Soliton-Limited Superflow in 3He-A Between Parallel Plates

We have studied theoretically the flow of superfluid ³ He-A in parallel-plate geometry. The equilibrium order-parameter texture is calculated numerically in two spatial dimensions consisting of the coordinates along the flow direction and perpendicular to the plates. The calculations have been done using the hydrostatic theory in the Ginzburg-Landau region and assuming a large external magnetic field perpendicular to the plane of calculation. We have studied a uniform texture and a dipole-unlocked splay soliton as initial configurations. In the former case we find the Freedericksz transition and a helical instability with increasing flow. In the latter case we find instability in the soliton. This instability is closely related to the critical velocity in the presence of a vortex sheet. Also, the transverse NMR frequency shift at the soliton has been calculated.     

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.     

NMR and axial magnetic field textures in stationary and rotating superfluid3He-B

We have performed NMR measurements on the flare-out texture of superfluid³He-B in a cylindrical container of 5 mm diameter in axial magnetic fields of 28.4 and 56.9 mT. The transverse cw NMR spectra have been analyzed both with respect to their overall shape and the spin-wave absorption peaks close to the Larmor frequency. Our analysis of the stationary state spectra, based on texture computations, yields the longitudinal resonance frequency v _L (T), the magnetic healing length _H (T), and the dipolar length _D (T), which we report for pressures below 29 bar. A lattice of quantized vortex lines appears in the rotating state, and two additional textural free energy terms have to be included in the analysis. One of the terms is linear in the applied magnetic field and arises from the spontaneous magnetization of the vortex cores. The second term is quadratic in magnetic field; it is generated both by the superflow field v _s (r) about the vortex core and the difference in the induced magnetizations of the vortex-core and the bulk superfluids. The rotational orienting effects have been studied for rotation speeds up to 2red/sec.     

Nuclear magnetic resonance of3He superfluid confined in high porosity aerogel

We report pulsed nuclear magnetic resonance (NMR) measurements of the transverse frequency and magnetization of³ He confined in aerogel with 98.2% open volume porosity. A homogeneous superfluid phase is observed at pressures, P > 12 bar, accompanied by a sharp onset of frequency shifts showing little or no textural broadening; a result quite unexpected for³He confined in random porous media. The transition temperatures and order parameter are both significantly suppressed from their bulk values and the magnetization data indicate this low temperature phase is an equal-spin pairing superfluid. For NMR tipping angles greater than 40 ° the resonance frequency drops abruptly to the normal state value. This tip angle dependence is not consistent with either the bulk³He-A or³He-B superfluid phases.     

Relaxation of Bose-Einstein Condensates of Magnons in Magneto-Textural Traps in Superfluid 3He-B

In superfluid ³He-B externally pumped quantized spin-wave excitations or magnons spontaneously form a Bose-Einstein condensate in a 3-dimensional trap created with the order-parameter texture and a shallow minimum in the polarizing field. The condensation is manifested by coherent precession of the magnetization with a common frequency in a large volume. The trap shape is controlled by the profile of the applied magnetic field and by the condensate itself via the spin-orbit interaction. The trapping potential can be experimentally determined with the spectroscopy of the magnon levels in the trap. We have measured the decay of the ground state condensates after switching off the pumping in the temperature range (0.14÷0.2)T _c. Two contributions to the relaxation are identified: (1) spin diffusion with the diffusion coefficient proportional to the density of thermal quasiparticles and (2) the approximately temperature-independent radiation damping caused by the losses in the NMR pick-up circuit. The measured dependence of the relaxation on the shape of the trapping potential is in a good agreement with our calculations based on the magnetic field profile and the magnon-modified texture. Our values for the spin diffusion coefficient at low temperatures agree with the theoretical prediction and earlier measurements at temperatures above 0.5T _c.     

The development of an NMR spectrometer for the precision determination of the ratio of the resonance frequencies of nuclei

A nuclear magnetic resonance (NMR) spectrometer for determining the resonance frequencies of various nuclei at a magnetic field induction of 2.142 T is described. The spectrometer enables the NMR frequency of a nucleus to be recorded simultaneously with the frequency of the signal from a comparison nucleus and enables the magnetic field to be stabilized using the NMR signal from a third nucleus. The ratios of the resonance frequencies of protons and of the lithium-7 nuclei: F(H₂O)F(⁷Li) = 2.573041789(3) are obtained for a solution of lithium chloride in water, and also the ratio for protons and deuterons of an isotopic solution of water: F(H₂O)/F(D₂O) = 6.514399603(2). Methods of determining the systematic errors which occur when there are quadratic gradients of the magnetic field in the sample when processing spectral numerical data matrices are discussed.     

Vortices in 3He-A in a weak magnetic field

The structure and the energy of vortices in rotating ³He-A are considered in the presence of a weak magnetic field. It is shown, using the logarithmic approximation for the free energy, that there will be a sequence of textural transitions when the magnetic field is increased. The transition from a nonsingular texture to a singular texture is studied in detail. It is shown that the l vector is almost uniform outside the cores of vortices. To verify these results, measurements by NMR and by ultrasound are suggested.This work has been financially supported by the Academy of Science of the USSR, by the Academy of Finland, and by the Committee of Scientific and Technical Cooperation between Finland and the USSR.     

