Coherent spin precession in a separated solution of 3He in 4He

It is suggested that a coherently precessing spin structure in a normal Fermi liquid should be used to study the interface of two Fermi liquids. It is shown that the interface makes an additional contribution to the attenuation of the precessing structure. This contribution is determined by the kinetic coefficient which relates the magnetization flux across the interface to the magnetization jump at the interface. A relationship is established between this kinetic coefficient and the nature of the scattering of Fermi quasiparticles at the interface. Results of numerical calculations of the attenuation of the structure are presented for a specific object, a separated solution of ³He in ⁴He.     

Experiments on coherently precessing spin state in He---He solution

Pulsed NMR experiments in saturated liquid ³He---⁴He solution were done at temperatures down to 1 mK. The results are well described by a formation of a coherently precessing two-domain structure. In one of these domains the magnetization is oriented along the external magnetic field and in the other domain it is oriented opposite to the field. This structure arises due to spin currents, which are caused by Fermi liquid interaction.     

Spin vortices and stationary spin flows in a normal Fermi liquid

We solve the equations for the collisionless spin dynamics of a normal Fermi liquid, which describe structures resembling spin vortices coherently precessing in a uniform magnetic field. We examine their stability and relaxation, and consider various regimes of stationary magnetization transport along a channel. Zh. éksp. Teor. Fiz. 114, 1266–1283 (October 1998)     

Transverse spin dynamics of a spin-polarized Fermi liquid

A microscopic derivation of the equations of transverse spin dynamics of a spin-polarized Fermi liquid at zero temperature is given in the leading-order approximation in the frequencies and wave vectors characterizing the spin motion. The equations are applicable for arbitrary degree of polarization and arbitrary deviations of the spin direction from the equilibrium orientation. The solutions describing a coherently precessing two-domain structure and spin waves are examined. In contrast to the assertion discussed in the literature that spin waves are damped at zero temperature, spin waves are found to be undamped in the long-wavelength limit. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 9, 717–721 (10 May 1997)     

Spin-wave reflection from an interface of two Fermi liquids

The boundary condition for the magnetization jump at an interface of two Fermi liquids and the spin current through the interface is rederived. With the use of the derived condition the coefficient of reflection of a spin wave from a boundary of two Fermi liquids for normal incidence is found and applied to the case of interface of phase separated liquid mixture of ³He in ⁴He. The effect of the phase separation boundary on the coherently precessing spin pattern is discussed.     

Coupling of the zero sound to transverse spin waves for neutral and normal Fermi liquids in dc magnetic field at precessing magnetization

Following the idea by Ketterson, this author showed that in neutral and normal Fermi liquids, the polarization effects lead to coupling of transverse spin waves to zero sound at precessing magnetization of the system. The observable effects, at the range of dc fields applied to³He, can appear only if the zero sound is degenerate with transverse spin waves excited in the reference frame rotating with the Larmor frequency about theH _dc-axis. This possibility is investigated at Landau parameters vanishing atl>1 and nonzero, though small, coupling of the density to the spin density and the particle current to the spin current, resulting from the polarization of the system byH _dc. The degeneration is, in general, possible but, at large values of the zero sound velocity with respect to the Fermi velocity, caused by large values of the Landau parameterF ₀ ^s and alsoF ₁ ^s for³He, atF ₀ ^a –0.7, it appears only at positiveF ₁ ^a . All experimental estimations of this parameter agree in its negativity excluding the degeneration of the zero sound and transverse spin waves for³He.     

Study of the two-domain processing structure in the superfluid3He-B

The systematic experimental and theoretical investigation of the longlived induction signal, known to exist in the³He-B, has shown that even very small nonuniformity of a steady magnetic fieldH ₀ changes qualitatively the precession pattern arising in the pulsed NMR experiments after tipping of the magnetization. The spin supercurrents redistribute magnetization within the experimental cell to produce the precessing structure, consisting of two domains. In one-domain, situated in the higher field region, magnetizationM has its equilibrium value and is parallel toH ₀. In the other domain the angle betweenM andH ₀ is slightly larger than? ₀=arc cos (?1/4). The structure precesses with frequency, equal to the Larmor frequency at the site of the wall, separating the domains. The relaxation of this structure goes via the growth of the equilibrium domain at the expense of the precessing domain; therefore in the course of the relaxation the frequency of the precession has to decrease with time. The calculated rate decrease agrees with the observed value. Experiments were carried out directly demonstrating the existence of the two-domain structure. After the formation of the two-domain structure, as well as after a perturbation of the structure by short r.f. pulses, low frequency (≈200 Hz) modulation of the induction signal is observed due to vibration of the structure. These vibrations are the standing spin waves in the precessing domain, their frequency being proportional to the size of the domain. The observed dependence of the frequency on other parameters is in agreement with theoretical calculations. The analysis of the data on the vibration and relaxation of the two-domain structure enables us to find the spin wave velocity and the spin diffusion coefficient in³He-B. Further investigation of the two-domain structure enables the study of spin supercurrents in³He-B.     

