Zero-temperature attenuation and transverse spin dynamics in fermi liquids. II. Dilute fermi systems

This is the second in a series of papers on a consistent microscopic theory of transverse dynamics in spin-polarized or binary Fermi liquids. We demonstrate when and how the exact theory of Ref. 1 reduces to the conventional theory of highly polarized degenerate low-density Fermi liquids and gases. In the lowest approximations, i.e. for an ideal polarized Fermi gas and in the first (Born) order, our theory assumes the standard form. In the next order in density and/or interaction, the main equations still have a fairly conventional form, though they already contain the peculiar zero-temperature attenuation which is missing in the standard theory. This attenuation can be incorporated into the standard Fermi liquid formalism by adding an imaginary part to a mixed spin component of the Landau interaction function. The source of this imaginary contribution atT = 0 is a pole in the integral expression for the Landau interaction function (the situation is very similar to the case of collisionless Landau damping). In the next order, the standard theory fails completely, and even the form of the equations of transverse dynamics becomes very unconventional. We calculated explicitly the parameters of transverse spin dynamics and the spectrum of spin waves, including the zero-temperature attenuation, and, as a by-product, the polarization dependencies of thermodynamic parameters. The calculation includes a possible non-locality of the interaction. An application of the results to³He-⁴He mixtures covers the non-locality in the direct interaction channel as well as the non-locality and retardation associated with a phonon-mediated part of particles' interaction.     

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.     

Zero-temperature relaxation in spin-polarized fermi liquids

We discuss the effect of zero-temperature attenuation, which has been recently observed in spin dynamics of spin-polarized Fermi liquids, on other Fermi-liquid processes. The transfer of this attenuation mechanism from transverse spin dynamics to longitudinal processes can be caused by the magnetic dipole interaction, namely, by the direct dipole processes and the dipole coupling between the transverse spin dynamics and the longitudinal transport and relaxation processes. We calculated the zero-temperature sound attenuation in spin-polarized Fermi liquids, corrections to the threshold of spin-wave (Castaing) instability, and the effective zero-temperature viscosity and longitudinal relaxation time in low- and high-frequency regimes.     

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.     

Boundary effects in transverse spin dynamics of spin-polarized quantum gases

Spin dynamics of spin-polarized quantum gases near nonmagnetic walls is discussed. We consider boundary-induced line shifts and attenuation of spin-waves, and a possible macroscopic boundary condition for systems close to a Knudsen ballistic regime. By a coordinate transformation, we reduce the problem of collisions with a rough wall to an equivalent problem with a specular wall but with stochastic bulk perturbations. The boundary effects are described by a bulk-like transverse spin-diffusion coefficient inversely proportional to the correlation function of surface inhomogeneities. This leads to an effective macroscopic boundary condition applied for the spin-wave resonances. The situation is changed at low temperatures by an appearance of absorbed boundary layers which lead to additional exchange processes and renormalize the molecular field near the walls. The experimental implications for helium and hydrogen systems are discussed, including the signs of surface spin modes.     

Quantum spin dynamics of the transverse Ising model in two dimensions

We use the method of recurrence relations to obtain the time-dependent spin correlation function of the Ising model in a transverse field in 2D. We find that the correlation function decays algebraically at long times as t_– where 2.2. This is to be contrasted with the 1D case where the decay is Gaussian. We expect that in 3D the dynamical correlation will also exhibit a power law decay. Our results can be used to understand the experimental shape functions for the induced moment in LiTb_pY _1–pF ₄ .     