Experimental determination of the\hat n-texture of superfluid3He-B in a cylinder

The texture formed in a 2mm diameter cylinder of superfluid³He-B has been studied by continuous wave NMR near T_c. The experiments were performed at low pressures (0.82 and 2.89 bar) and using an axial magnetic field of 286 G to preserve the cylindrical symmetry of the texture. A method of deconvolution of the NMR lineshapes is presented along with the texture map obtained from the data. The texture resembled the calculated flare-out texture although differing in details including the existence of an azimuthal component to (r). By comparison to the Ginzburg-Landau expressions expected to hold near T_C, the magnetic bending length of R_CH_B=37(1–T/T_c)^1/2 cm G was found, verifying the Ginzburg-Landau prediction.     

Magnetic field dependence of the Leggett angle,the susceptibility,and the longitudinal nuclear magnetic resonance of3He-B

The magnetic field dependences of the Leggett angle, the susceptibility, the free energy, and the longitudinal NMR frequency of³He-B are calculated from a generalized weak coupling theory. Employing the experimental values for the Landau parametersF ₀ ^a andF ₂ ^a , reasonable agreement with the susceptibility data measured recently by Hoyt, Scholz, and Edwards is obtained. Substantial field dependence of the Leggett angle and the longitudinal NMR frequency is predicted.     

NMR in flowing superfluid 3He

The effects of flow on the NMR absorption in the A and B phases of ³He have been studied. While no flow-induced changes in the absorption were seen in the B phase, a variety of phenomena were observed in the A phase. The phenomena include the development of time-dependent satellite peaks, height reductions of the signal, and a splitting of the signal, with a fraction of the signal shifting to lower frequencies. These effects are described and discussed in light of the existing theoretical models. In addition, the NMR shift in the static B-phase liquid confined between 135-m-spaced parallel plates has been measured as a function of temperature and the angle between the magnetic field and the plates. These results are compared with previous measurements and are found to be in good agreement. Finally, two effects observed in the static liquid, the disappearance of the B-phase signal under certain conditions and the splitting of the A-phase signal, are described.Research supported by the National Science Foundation.     

Spin Diffusion Measurements in Spin-Polarised Liquid 3He-4He Mixtures

We report on investigations of spin diffusion in isotopic helium liquid mixtures using a multi-echo technique in applied magnetic field gradients. Samples (up to 1 cm ³ in volume) are obtained by liquefaction of optically polarised gas. NMR measurements are performed at saturated vapour pressure in a low magnetic field (2.2 mT). Signal-to-noise ratios stay high down to ³ He concentrations of order a few parts per thousand at 1K for instance. We demonstrate that the experimental accuracy of spin diffusion measurements is substantially improved using optically polarised mixtures. We have observed that the dynamics of the precession of the transverse magnetisation can be altered due to large dipolar fields at high magnetisation densities. Effects on spin-echo signals and implications for the extension of spin diffusion measurements with our technique are discussed.     

Hartmann flow over a permeable bed

Hartmann flow past a permeable bed is investigated in the presence of a transverse magnetic field with an interface at the surface of the permeable bed. The flow above the bed, called Zone 1, is governed by the Hartmann equation and that below the bed, called Zone 2, is governed by the modified Darcy law. Solutions for these two zones are separately obtained and are matched at the interface using suitable boundary conditions. The mass efflux, change in volume rate of flow, the induced magnetic field and current density are evaluated to determine whether a magnetic method might be potentially useful in the study of pore-size distribution.We find that, for mercury flowing over a long permeable channel of width 0.7 cm, the effect of magnetic field (of strength 0.25 Web/m², i.e. the Hartmann number M = 8.8) in the presence of a porous wall (of porosity k = 5 × 10^?6 Darcy) is to retard the mass flow and to increase the friction factor relative to the corresponding quantities for non-magnetic flow. The amount of retardation is 22 per cent more than that obtained by Wallace et al. [12] in the experiments on the flow of mercury in porous media in a transverse magnetic field. Since the magnitude of retardation is related to the pore size distribution, our model is potentially useful to study the pore size distribution than that of Wallace et al. [12]. In addition, transition to turbulence occurs at a higher Reynolds number owing to the presence of a magnetic field.     

