Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0101368 · Physical review. B, Condensed matter

Effects of a dipolar field in the spin dynamics of a Fermi liquid

Pavel Krotkov, V. Mineev, Gérard Vermeulen

Published Jan 1, 2002• 9 citations
arXivHTMLPDF

Abstract

We study the spin dynamics of a normal Fermi liquid taking into account the demagnetizing field produced by the spin system itself. Linear solutions of the spin dynamics equations in the form of standing spin waves in a finite volume of liquid are found. At almost all known experimental conditions the influence of demagnetizing field can be satisfactorily described by the first order of perturbation theory. We carried out perturbational calculations for two geometries of experimental cell---spherical and finite cylindrical. We performed also exact numerical simulations of the spin-wave spectra in a spherical cell at an arbitrary strength of the demagnetizing field. The obtained results are applied in particular to conditions of recent experiment [G. Vermeulen and A. Roni, Phys. Rev. Lett. 86, 248 (2001)] related to the problem of zero-temperature transverse relaxation in a polarized Fermi liquid. We found that not taking into account the demagnetizing field leads to negligible errors in the measured relaxation time, thus supporting the conclusion of the absence of zero-temperature spin-wave damping.

DOI
10.1103/physrevb.65.054301

Related papers

Transverse spin dynamics in a spin-polarized Fermi liquid

V. P. Mineev

The linear equations for transverse spin dynamics in a weakly polarized degenerate Fermi liquid with arbitrary relationship between temperature T and polarization $\ensuremath{\gamma}H$ are derived from Landau-Silin phenomenological kinetic equation with general form of two-particle collision integral. The temperature and polarization dependence of the spin current relaxation time is established. It is found in particular that at finite polarization transverse spin wave damping has a finite value at $T=0.$ The analogy between temperature dependences of spin wave attenuation and ultrasound absorption in degenerate Fermi liquid at arbitrary temperature is presented. We also discuss spin-polarized Fermi-liquid in the general context of the Fermi-liquid theory and compare it with ``Fermi liquid'' with spontaneous magnetization.

arXiv:cond-mat/0310620•Physical Review B•Apr 28, 2004•25 citations

Transverse spin dynamics of a spin-polarized Fermi liquid

I. A. Fomin

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.

Journal of Experimental and Theoretical Physics Letters•May 1, 1997•23 citations

Theory of transverse spin dynamics in a polarized Fermi liquid and an itinerant ferromagnet

V. P. Mineev

Linear equations for the transverse spin dynamics in a weakly polarized degenerate Fermi liquid are derived from the Landau-Silin phenomenological kinetic equation with a general two-particle collision integral. Unlike a previous treatment where the Fermi velocity and density of states were taken to be constant independent of polarization we make no such assumption. The equations found describe the spin dynamics in a paramagnetic Fermi liquid with finite polarization as well in an itinerant ferromagnet. The results are confirmed by field theoretical calculations based on the integral equation for the vertex function. The transverse spin wave frequency in a polarized paramagnetic Fermi liquid is found to be proportional to ${k}^{2}$ with a complex diffusion coefficient such that the damping has a finite value proportional to the quasiparticles scattering rate at $T=0$. This behavior of a polarized Fermi liquid contrasts with the behavior of a Heisenberg ferromagnet in the hydrodynamic regime where the transverse spin-wave attenuation appears in terms proportional to ${k}^{4}$. The reactive part of the diffusion coefficient in a paramagnetic state at $T=0$ proves to be inversely proportional to the magnetization whereas in a ferromagnetic it is directly proportional to the magnetization. The dissipative part of the diffusion coefficient at $T=0$ in the paramagnetic state is polarization independent, whereas in the ferromagnetic state it is proportional to the square of the magnetization. Moreover, the spin wave spectrum in a ferromagnetic Fermi liquid proves to be unstable demonstrating the difficulty of applying a Fermi liquid description to itinerant ferromagnetism.

arXiv:cond-mat/0507675•Physical Review B•Oct 20, 2005•23 citations

Transverse dynamics and relaxation in spin-polarized or two-level Fermi systems

A. E. Meyerovich, Karen A. Musaelian

A microscopic theory is proposed for transverse dynamics and zero-temperature attenuation in polarized Fermi liquids. The transport equations are a set of two coupled equations in two ``partial transverse densities,'' which do not reduce to a single equation in a mixed component of a single-particle distribution. The effective interaction is linked to an irreducible vertex by an integral equation, and cannot be given as a limit of a full vertex. A framework for a generalized nonlocal Landau theory is established. The spectrum of attenuating spin waves is calculated at arbitrary polarizations and densities.

