Multiple spin echoes in spin polarized Fermi liquids

Multiple spin echoes (MSEs) in³He and in³He-⁴He mixtures have been analyzed using a theoretical technique proposed by Einzel et al. In both systems MSEs are generated by Fermi liquid interactions, but for³He, MSEs are also generated at higher temperatures by the dipolar demagnetizing field. The theory is compared with the experimental results for³He and with our measurements for³He-⁴He mixtures. We have improved on the fit to the second echo heights for³He given by Einzel et al. by taking account of both the Leggett-Rice effect and the dipolar interaction in the calculation. Good fits were also found for the first and second echo heights for the³He-⁴He data. The third echo height is larger than expected if we assume that the total magnetization remains uniform in space. We have developed the theory for the case when this approximation is not made, and we find good agreement for the first five echoes.     

Transverse surface impedance of pair-correlated Fermi liquids. Application to normal and superfluid3He

Hydrodynamic experiments in quantum liquids at low temperatures are sensitively influenced by the interaction of the elementary excitations with the confining walls of the measuring cell. In the case of transverse oscillations of the walls such that the viscous penetration depth of the liquid is small compared to the container dimensions, the dynamical behavior of the quantum liquid is governed by the transverse surface of shear impedance. We calculate the shear impedance for an isotropic, pair-correlated Fermi liquid from a microscopic quasiparticle Landau-Boltzmann equation using variational methods. A general class of elastic quasiparticle-wall scattering laws is considered in deriving the impedance functional. We give exact results for the variational surface impedance in the low-frequency limit and discuss approximate results in context with special wall-scattering laws such as specular, backward and Andreev scattering. Finally we apply our theory to the experimentally accessible, pair-correlated Fermi liquid³He and particularly investigate the influence of pressure, temperature, frequency, and the parameters specifying the wall-scattering process on the shear impedance.     

Transverse spin dynamics in spin-polarized Fermi liquids

A microscopic framework for a generalized Landau theory is established in the form of two coupled equations in partial transverse densities. The 4-component effective interaction is related to the irreducible vertex, and not to the full vertex. The results explain the zero-temperature transverse relaxation and attenuation of spin waves. The spectrum of spin waves is expressed via harmonics of the interaction operator and its derivatives at arbitrary polarization. Our exact equations differ from previous semi-phenomenological ones, and reproduce all proper limiting cases like spin-polarized quantum gases or the Silin-Leggett low field equations.     

Coherent precession of spin in Fermi liquids

The equations of spin dynamics of a normal Fermi liquid in a nonuniform magnetic field have a special symmetry. Because of this symmetry the equations have steady-state solutions which describe coherently precessing structures. The structures consist of two domains. In one of the domains the magnetization is parallel and in the other it is antiparallel to the magnetic field. Within the domain wall the magnetization can rotate by any odd multiple of . The possibility of realization of analogous structures in the other physical systems is discussed.     

Surface impedance and slip length of superfluid Fermi liquids. Exact results

Exact results for the slip length and the surface impedance of a superfluid Fermi liquid are reported for the case of diffuse boundary scattering and compared with previous approximate results based on variational methods. We also derive upper and lower bounds on the slip length for a general class of scattering laws, including the case of Andreev reflection due to suppression of the order parameter near the walls.     

Experiments on Fermi liquid domains in normal and superfluid3He

We report on pulsed and CW NMR experiments in liquid³He at temperatures below 10 mK, when the Fermi liquid interaction gives rise to a nondissipative spin currents. Due to these currents, a coherently precessing spin state may be formed in NMR-experiments with Fermi liquids. The state consists of two domains. In one of the domains the magnetization is oriented along, and in the other opposite to the direction of the magnetic field. Hitherto such a state has only been observed in³He-⁴He solutions. We have found that the domains can also be formed in normal³He. Experimental results for normal³He are in a good agreement with theory and computer simulations. The conditions necessary for the formation of the state have been determined. We also have found that the two-domain state may be also created in the super fluid state (at least near T_c).     