Localised precessing spin patterns in the B-phase of 3He

A new one-dimensional steady-state solution of the equations of spin dynamics for ³HeB is found. It describes a spin pattern, which is localised in the direction of the magnetic field and precesses with a frequency slightly smaller than the Larmor frequency. Stability of the pattern is provided by the topology of the field of the anisotropy axis. The pattern is a precessing n-soliton. The possibility of the existence of a three-dimensional localised precessing “flying saucepan” pattern is demonstrated. The relation of both patterns to the previously observed persistent signal is discussed.     

The spin dynamics of an anisotropic fermi supefluid (3He?)

In this paper we develop a general theory of the spin dynamics of anisotropic Fermi superfluids of the generalized BCS type, under conditions which should be realistic for any such phase of liquid ³He occurring below 3 mK. No restrictions are placed on the nature of the pairing configuration. The system is described in terms of the total spin vector S, and a vector T(n) which describes the amplitude and spin quantization axes of the pairs forming at a given point n on the Fermi surface; the kinematic relations between these quantities are emphasized. An approximation of the Born-Oppenheimer type is used to derive the general equations of motion of S and T; it is pointed out that relaxation of T due to collisions is inhibited by the coherent nature of the superfluid state. The equations of motion are solved for the particular case of unsaturated c.w. resonance, and it is shown that the nature of the transverse (usual) resonance spectrum is a strong function of the kind of configuration occurring; in particular, either one or two finite-frequency resonances may occur, depending on the configuration. A resonance is also predicted to occur when the r.f. field is polarized along the static external field. Specific predictions of the form of the transverse and “longitudinal” spectra are made for all the unitary l = 1 states, and it is shown that these predictions are unaffected by renormalization effects. The “Balian-Werthamer” state is predicted to show a longitudinal resonance but no transverse shift. The theory is compared with other approaches to the problem and its relevance to the anomalous low-temperature phases of liquid ³He is discussed.     

On the specific heat of Fermi liquids

The contributions of long-wavelength spin fluctuations to the specific heat of Fermi liquids is consistently calculated on the basis of the Landau theory of Fermi liquids. More satisfactory estimations of the Landau parameter F₁^a for liquid ³He are obtained.     

Coherently Precessing Spin Structure in 3He-B High-Resolution Quantum Amplifier

We present results of the study of surface oscillation modes of coherently precessing nuclear spins in the superfluid ³He-B known as a homogeneously precessing domain (HPD). HPD represents the first macroscopic experimental manifestation of magnetic superfluidity phenomenon. The measurements showed that HPD is extremely sensitive to longitudinal perturbations and it behaves as tuned (by magnetic field gradient) quantum amplifier that allows to measure very small changes of magnetic field with very high relative resolution, of the order of 10^-7.     

Optimised adiabatic fast passage spin flipping for He neutron spin filters

We describe here a method of performing adiabatic fast passage (AFP) spin flipping of polarized ³He used as a neutron spin filter (NSF) to polarize neutron beams. By reversing the spin states of the ³He nuclei the polarization of a neutron beam can be efficiently reversed allowing for the transmission of a neutron beam polarized in either spin state. Using an amplitude modulated frequency sweep lasting 500 ms we can spin flip a polarized ³He neutron spin filter with only 1.8×10⁻⁵ loss in ³He polarization. The small magnetic fields (10-15 G) used to house neutron spin filters mean the ³He resonant frequencies are low enough to be generated using a computer with a digital I/O card. The versatility of this systems allows AFP to be performed on any beamline or in any laboratory using ³He neutron spin filters and polarization losses can be minimised by adjusting sweep parameters.     

Ultra-sensitive magnetometry based on free precession of nuclear spins

We discuss the design and performance of a very sensitive low-field magnetometer based on the detection of free spin precession of gaseous, nuclear polarized ³He or ¹²⁹Xe samples with a SQUID as magnetic flux detector. The device will be employed to control fluctuating magnetic fields and gradients in a new experiment searching for a permanent electric dipole moment of the neutron. Furthermore, with the detection of the free precession of co-located ³He/¹²⁹Xe nuclear spins it can be used as ultra-sensitive probe for non-magnetic spin interactions, since the magnetic dipole interaction (Zeeman-term) drops out. Characteristic spin precession times T₂ ^* of up to 60 h were measured. The achieved signal-to-noise ratio of more than 5000:1 leads to an expected sensitivity level (Cramer-Rao lower bound) of δB≈1 fT after an integration time of 220 s and of δB≈10^-4 fT after one day. By means of a co-located ³He/¹²⁹Xe magnetometer, noise sources inherent in the magnetometer could be investigated, showing that CRLB is fulfilled, at least down to δB≈10^-2 fT. The reason for such a high sensitivity is that free precessing ³He (¹²⁹Xe) nuclear spins are almost completely decoupled from the environment. Therefore, this type of magnetometer is particularly attractive for precision field measurements where long-term stability is required.     