Physical review. B, Condensed matter•Feb 1, 1993•11 citations

Longitudinal Relaxation Time in a Degenerate, Polarized Fermi Gas

Erik D. Nelson

The longitudinal relaxation time T$\\sb1$ is calculated for a dilute Fermi gas. We include the possibility of arbitrary degrees of polarization P, and uniform external magnetic fields. At low temperatures T$\\sb1$ is proportional to T$\\sp{-2}$ for the unpolarized gas in agreement with earlier calculations. For a polarized system in zero applied field the separation between up and down Fermi spheres provides an open channel in phase space for spin flipping processes. As temperature is reduced to zero T$\\sb1$ levels off and approaches a constant value which depends sensitively on P, leading to much smaller values of T$\\sb1$ than in the unpolarized case. For relaxation in a uniform external field H, Zeeman energy conservation during spin flipping interactions essentially shifts the location of the T$\\sp{-2}$ behavior from zero polarization to the polarization P(H) which would be produced in equilibrium with the external field H. When the initial polarization of the system is different from P(H), T$\\sb1$ again approaches a constant value which is equally sensitive to the initial polarization as temperature is reduced to zero. We apply our calculations to the case of dilute $\\sp3$He-HeII solutions. We also consider the calculation of density dependent corrections to T$\\sb1$ for unpolarized, or weakly polarized $\\sp3$He-HeII using the long wavelength limit of the Bardeen-Baym-Pines interaction as a form for the spin independent part of the $\\sp3$He-$\\sp3$He interaction. Owing to the positive sign of the antisymmetric Landau parameter $\\rm F\\sbsp{o}{a}$ in dilute $\\sp3$He-HeII Fermi Liquid interactions act to screen the magnetic dipole interactions which cause relaxation. To lowest order in density we find that the relaxation rate 1/T$\\sb1$ is reduced by factor $\\rm (1 - 3F\\sbsp{o}{a})$ which compares favorably with recent calculations of T$\\sb1$ for pure $\\sp3$He.

•Jan 1, 1993•0 citations

Collective spinon spin wave in a magnetized U(1) spin liquid

Leon Balents, Oleg A. Starykh

We study the transverse dynamical spin susceptibility of the two-dimensional U(1) spinon Fermi-surface spin liquid in a small applied Zeeman field. We show that both short-range interactions, present in a generic Fermi liquid, as well as gauge fluctuations, characteristic of the U(1) spin liquid, qualitatively change the result based on the frequently assumed noninteracting spinon approximation. The short-range part of the interaction lead to a collective ``spinon spin wave'' mode, which splits off from the two-spinon continuum at a small momentum and disperses downward. Gauge fluctuations renormalize the susceptibility, providing nonzero power-law weight in the region outside the spinon continuum and giving the spin wave a finite lifetime, which scales as momentum squared. We also study the effect of Dzyaloshinskii-Moriya anisotropy on the zero momentum susceptibility, which is measured in electron spin resonance (ESR), and obtain a resonance linewidth linear in temperature and varying as ${B}^{2/3}$ with magnetic field $B$ at low temperatures. Our results form the basis for a theory of inelastic neutron scattering, ESR, and resonant inelastic x-ray scattering studies of this quantum spin-liquid state.

