displacement with respect to the ground state. To our knowledge this DFT study is the first one on off-center d 9 ions in CaF 2 -type lattices. The present results stress that the phenomenon though subtle can be understood with a modest computational effort.

Torque Sensor based on Magnetostrictive Effect for Automobile Engine

A miniature torque sensor based on magnetostrictive effect, has been developed to be mounted inside an automobile engine (TOYOTA 4A-FE; 1.6-liter 4-cylinder). The sensor was installed in a last main bearing of the engine crankshaft so as to directly detect the torque generated by engine. This sensor was composed of two magnetic head-type elements, which were placed opposite to each other through the crankshaft in order to eliminate the influence of the off-center motion of the shaft on the sensor output. Furthermore, a commercial crankshaft made of cast nodular iron (JIS standard: FCD70) was adopted, taking account of high sensor sensitivity and mechanical stiffness.It was confirmed by tests on an engine-dynamometer arrangement that this sensor could clearly detect instantaneous torque waveform with four peaks during two crankshaft rotations, corresponding to four cylinder combustions, and peculiar torque fluctuation due to engine lean burn. In addition, it was found that true torque produced by engine could be detected in in-vehicle experiment. This sensor is useful for various automobile applications.

磁歪効果による磁気ヘッド型トルクセンサ

A magnetic head type torque sensor has the following advantages; easiness of incorporation, noncontact detection, high sensitivity, small size and light weight. On the other hand, two major issues to be considered on this type of sensor are the strong dependence of the sensor output on variation of gap between the sensor head and a torque transmitting shaft due to its off-center motion, and the fluctuation of the sensor output around a circumference of the shaft due to heterogeneousness of magnetic properties on the shaft surface.Two issues described above, have been overcome by means of the correction of the sensor output at each detecting position using the correction coefficients of the sensor sensitivity and the offset output, and the multi-arrangement of sensor heads around the shaft, respectively. Furthermore, it is shown that the dependence of sensor output on temperature is reduced to one seventh in comparison with a conventional single-head type sensor and this sensor is useful for measurement of combustion torque generated by automobile engine.

Possibility of off-center-exciton formation in BaFBr.

Extended-ion calculations have been performed in order to test the possibility of spontaneous off-center motion of excitons in BaFBr. The off-center motion is a mode of decay to F,H centers in the material. The lattice distortion energy is computed self-consistently with the extended-ion method. It is energetically favorable to form off-center excitons displaced roughly 2 a.u. along the molecular axis for fluorine and bromine centers. The fluorine center is stabilized most due to its low-energy F-center ground state.

Excited state dynamics of NaF:Cu+

We have previously used one- and two-photon spectroscopy to characterize the vibronic structures observed for NaF:Cu+ in the excited states of the d 9s configuration. We were able to resolve the zero-phonon lines and a progression of the first three or four quanta of the t1u vibration (involving the off-center motion of Cu+). In the present work we model the line positions and intensities with a mixed quadratic–quartic spherical potential. The spherical potential along with a perturbative treatment of the crystal field describes the members of the 1T2g state progression well. We also semiquantitatively treat the Jahn–Teller effect, operative in the 1Eg state only. The fits indicate the existence of a radial barrier in the potential for the off-center motion of Cu+ in the 1T2g and the 1Eg states of approximate magnitude 1.9 and 73 cm−1, respectively. We also find that the Cu+ ion moves preferentially toward the fluorines rather than between them in the 1T2g state. The derived potential energy surfaces are discussed in terms of the dynamical mixing of the excited 4s and 4p orbitals of Cu+.