A heterodyne laser system to study frequency stabilized Zeeman 633 nm He-Ne lasers deficient in temperature steadiness

A heterodyne laser system is constructed to study the effect of external transverse magnetic field on the dynamic instability of internal mirror TEM_00q He-Ne lasers having temperature instability. The system could provide precise detailed knowledge about the roles of both the temperature and the applied magnetic field separately. Two different internal mirror 633 nm TEM_00q He-Ne lasers with frequency stability of 10⁻⁶ are studied. The applied transverse magnetic field on He-Ne lasers increased the frequency stability to be in the order of ∼10⁻¹⁰, in spite of temperature instability. In the same time, a single-mode operation with an enhanced laser output power is obtained. The sensitivity of the method showed that the laser exhibits a short-term frequency stability of 4.7×10⁻¹⁰, which after one minute, when mode collapse starts, decreased to 2.6×10⁻⁸, over the next four minutes. This increase in the frequency difference of the inter-mode beat signal that affect the stability is attributed to the uncontrolled temperature of the laser tube. The results revealed that the magnetic field plays the dominant role to achieve the maximum frequency stability, while the unsteadiness of temperature of the laser tubes limits the long term single-mode laser operation.     

Field-induced surface texture in 3He-A in the presence of superflow

The effect of superflow on the magnetic field-induced surface texture in ³He-A is studied theoretically. We find that in the presence of small superflow the surface texture becomes nonplanar. The NMR satellite frequencies associated with the surface texture are obtained.Supported by National Science Foundation grant No. DMR76-21032.     

Study of mode structure of a 612 nm He-Ne laser in a transverse magnetic field

We studied the mode structure of a 612 nm He-Ne laser in a transverse magnetic field. The study showed that a mode coupling results in a collapse into a single mode operation of the laser at a magnetic field strength of approximately 267 Gauss. It was also found that the mode collapse lasted for a period of 160 s and the overall laser power was slightly increased from 500 to 535 μW. The calculated frequency stability during the time of mode collapse was 3×10⁻⁷ at room temperature.     

Magnetic field dependence of ac losses in multi-filamentary superconducting wires

The magnetic field dependence of ac losses due to nonlinear flux penetration into superconducting filaments, ie, nonlinearity between an applied magnetic field and a penetrated flux, has been studied experimentally for multi-filamentary superconducting wires with Nb-Tl filaments and Cu matrix. In order to observe this effect, ac loss measurements were extensively carried out for the cases of applied transverse ac magnetic fields ranging from 0.06 to 50 Hz in frequency and from 10^?3 to 0.2 T in amplitude. Shifting of the frequency corresponding to the peak of the eddy current loss with the amplitude of applied magnetic fields was revealed experimentally. The results obtained were explained by taking into account the magnetic field dependence of the effective permeability of the wire originated from nonlinear flux penetration into superconducting filaments. The associated frequency dependence of the hysteresis loss is also discussed.     

NMR Line Shape of Rotating 3He-B at Large Counterflow Velocity

We have investigated the NMR line shapes of superfluid ³He-B in a rotating cylinder. In the vortex-free state at sufficiently large angular velocity of rotation, 1 rad/s, the main feature of the absorption spectrum is a large frequency-shifted peak above the Larmor frequency. The shape of this counterflow peak is both measured and calculated as a function of external magnetic field strength, angular velocity, temperature, and number of vortex lines. The NMR spectrum is derived from the calculated order-parameter texture. Reasonable agreement with the measured line shape is obtained by including line-broadening effects due to the external field inhomogeneity and Leggett–Takagi relaxation.     

Spin Dynamics of 3He in Aerogel

We report continuous-wave NMR measurements on superfluid ³ He contained inside high porosity aerogel at 3.24 MPa, in a 28.4 mT magnetic field, and down to 0.9 mK. Three different purities of ³ He were used: pure ³ He, ³ He with enough ⁴ He to replace the first localized layer, and ³ He with enough ⁴ He to replace both localized layers. Below 2.26mK, the NMR spectrum does not consist of a single Lorentzian, but a distribution of NMR resonant frequencies both above and below the Larmor frequency, _L . Upon cooling, the component of the spectrum at frequencies below the Larmor frequency moves to higher frequencies over a narrow temperature range and does not return to < _L upon warming. The higher frequency component of the spectrum displays two resolvable peaks which become a complex structure upon removal of the localized ³ He spins. The spectrum changes as the magnetic field is rotated about the axis of the aerogel sample, indicating that the ³ He is able to detect a preferred direction in the aerogel. The shape of the spectrum shows no rotation or magnetic field hysteresis. We find that the average frequency shifts of our NMR spectra do not depend on the presence of the localized ³ He spins. These frequency shifts and the presence of a temperature-independent magnetization for the liquid ³ He suggest that the aerogel stabilizes a single equal-spin-pairing state in our experiments.     

NMR Manifestations of Nuclear Anapole Moments

We suggest to use insulating garnets doped by rare-earth ions for measurements of nuclear anapole moments. A parity violating shift of the NMR frequency arises due to the combined effect of the lattice crystal field and the anapole moment of the rare-earth nucleus. We show that there are two different observable effects related to frequency: (a) shift of the NMR frequency in an external electric field applied to the solid; the value of the shift is about Δν₁ ∼ 10⁻⁵ Hz with E = 10 kV/cm, and (b) splitting of the NMR line into two lines. The second effect is independent of the external electric field. The value of the splitting is about Δν₂ ∼ 0.5 Hz; it depends on the orientation of the crystal with respect to magnetic field. Both estimates are presented for the magnetic field of about 10 T.