Collisionless spin waves in normal and superfluid3He

Standing spin-wave modes in liquid³He have been studied by cw NMR at Larmor frequencies of 1, 2, and 4 MHz and pressures of 0, 6.3, and 12.3 bar. The spin waves, which produce peaks in the NMR line, are visible at temperatures below 5 mK at zero pressure. With the assumption of a slightly simplified sample shape and no transverse spin relaxation at the walls, the theory of Leggett fits the spin-wave frequencies in the normal liquid very well, giving a value of the Fermi liquid parameterF ₁ ^a =–0.6±0.2 at zero pressure. The width of some of the peaks is larger than expected from other determinations of the quasiparticle diffusion time _D . This could be due to wall relaxation or to deviations from the assumed sample geometry. In the superfluid A₁ and A phases, where the data cannot be fitted to existing theories, the spin-wave modes are shifted in frequency and suffer additional damping as the temperature is decreased. At still lower temperatures in the B phase an inversion of the spin-wave spectrum from one side of the NMR line to the other is observed, agreeing quantitatively with the predictions of the 1975 theory of Combescot.     

Spin singlet-triplet states of superfluid Fermi liquids in the presence of strong magnetic fields

The unitary singlet-triplet states of superfluid Fermi liquids are investigated in the presence of strong magnetic fields. The static spin susceptibility is calculated in the limith 0 in the framework of the weak coupling approximation. It is predicted that BS (a mixture of the Balian- Werthamer anisotropic state andD-wave singlet state) and 2DS (a mixture of the planar 2D state andD-wave singlet state) spin singlet-triplet states become stable at some temperatures and magnetic fields.     

Superflow and the depairing critical current for spin singlet-triplet states of superfluid Fermi liquid

The unitary states of superfluid Fermi liquid with singlet D and triplet P type of pairing are investigated in the framework of the weak coupling approximation. The superflow pair-breaking critical current is calculated at zero temperature and in the Ginzburg-Landau region for various values of the respective strengths of singlet and triplet components of the pairing interaction. The dependence of the mass superflow on the a ₁ (F ₁ ^s ) Landau amplitude is determined. The mixed singlet-triplet states BS (a mixture of BW anisotropic and D-wave states) and 2DS (a mixture of 2D planar and D-wave states) are found to be stable for some region of the superfluid velocity.     

Sum rules for normal Fermi liquids in the low temperature limit

Sum rules for longitudinal and transverse excitations in normal Fermi liquids are calculated in the low-temperature limit using the Landau theory. The analysis provides a physical interpretation of sum rules in terms of the collective parameters of macroscopic models such as the hydrodynamic and the elastic models. Different mean excitation energies are defined in terms of sum rules and compared with the frequency of the collective motion of the system (zero sound).     

Zero-temperature attenuation and transverse spin dynamics in Fermi liquids. I. Generalized Landau theory

This is the first in a series of papers on a consistent microscopic theory of transverse dynamics in spin-polarized or binary Fermi liquids. We start from exact microscopic equations in Green's functions at zero temperatures and consider slightly inhomogeneous perturbations. The transverse dynamics is described by an integral equation in a 4D momentum space with inevitable spatial and temporal non-localities. This equation can be reduced only to a set of two coupled equations for partial transverse densities corresponding to independent contributions to a transverse magnetic moment from transverse components of slightly tilted up and down spins. It is shown that, in contrast to previous phenomenological theories of polarized Fermi liquids, these equations reduce to a single Landau-like kinetic equation only in cases of low polarization or density. This implies the existence of two different sorts of (attenuating) transverse quasi-particles. The molecular field (an analog of a Landau function) has a form of a 4-component non-local operator. This interaction operator is expressed via the off-diagonal component of the exact irreducible vertex with the help of some integral equation, and cannot be given, as it is usually assumed, as any limit of the full vertex. The proper Landau-like phenomenological approach corresponding to our exact microscopic equations, should operate with two types of attenuating transverse quasi-particles each oscillating between its Fermi surface and some other 3D surface in a 4D momentum space. The dephasing of inhomogeneous precession between two different types of dressed transverse quasi-particles leads to an inhomogeneous broadening which manifests itself as a peculiar zero-temperature relaxation.     