Phonons in a magnon superfluid and symmetry-breaking field

Recent experiments [1,2] on the measurement of the spectrum of the Goldstone collective mode of a coherently precessing state in ³He-B are discussed using the presentation of the coherent-spin precession in terms of the Bose-Einstein condensation of magnons. The mass in the spectrum of the Goldstone boson—a phonon in the superfluid magnon liquid—is induced by the symmetry-breaking field, which is played by the RF magnetic field. The text was submitted by the author in English.     

Fermi points and the Nambu sum rule in the polar phase of <Superscript>3</Superscript>He

We discuss the polar phase of ³He, which is realized in the anisotropic aerogel. We consider it in the framework of the BCS model. In the absence of the spin–orbit interaction, this model predicts the appearance of the Fermi line. However, it is topologically unstable. We demonstrate that the spin–orbit interaction gives rise to the appearance of the two Fermi points instead of the Fermi line. In addition to the gapless Nambu–Goldstone bosons in this system the collective gapped bosonic states exist. Their gaps are calculated, and the corresponding Nambu sum rule is established.     

Paramagnetic relaxation of spin polarized 3He at bare glass surfaces

In this first in a series of three papers on wall relaxation of spin polarized, gaseous ³He we investigate both by theory and by experiment surface-induced spin relaxation due to paramagnetic sites in the containing glass. We present experimental and theoretical evidence that — contrary to the traditional opinion — distant dipolar coupling to paramagnetic impurities in the glass, in particular iron ions, cannot be the dominant relaxation mechanism of ³He-spins, although iron dominates the bulk static permeability. Instead dangling-bond type defects in the glass matrix are found to interact much stronger via the isotropic Fermi contact interaction. A model of paramagnetic site controlled ³He relaxation including the Fermi contact interaction is presented. With reasonable semi-empirical assumptions our model allows to describe satisfactorily the measured relaxivities, both in the dissolution-dominated regime of fused silica or borosilicate glasses of the Pyrex type as well as in the surface dominated situation of aluminosilicate glasses which have only a low permeability for He atoms. In a large sample of 1.1 litre cells, built from various aluminosilicate glasses, an average relaxation time of 150 h is reached in case contaminant ferromagnetic particles have been demagnetized beforehand. From the maximum observed value of 250 h we derive after subtraction of dipolar relaxation in the gas phase a paramagnetic surface relaxivity of ρ<0.005 cm/h at room temperature.     

Possible existence of bound state Frenkel vacancies in solid 3He

The effects on the low temperature (T ? 15 mK) magnetic and thermal properties of solid ³He due to the presence of bound state Frenkel vacancies (BFV) are analyzed. The coupling of a ³He to a BFV contributes to the zero point motion of the ³He. Assuming that the BFV are strongly interacting and propagate coherently through the crystal, we find good qualitative agreement with $\text{both}$ the specific heat and magnetic susceptibility data.     

In situ SEOP polarised He neutron spin filter for incident beam polarisation and polarisation analysis on neutron scattering instruments

We discuss the development and characterisation of a new in situ spin exchange optical pumping (SEOP) based ³He neutron spin filter polarisation device. We present results from a recent test of the prototype system developed with the Institut Laue-Langevin. The polariser was installed on the polarised reflectometer CRISP at ISIS in the analyser position. The ³He was pumped continuously in situ on the beamline. The system also integrated a ³He adiabatic fast passage spin flipper that allowed reversal of the ³He and therefore neutron polarisation state, allowing for measurement of all four polarisation cross-sections. The system was run for a number of days reaching a ³He polarisation of 63%.     

The superfluidd transition temperature of a Fermi liquid: 3He and 3He4He mixtures

The superfluid transitions temperature is calculated from the microscopic theory of a Fermi liquid in terms of the Landau parameters and one unknown scale factor. Determining the latter from the observed transition in ³He leads to an estimate that the superfluid transition in ³He⁴He mixtures may be presently observable.     

The entropy expression of a Fermi liquid in shielded potential approximation. Application to3He

Using the functional representation of the thermodynamical potential, a simple expression for the entropy of a normal Fermi liquid in shielded potential approximation is derived. The result is valid for arbitrary temperatures above a possible phase transition and contains both Fermi (single-particle) and Bose (collective) contributions. It thus represents an improvement over the quasi-particle approximation. — Applying this result to the fluctuation model of liquid³He, we find a Bose contribution of the orderT ³ logT/Θ from spin fluctuations as well as the usual quasi-particle term.