NMR in Superfluid A-Like Phase of 3He Confined in?Globally Deformed Aerogel in?Tilted Magnetic Field

NMR spectra in superfluid A-like phases confined in axially deformed aerogel in the presence of a magnetic field inclined with respect to deformation axis is considered. The characteristic features of dipole frequency shift in axially compressed and axially stretched cases are compared. In particular, it is shown that in axially stretched aerogel environment the stability region of coherently spin-precessing mode is rather narrow due to the U(1) LIM effect. The spectrum of high-frequency spin fluctuations accompanying coherently precessing spin modes is constructed.     

Phase Transitions of Superfluid 3He in 0.8-μm Slab Geometry

We have studied superfluid ³ He in 0.8 m slab geometry by cw-NMR method. The static magnetic field for NMR was 22 mT and was perpendicularly applied to the surface. At pressures from 5 bar to 27 bar, we observed the negative shifts of NMR frequencies below the transition temperatures. Moreover we observed the fast order phase transition with the supercooling phenomena at lower temperatures, but NMR frequencies did not show a jump as they do at the A-B transition in the bulk liquid. Although the phase at low temperatures seemed to be B-phase, NMR frequencies still had the negative shifts.     

Soliton-Like Spin State in the A-Like Phase of 3He in Anisotropic Aerogel

We have found a new stable spin state in the A-like phase of superfluid ³He confined to intrinsically anisotropic aerogel. The state can be formed by radiofrequency excitation applied while cooling through the superfluid transition temperature and its NMR properties are different from the standard A-like phase obtained in the limit of very small excitation. It is possible that this new state is formed by textural domain walls pinned by aerogel.      

Spin Fluctuations in A-like Superfluid Phase of 3He in Aerogel

The frequency spectrum of the spin fluctuations δ S(t) superimposed on the coherently precessing spin modes in the A-like superfluid phase in aerogel is analysed. It is shown that the low amplitude spin fluctuations could be most easily observed in the case of an uni-axially deformed aerogel. It is demonstrated, in particular, that for axially stretched (radially squeezed) aerogel described by the U(1)LIM model the fourth order harmonic in δ S _z (t) is erased, in contrast with what is expected for the long range Leggett orbital configuration in the ³He-A (ABM state).     

Dispersion-Induced Splitting of the Collective Mode Spectrum in Axial and Planar Phases of Superfluid 3He

The whole collective mode spectrum in axial and planar phases of superfluid ³He with dispersion corrections is calculated for the first time. In axial A-phase the degeneracy of clapping modes depends on the direction of the collective mode momentum k with respect to the vector l (mutual orbital moment of Cooper pairs), namely: the mode degeneracy remains the same as in case of zero momentum k for k‖l only. For any other directions there is a threefold splitting of these modes, which reaches maximum for k ⊥ l. In planar 2D-phase, which exists in the magnetic field (at H>H _C ) we find that for clapping modes the degeneracy depends on the direction of the collective mode momentum k with respect to the external magnetic field H, namely: the mode degeneracy remains the same as in case of zero momentum k for k‖H only. For any other directions different from this one (for example, for k ⊥ H) there is twofold splitting of these modes. The obtained results imply that new interesting features can be observed in ultrasound experiments in axial and planar phases: the change of the number of peaks in ultrasound absorption into clapping mode. One peak, observed for these modes by Ling et al. (J. Low Temp. Phys. 78:187, 1990), will split into two peaks in a planar phase and into three peaks in an axial phase under the change of ultrasound direction with respect to the external magnetic field H in a planar phase and with respect to the vector l in an axial phase. In planar phase, some Goldstone modes in the magnetic field become massive (quasi-Goldstone) and have a similar twofold splitting under the change of ultrasound direction with respect to the external magnetic field H. The obtained results as well will be useful under interpretation of the ultrasound experiments in axial and planar phases of superfluid ³He.     