Sum rules and the landau theory of fermi liquids

The Landau theory predicts spectral weight functions for density and spin-density fluctuations which in the long-wavelength, low-frequency limit should be equal to the true spectral weight functions of a system of interacting fermions. This correspondence plus well-known frequency sum rules provides a means to examine the Landau quasiparticle interaction parameters. Two inequalities are derived:F ₁ G ₁ and another relating the first three spin-symmetric Landau coefficients to the radial distribution function and the two-particle potential. We find that the third-moment sum rule is not entirely exhausted by Landau-accountable excitations, and therefore it is the highest order sum rule which can still probe the theory. A third-moment sum rule for the spin-spin correlation function is derived and is found to have an unexpected dependence onk, i.e., one that disagrees with the corresponding Landau prediction. We do not examine this result in detail, but merely conjecture that it may indicate a basic weakness in the Landau theory of spin-density fluctuations.     

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.     

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.     

The spin diffusion in normal and superfluid Fermi liquids

Spin diffusion in paramagnetic spin systems is a dissipative process which acts so as to remove all spatial variation of the magnetization. In normal and superfluid Fermi liquids its physical origin lies in the nonconservation property of the macroscopic magnetization current associated with the thermal excitations, the Landau and Bogoliubov quasiparticles, respectively. In the hydrodynamic limit this dissipative process manifests itself in a constitutive relation connecting the decaying magnetization current with gradients in the magnetization density via a coefficient of spin diffusion. Exchange contributions to the quasiparticle interaction introduce, in addition, reactive processes, which can be associated with a rotation of the quasiparticle spin current about the direction of the spin polarization. This so-called spin current rotation—or Leggett-Rice effect—leads to nonhydrodynamic behavior of the spin diffusion whenever the exchange frequency becomes comparable to the inverse spin current relaxation time. In this article I would like to review our current understanding of diffusional spin transport, as influenced by nonhydrodynamic effects, in normal and superfluid Fermi systems.Dedicated to Ludwig Tewordt on the occasion of his 65th birthday.     

Dynamic-scaling theory of critical ultrasonic attenuation in binary liquids

The critical slowing down that sets in near the critical point of a second-order phase transition is manifested in fluids by a diverging relaxation time for the long-wavelength order-parameter fluctuations. This divergence has a profound effect on all of the transport properties. In sound propagation, the adiabatic compressions and dilations produce temperature swings which the order-parameter fluctuations can follow fully only if the sound frequency is smaller than the relaxation rates in the fluid. As the critical point is approached this condition is violated and a lagging, or hysteretic, response results. As demonstrated by Clerkeet al., the known amplitude of the temperature swings leads to a prediction of ultrasonic attenuation at the critical point that agrees, in magnitude, exactly with that found by Harada et al. The theoretically predicted scaling function that describes how the attenuation and dispersion vary as the critical point is approached is in good agreement with the experimental findings of Garland and Sanchez.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

The effect of the demagnetizing field on coherent spin precession in a normal fermi liquid

We consider an effect of the demagnetizing field, produced by the magnetic moments of nuclei of³He, on coherent precession of spin in liquid spin polarized³He or in spin polarized solutions of³He in⁴He. Formulae for the shape of the precessing domain wall and for the relaxation rate of the coherently precessing structure are rederived taking into account the demagnetizing field. For pure³He and concentrated solutions of³He in⁴He the width of the domain wall increases and the relaxation rare decreases with polarization. Measurement of the relaxation rate of the precessing structure can be used as an alternative method for the determination of the spin diffusion coefficient in Fermi liquids.     

Relative measurements of the velocity and attenuation of ultrasound in highly absorbing liquids

It is shown that it is possible to use a continuous sinusoidal signal to make relative measurements of the velocity and absorption coefficient of ultrasound in highly absorbing liquids such as liquid crystals. Compared with the traditional variable-frequency pulse-phase method, the technique described has the advantage of giving a direct reading of the results under dynamic measurement conditions. A block diagram and the characteristics of the equipment for measuring the anisotropy of acoustic parameters by both pulse and continuous methods are presented.Translated from Izmeritel'naya Tekhnika, No. 1, pp. 66–67, January, 1995.     