Spin diffusion and spin echo in normal liquid3He

The problem of spin diffusion in normal liquid³He in the presence of precessional effects is reexamined taking into account the energy dependence of the quasiparticle relaxation time. This leads to a generalization of Leggett's relation for the successive height of the echoes in a φ-180°-180° experiment. Reanalyzing the experiment of Corruccini et al. (including finite-temperature corrections) leads to almost exact and model-independent values for F ₁ ^a and λ_D.     

Transverse relaxation in two-level Fermi liquids and gases

An exact microscopic theory is developed for transverse dynamics in two-level Fermi systems like spin-polarized Fermi liquids. The origin of a transverse zero-temperature attenuation is a dephasing of interlevel transitions in inhomogeneous conditions. We analyze different sources of this relaxation using an extrapolation from low polarizations or densities. These sources include imaginary terms in the vertex and single-particles' energies and pseudo-energies away from the Fermi spheres, and derivatives of the vertex function in off-shell directions. The attenuation for dilute systems starts from a second order term in density. The main non-local contribution is of the next order in density, but is not negligible if the interaction range is large. At very low polarizations and densities, one recovers the already known results. The implications for liquid³He and³He-⁴He mixtures are discussed.     

Collective modes and spin waves in superfluid3He-B

Making use of a model Hamiltonian, which includes, besides the kinetic energy and the BCS-like pairing energy, the spin exchange energy as well as the dipolar interaction energy, we study theoretically the collective modes of the Balian - Werthamer state in the collisionless limit. In the absence of the dipolar interaction energy, the collective modes are classified according to their total angular momentumJ. Among 18 distinct modes, one mode withJ=0 and three modes withJ=1 are gapless. The latter modes couple with the spin fluctuation and are identified with spin wave modes. The effect of the dipolar interaction on these modes is discussed.Supported by the National Science Foundation.     

Electric dipole moment and spin supercurrent in superfluid3He

The SU(2) gauge invariant theory of the relativistic interaction of the electrically neutral superfluid³He with electric and magnetic fields is formulated. The spin supercurrent response on the electric field is calculated for this interaction. The comparison with the nonrelativistic flexoelectric effect, arising due to the distortion of the atomic shell by the gradients of the superfluid order parameter, is made.     

Boundary conditions for quasiclassical Green's Function for superfluid Fermi systems

We show that the quasiclassical Green's Function for Fermi liquids can be constructed from the solutions of the Bogoliubov-de Gennes equation within the Andreev approximation and derive self-consistent relations to be satisfied by the quasiclassical Green's function at the surfaces. The so-called normalization condition for the quasiclassical Green's function is obtained from this self-consistent relation. We consider a specularly reflecting wall, a randomly rippled wall, and a proximity boundary as model surfaces. Our boundary condition for the randomly rippled wall is different from that derived by Buchholtz and Rainer and Buchholtz.     

Flow dependence of spin susceptibilities in superfluid3He

The flow dependence of spin susceptibilities in superfluid ³ He-A and -B is studied theoretically. It is shown that in the A phase _A, the component of the static spin susceptibility parallel to , increases rapidly in the presence of mass current. A similar behavior is found for all components of _B, the susceptibility tensor of the B phase.Work supported by the National Science Foundation under grant No. DMR76-21032.Recipient of a scholarship from the Studienstiftung des Deutschen Volkes.     

Textures and spin waves in rotating superfluid3H3-B

The spin wave modes in rotating superfluid³He-B have been calculated for a texture of cylindrical symmetry. The textural configuration is determined by minimizing the appropriate free energy and solving the resulting Euler-Lagrange equations for then vector. The texture determines the effective potential entering the spin wave equation. The potential deviates significantly from a harmonic oscillator under realistic experimental conditions, giving rise to shifts of the oscillator frequencies. The agreement with the recent experimental observations of Ikkalaet al. is excellent at all temperatures studied.