Specific Heat Near the Superfluid Transition of a 0.9869 μm 4He Film

We report measurements of the specific heat of ⁴He near the superfluid transition while confined between silicon wafers at 0.9869 m separation. These data are analyzed to check on the behavior expected from correlation-length scaling. Comparison is also made with other data for planar confinement, as well as data for cylindrical confinement. These represent different lower-dimensional crossovers. We find that the present data scale very well above the bulk transition temperature, and in the region immediately below it. Near the specific heat maximum however, the data for planar confinement do not collapse on a universal curve. We compare these results with specific theoretical scaling functions. In particular we find that on the normal side, and for large enough values of the scaling variable, one can describe the data well using the concept of the surface specific heat. The locus of the data in this region agrees well with the most recent theoretical calculations.     

Proximity Effect between a Dirty Fermi Liquid and Superfluid 3He

The proximity effect in superfluid ³He partly filled with high porosity aerogel is discussed. This system can be regarded as a dirty Fermi liquid/spin-triplet p-wave superfluid junction. Our attention is mainly paid to the case when the dirty layer is in the normal state owing to the impurity pair-breaking effect by the aerogel. We use the quasiclassical Green’s function to determine self-consistently the spatial variations of the p-wave order parameter and the impurity self-energy. On the basis of the fully self-consistent calculation, we analyze the spatial dependence of the pair function (anomalous Green’s function). The spin-triplet pair function has in general even-frequency odd-parity and odd-frequency even-parity components. We show that the admixture of the even- and odd-frequency pairs occurs near the aerogel/superfluid ³He-B interface. Among those Cooper pairs, only the odd-frequency s-wave pair can penetrate deep into the aerogel layer. As a result, the proximity-induced superfluidity in a thick aerogel layer is dominated by the Cooper pair with the odd-frequency s-wave symmetry. We also analyze the local density of states and show that it has a characteristic zero-energy peak reflecting the existence of the odd-frequency s-wave pair, in agreement with previous works using the Usadel equation.     

Textures of Rotating Superfluid 3He–A in a Single Narrow Cylinder

We have studied textures of the rotating superfluid ³He–A in a single narrow cylinder by NMR measurement. In a narrow cylinder, the characteristic textures such as Mermin-Ho texture (Mermin and Ho in Phys. Rev. Lett. 36:594, 1976) can be formed in order to minimize the free energy of the system determined by the effect of the wall, the magnetic field, the dipole interaction, the flow of the superfluid and so on. We observed three types of NMR absorption spectra dependent on the processes used to form A-phase in a narrow cylinder. A particular texture shows a characteristic spectrum and we can determine the texture from the observed spectrum by comparing the resonance frequency of the peak in NMR spectrum with the calculated one of the spin wave mode. We present the identification and the phase diagram of textures of the rotating superfluid ³He–A in a single narrow cylinder.     

Developed Capillary Turbulence on the Surface of Normal and Superfluid 4He

The capillary turbulence on the surface of normal and superfluid liquid ⁴He has been studied experimentally. It is observed for the first time that the value of the high-frequency boundary ω _b of the inertial interval increases significantly when liquid helium transits from normal to superfluid state, and that in superfluid He-II the correlation function of the surface deviation from equilibrium state in frequency representation can be described well by a power dependence with the index m close to −4.3.      

The Transition to Turbulent Drag for a Cylinder Oscillating in Superfluid 4He: A Comparison of Quantum and Classical Behavior

We have measured the drag and inertial forces on wire resonators in superfluid ⁴He at millikelvin temperatures. At low velocities the behavior is dominated by the intrinsic properties of the resonators which can be measured in vacuum. On increasing velocity we see a sharp transition corresponding to the sudden appearance of drag and inertial forces arising from quantum vortex lines in the superfluid. We present detailed measurements of the superfluid drag and inertial forces as a function of the resonator velocity. We discuss results for two different wire diameters and for different resonant frequencies. We compare and contrast the observed behavior with that measured for cylinders in oscillating classical fluids.     

Transverse Acoustic Impedance Measurements for Surface States of Superfluid 3He A1 and A2 Phases

We measured the complex transverse acoustic impedance in both superfluid ³He A₁ and A₂ phases. This impedance is sensitive to surface states. In our preliminary results, the temperature dependence of the impedance in the A₁ phase is similar to that in A phase, and the imaginary part shows an anomaly in the A₂ phase. These anomalies occurred at the temperature defined as T _k , which is lower as the frequency gets higher. The similar frequency dependence of T _k in each phase suggests that the anomaly is attributed to the same origin. The frequency dependence of the T _k /T _c indicates that the shape of the surface density of each spin pair state did not greatly change in the present experimental temperature range.     