NMR studies of spin dynamics in cuprates

We report recent NMR results in cuprates. The oxygen Knight shift and the Cu nuclear spin-lattice relaxation rate in Bi_2.1Sr_1.94Ca_0.88Cu_2.07O₈₊ single crystals revealed a gapless superconducting state, which can be most naturally explained by a d-wave pairing state and the intrinsic disorder in this material. The Cu nuclear spin-spin relaxation rate in underdoped YBa₂Cu₃O_6.63 shows distinct temperature dependence from the spin-lattice relaxation rate, providing direct evidence for a pseudo spin-gap near the antiferromagnetic wave vector.     

Charge dynamics and spin order in doped Hubbard models

Hole motion in an antiferromagnetic (AF) environment is accompanied by the emission of spin wave excitations. Spin-wave shakeoffs are responsible for incoherent contributions to the dynamics of propagating holes. Using a spin-density-wave polaron scheme we calculate the optical conductivity () and show that the incoherent part of the hole spectrum contributes to the low-frequency part of ().Separately, we discuss the possible formation of spiral spin patterns upon doping of the half-filled one-band Hubbard model. In particular, we consider the influence of band structure effects arising from nearest- and next-nearest-neighbor hopping processes on a square lattice. Differences in the ground state spin patterns for hole and electron doping are obtained offering a possible explanation for the persistence of AF order in low electron-doped cuprate superconductors.     

Boojums on the fermi surface in3He-A and Hamiltonian dynamics of the orbital momentum

Boojums (nodes) on the Fermi surface of³He-A lead to peculiar behavior of the intrinsic orbital momentum L in this superfluid. AtT=0, L has the form L=(/2m ₃)l(–C ₀), whereC ₀ is the prefactor of the anomalous term in the supercurrent l(l rot l). From the algebra of the hydrodynamical Poisson brackets and from microscopic theory it follows thatC ₀ is a dynamical invariant, (/t)C ₀=0. The closed system of nonlinear hydrodynamic equations of³He-A atT=0 is constructed in the framework of the Poisson brackets scheme.     

Effect of transverse velocity and temperature gradients on sound attenuation in straight annular ducts

Abstract

In this paper, the effects of transverse mean velocity and temperature gradients on the acoustic propagation in a straight annular duct are studied so as to be the basis of further analyzing the sound propagation in nonuniform annular ducts. The wave equation governing this acoustic field is a difficult eigenvalue problem. The eigenvalue is solved by an IMSL package which is proposed to find suitable initial guess. By using the initial guess, in addition to the iterative process, the final results have been found. The results are proved to be of good accuracy by comparing with published data, and the errors are under 2.0%. From this paper we also find that, under the influence of the unsymmetric boundary condition, the attenuations of the axial symmetric radial mode are different from other modes, and this property of the former mode can not be expected by ray acoustic arguments, on the other hand, the attenuations of the lowest mode and the spinning modes can be expected.     

Ultrafast spin dynamics in colloidal ZnO quantum dots

Time-resolved Faraday rotation measurements in the ultraviolet have been performed to reveal the ultrafast spin dynamics of electrons in colloidal ZnO quantum dots. Oscillating Faraday rotation signals are detected at frequencies corresponding to an effective g factor of g = 1.96. Biexponential oscillation decay is observed that is due to (i) rapid depopulation of the fundamental exciton (tau = 250 ps) and (ii) slow electron spin dephasing ( T 2 = 1.2 ns) within a metastable state formed by hole-trapping at the quantum dot surface.     

Low acoustic attenuation in Stycast 1266 at very low temperatures

The attenuation of ultrasonic waves at moderately high frequencies has been measured in Stycast 1266 in the temperature range from 0.1 to 4.2 K to verify the very low attenuation expected from similar data observed in another epoxy resin. Below about 0.5 K the attenuation data are compatible with a T ³ dependence and a frequency independent behavior reminiscent of the standard result predicted by the Two Level System (TLS) theory and observed in amorphous materials. The observed low attenuation in Stycast 1266 confirmed our earlier expectation that this is a good material to use for acoustic microscopy purpose at very low temperatures.