arXiv:1904.02117•Physical review. B./Physical review. B•Jan 6, 2020•18 citations
We study the spin dynamics of a normal Fermi liquid taking into account the demagnetizing field produced by the spin system itself. Linear solutions of the spin dynamics equations in the form of standing spin waves in a finite volume of liquid are found. At almost all known experimental conditions the influence of demagnetizing field can be satisfactorily described by the first order of perturbation theory. We carried out perturbational calculations for two geometries of experimental cell---spherical and finite cylindrical. We performed also exact numerical simulations of the spin-wave spectra in a spherical cell at an arbitrary strength of the demagnetizing field. The obtained results are applied in particular to conditions of recent experiment [G. Vermeulen and A. Roni, Phys. Rev. Lett. 86, 248 (2001)] related to the problem of zero-temperature transverse relaxation in a polarized Fermi liquid. We found that not taking into account the demagnetizing field leads to negligible errors in the measured relaxation time, thus supporting the conclusion of the absence of zero-temperature spin-wave damping.
The linear equations for transverse spin dynamics in a weakly polarized degenerate Fermi liquid with arbitrary relationship between temperature T and polarization $\ensuremath{\gamma}H$ are derived from Landau-Silin phenomenological kinetic equation with general form of two-particle collision integral. The temperature and polarization dependence of the spin current relaxation time is established. It is found in particular that at finite polarization transverse spin wave damping has a finite value at T=0.T=0.T=0. The analogy between temperature dependences of spin wave attenuation and ultrasound absorption in degenerate Fermi liquid at arbitrary temperature is presented. We also discuss spin-polarized Fermi-liquid in the general context of the Fermi-liquid theory and compare it with ``Fermi liquid'' with spontaneous magnetization.
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.
Linear equations for the transverse spin dynamics in a weakly polarized degenerate Fermi liquid are derived from the Landau-Silin phenomenological kinetic equation with a general two-particle collision integral. Unlike a previous treatment where the Fermi velocity and density of states were taken to be constant independent of polarization we make no such assumption. The equations found describe the spin dynamics in a paramagnetic Fermi liquid with finite polarization as well in an itinerant ferromagnet. The results are confirmed by field theoretical calculations based on the integral equation for the vertex function. The transverse spin wave frequency in a polarized paramagnetic Fermi liquid is found to be proportional to k2{k}^{2}k2 with a complex diffusion coefficient such that the damping has a finite value proportional to the quasiparticles scattering rate at T=0T=0T=0. This behavior of a polarized Fermi liquid contrasts with the behavior of a Heisenberg ferromagnet in the hydrodynamic regime where the transverse spin-wave attenuation appears in terms proportional to k4{k}^{4}k4. The reactive part of the diffusion coefficient in a paramagnetic state at T=0T=0T=0 proves to be inversely proportional to the magnetization whereas in a ferromagnetic it is directly proportional to the magnetization. The dissipative part of the diffusion coefficient at T=0T=0T=0 in the paramagnetic state is polarization independent, whereas in the ferromagnetic state it is proportional to the square of the magnetization. Moreover, the spin wave spectrum in a ferromagnetic Fermi liquid proves to be unstable demonstrating the difficulty of applying a Fermi liquid description to itinerant ferromagnetism.
A microscopic theory is proposed for transverse dynamics and zero-temperature attenuation in polarized Fermi liquids. The transport equations are a set of two coupled equations in two ``partial transverse densities,'' which do not reduce to a single equation in a mixed component of a single-particle distribution. The effective interaction is linked to an irreducible vertex by an integral equation, and cannot be given as a limit of a full vertex. A framework for a generalized nonlocal Landau theory is established. The spectrum of attenuating spin waves is calculated at arbitrary polarizations and densities.
The longitudinal relaxation time Tsb1\\sb1sb1 is calculated for a dilute Fermi gas. We include the possibility of arbitrary degrees of polarization P, and uniform external magnetic fields. At low temperatures Tsb1\\sb1sb1 is proportional to Tsp−2\\sp{-2}sp−2 for the unpolarized gas in agreement with earlier calculations. For a polarized system in zero applied field the separation between up and down Fermi spheres provides an open channel in phase space for spin flipping processes. As temperature is reduced to zero Tsb1\\sb1sb1 levels off and approaches a constant value which depends sensitively on P, leading to much smaller values of Tsb1\\sb1sb1 than in the unpolarized case. For relaxation in a uniform external field H, Zeeman energy conservation during spin flipping interactions essentially shifts the location of the Tsp−2\\sp{-2}sp−2 behavior from zero polarization to the polarization P(H) which would be produced in equilibrium with the external field H. When the initial polarization of the system is different from P(H), Tsb1\\sb1sb1 again approaches a constant value which is equally sensitive to the initial polarization as temperature is reduced to zero. We apply our calculations to the case of dilute sp3\\sp3sp3He-HeII solutions. We also consider the calculation of density dependent corrections to Tsb1\\sb1sb1 for unpolarized, or weakly polarized sp3\\sp3sp3He-HeII using the long wavelength limit of the Bardeen-Baym-Pines interaction as a form for the spin independent part of the sp3\\sp3sp3He-sp3\\sp3sp3He interaction. Owing to the positive sign of the antisymmetric Landau parameter rmFsbspoa\\rm F\\sbsp{o}{a}rmFsbspoa in dilute sp3\\sp3sp3He-HeII Fermi Liquid interactions act to screen the magnetic dipole interactions which cause relaxation. To lowest order in density we find that the relaxation rate 1/Tsb1\\sb1sb1 is reduced by factor rm(1−3Fsbspoa)\\rm (1 - 3F\\sbsp{o}{a})rm(1−3Fsbspoa) which compares favorably with recent calculations of Tsb1\\sb1sb1 for pure sp3\\sp3sp3He.
We study the transverse dynamical spin susceptibility of the two-dimensional U(1) spinon Fermi-surface spin liquid in a small applied Zeeman field. We show that both short-range interactions, present in a generic Fermi liquid, as well as gauge fluctuations, characteristic of the U(1) spin liquid, qualitatively change the result based on the frequently assumed noninteracting spinon approximation. The short-range part of the interaction lead to a collective ``spinon spin wave'' mode, which splits off from the two-spinon continuum at a small momentum and disperses downward. Gauge fluctuations renormalize the susceptibility, providing nonzero power-law weight in the region outside the spinon continuum and giving the spin wave a finite lifetime, which scales as momentum squared. We also study the effect of Dzyaloshinskii-Moriya anisotropy on the zero momentum susceptibility, which is measured in electron spin resonance (ESR), and obtain a resonance linewidth linear in temperature and varying as B2/3{B}^{2/3}B2/3 with magnetic field BBB at low temperatures. Our results form the basis for a theory of inelastic neutron scattering, ESR, and resonant inelastic x-ray scattering studies of this quantum spin-liquid state.