Microkelvin Thermometry with Bose–Einstein Condensates of Magnons and Applications to Studies of the AB Interface in Superfluid ^3He

Coherent precession of trapped Bose–Einstein condensates of magnons is a sensitive probe for magnetic relaxation processes in superfluid $^3$ He-B down to the lowest achievable temperatures. We use the dependence of the relaxation rate on the density of thermal quasiparticles to implement thermometry in $^3$ He-B at temperatures below $300\,\upmu $ K. Unlike popular vibrating wire or quartz tuning fork based thermometers, magnon condensates allow for contactless temperature measurement and make possible an independent in situ determination of the residual zero-temperature relaxation provided by the radiation damping. We use this magnon-condensate-based thermometry to study the thermal impedance of the interface between A and B phases of superfluid $^3$ He. The magnon condensate is also a sensitive probe of the orbital order-parameter texture. This has allowed us to observe for the first time the non-thermal signature of the annihilation of two AB interfaces.     

Electrical and Magnetic Properties of the Pr2/3 + xTiO3 ± yPerovskite Phase

The thermoelectric power, electrical resistivity, and magnetic susceptibility of the praseodymium titanium bronze phase Pr_{2/3 + x} TiO_{3 ± y} were measured for compositions in the range 0 x 1/3. The conductivity of the bronze was found to exhibit metallic behavior between 77 and 450 K. The transport data were used to evaluate the electron mobility and Fermi energy. In the range 77–300 K, the magnetic susceptibility of Pr_{2/3 + x} TiO_{3 ± y} consists two contributions—those from Pr³⁺(a strong function of temperature) and Ti³⁺(a weak function of temperature).     

The Effect of AgNO<Subscript>3</Subscript> Addition on the Formation and Superconducting Properties of the Bi2223 Phase

Superconducting samples with nominal composition Bi_1.66Pb_0.34Sr₂Ca₂Cu₂O _x –Ag are prepared by the solid-state reaction method. The samples are characterized by X-ray diffraction and DC electrical resistivity. According to X-ray diffraction patterns of specimens, the highest amount of Bi-(2223) phase along with the minimum amount of Bi-(2212) phase and minimum effect on the crystal structure was accessible in the sample with 10 wt. % of AgNO₃ content. The standard four-probe technique is applied to measure the DC electrical resistivity in the temperature range from 77 to 250 K and the influence of different Ag contents on the normal phase resistance, transition width and critical temperature T _c has been investigated comparatively.     

Mass Coupling and Q ?1 of Impurity-Limited Normal 3He in?a?Torsion Pendulum

We present results of the Q ^?1 and period shift, ??P, for ³He confined in a 98% nominal open aerogel on a torsion pendulum. The aerogel is compressed uniaxially by 10% along a direction aligned to the torsion pendulum axis and was grown within a 400???m tall pancake (after compression) similar to an Andronikashvili geometry. The result is a high Q pendulum able to resolve Q ^?1 and mass coupling of the impurity-limited ³He over the whole temperature range. After measuring the empty cell background, we filled the cell above the critical point and observe a temperature dependent period shift, ??P, between 100?mK and 3?mK that is 2.9% of the period shift (after filling) at 100?mK. The Q ^?1 due to the ³He decreases by an order of magnitude between 100?mK and 3?mK at a pressure of 0.14??0.03?bar. We compare the observable quantities to the corresponding calculated Q ^?1 and period shift for bulk ³He.     

Integral as a Function of the Upper Limit to Solve Axial Symmetrical Rod Drawing and Extrusion

A kinematically admissible velocity field which is different from Avitzur's has been proposed for axialsymmetrical rod drawing and extrusion.An upper-bound analytical solution in cylindrical coordinates hasbeen obtained without any mathematical simplification in this paper.     

Phase Transitions and Ferroelectric and Superionic Properties of K3Nb3B2O12–K3Nb3Si2O13 Single Crystals

Data are presented on K₃Nb₃O₆(B₂O₆)_1–x (Si₂O₇) _x solid solutions in the K₃Nb₃B₂O₁₂–K₃Nb₃Si₂O₁₃ system. The system is shown to contain two partial solid-solution series in the composition ranges 0 < x< 0.2 (KNB:Si) and 0.8 < x< 1 (KNS:B). KNB:Si crystals are grown from off-stoichiometric melts, and their polymorphism and physical properties are studied. Similar to K₃Nb₃B₂O₁₂, KNB:Si crystals exhibit a complex polymorphism and combine ferroelectric, ferroelastic, and superionic properties. Si substitution for B is shown to have a significant effect on the phase-transition temperatures and electrical properties of K₃Nb₃B₂O₁₂ crystals. The results obtained for K₃Nb₃Si₂O₁₃ crystals demonstrate that, in spite of their hexagonal habit, their room-temperature structure possesses orthorhombic or lower symmetry. The room-temperature dielectric permittivity ₃₃ of K₃Nb₃Si₂O₁₃ crystals is as high as 4000.     

Superfluid fraction of4He from 1.5 K toT λ(P) and from vapor pressure to the melting curve

New measurements of the first-, second-, and fourth-sound velocities are reported and used to obtain the superfluid fraction _s / at pressures from vapor pressure to the melting curve and from 1.5 K to within 1% of the superfluid transition temperatureT (P). Close toT , the new results agree very well with previous measurements by Greywall and Ahlers. At low temperatures they agree well with the tabulations by Maynard; but in the range within 10% or so ofT (P) and at the higher pressures they differ from Maynard's values by several percent.     

The Interpretation of Phase-Slip and Critical-Velocity Data from the Flow of Superfluid 4He through a 2 μm by 2 μm Aperture

An analysis has been made of phase-slip and critical-velocity data for both the ac and dc flow of superfluid ⁴ He through a 2 m by 2 m aperture in a 0.1-m-thick titanium foil between 0.36 and 2.10 K. Single-2 phase slips were resolvable over the entire range of temperature in the ac flow measurements, carried out between 10 and 20 Hz, making it possible to determine the width of the critical-velocity distribution throughout the temperature range from these measurements. These data have been interpreted in terms of the thermal nucleation of vortex half-rings at the walls of the aperture, involving a velocity- and temperature-dependent energy barrier. The barrier can be modeled with moderate success using an approach close to that of Avenel and Varoquaux and coworkers.     

Considerations Relating to Type 1 and Type 3 Non-uniqueness in SPRT Interpolations of the ITS-90

It is well known that different allowed interpolations using a given standard platinum resistance thermometer (SPRT) in overlapping subranges of the ITS-90 do not lead to identical results. This is termed Type 1 non-uniqueness, or subrange inconsistency (SRI), and it arises because of small incompatibilities in the SPRT characteristic \(W(T_{90})\) with respect to the ITS-90 reference function \(W_{r}(T_{90})\), such that the alternative low-order interpolations, fitted to the deviations \(W(T_{90})\) – \(W_{r}(T_{90})\) at different sets of fixed points, are not in general identical. To some extent SRI may be ‘scale-intrinsic,’ i.e., caused by incompatibilities between the resistance ratios, \(W_{r}(T_{90})\), specified at the fixed points of the ITS-90, and hence the same for all SPRTs. However, it has been found that the SRI varies strongly between different SPRTs, and that variability of \(W(T_{90})\) is much the dominant cause. This raises the question of how SRI is linked to Type 3 non-uniqueness between SPRTs in each separate subrange, which is entirely due to differences in SPRT characteristics. This paper explores the connection between them and concludes that they are of similar magnitude and consequently, being different manifestations of the same effects, it is argued that non-uniqueness should be covered by a single component of uncertainty. Following the stated rationale of the ITS-90, it is further suggested that this uncertainty should be estimated only within each subrange, i.e., that shorter subranges should not be deemed subject to potential effects caused by out-of-range data.