Physical Review Letters

Anomalous spin dynamics and relaxation in Fermi liquids

A. E. Meyerovich, Karen A. Musaelian

Published Mar 14, 1994• 31 citations

Abstract

We explain the anomalous temperature dependence of spin diffusion in liquid $^{3}\mathrm{\ensuremath{\uparrow}}$ and $^{3}\mathrm{\ensuremath{-}}^{4}$He mixtures. The anomaly is an experimental manifestation of a unique zero-temperature attenuation in the Fermi liquid theory. We extended our microscopic theory of spin dynamics in spin-polarized Fermi liquids to finite temperatures. The zero-temperature attenuation changes the behavior of the spectrum near the singular point. The data indicate that the superfluid transition temperature for $^{3}\mathrm{He}$ in $^{3}\mathrm{\ensuremath{-}}^{4}$He mixtures is much lower than the current estimates.

DOI: 10.1103/physrevlett.72.1710

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Transverse spin dynamics in a spin-polarized Fermi liquid

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Physical Review Letters

Anomalous spin dynamics and relaxation in Fermi liquids

A. E. Meyerovich, Karen A. Musaelian

Published Mar 14, 1994• 31 citations

Publisher

Abstract

We explain the anomalous temperature dependence of spin diffusion in liquid

^{3}\mathrm{\ensuremath{\uparrow}}

and

^{3}\mathrm{\ensuremath{-}}^{4}

He mixtures. The anomaly is an experimental manifestation of a unique zero-temperature attenuation in the Fermi liquid theory. We extended our microscopic theory of spin dynamics in spin-polarized Fermi liquids to finite temperatures. The zero-temperature attenuation changes the behavior of the spectrum near the singular point. The data indicate that the superfluid transition temperature for

^{3}\mathrm{He}

^{3}\mathrm{\ensuremath{-}}^{4}

He mixtures is much lower than the current estimates.

DOI: 10.1103/physrevlett.72.1710

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.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/0310620Physical Review BApr 28, 200425 citations

Low-Temperature Spin Diffusion in a Spin-Polarized Fermi Gas

Denis I. Golosov, Andrei E. Ruckenstein

We present a finite temperature calculation of the transverse spin-diffusion coefficient ${D}_{\ensuremath{\perp}}$ in a dilute degenerate Fermi gas, in the presence of a small external magnetic field $H$ . While the longitudinal diffusion coefficient displays the conventional Fermi-liquid dependence, ${D}_{\ensuremath{\parallel}}\ensuremath{\propto}{T}^{\ensuremath{-}2}$, the behavior of ${D}_{\ensuremath{\perp}}$ shows three separate regimes: (a) ${D}_{\ensuremath{\perp}}\ensuremath{\sim}{H}^{\ensuremath{-}2}$ for $T\ensuremath{\ll}H$, (b) ${D}_{\ensuremath{\perp}}\ensuremath{\sim}{T}^{\ensuremath{-}2}$, $\frac{{D}_{\ensuremath{\perp}}}{{D}_{\ensuremath{\parallel}}}\ensuremath{\ne}1$ for $T\ensuremath{\gg}H$ and large spin-rotation parameter $\ensuremath{\xi}\ensuremath{\gg}1$, and (c) ${D}_{\ensuremath{\perp}}={D}_{\ensuremath{\parallel}}\ensuremath{\propto}{T}^{\ensuremath{-}2}$ for $T\ensuremath{\gg}H$ and $\ensuremath{\xi}\ensuremath{\ll}1$. Our results are qualitatively consistent with the experimental data in weakly spin-polarized $^{3}\mathrm{He}$ and $^{3}\mathrm{He}$ - $^{4}\mathrm{He}$ mixtures.We present a finite temperature calculation of the transverse spin-diffusion coefficient ${D}_{\ensuremath{\perp}}$ in a dilute degenerate Fermi gas, in the presence of a small external magnetic field $H$. While the longitudinal diffusion coefficient displays the conventional Fermi-liquid dependence, ${D}_{\ensuremath{\parallel}}\ensuremath{\propto}{T}^{\ensuremath{-}2}$, the behavior of ${D}_{\ensuremath{\perp}}$ shows three separate regimes: (a) ${D}_{\ensuremath{\perp}}\ensuremath{\sim}{H}^{\ensuremath{-}2}$ for $T\ensuremath{\ll}H$, (b) ${D}_{\ensuremath{\perp}}\ensuremath{\sim}{T}^{\ensuremath{-}2}$, $\frac{{D}_{\ensuremath{\perp}}}{{D}_{\ensuremath{\parallel}}}\ensuremath{\ne}1$ for $T\ensuremath{\gg}H$ and large spin-rotation parameter $\ensuremath{\xi}\ensuremath{\gg}1$, and (c) ${D}_{\ensuremath{\perp}}={D}_{\ensuremath{\parallel}}\ensuremath{\propto}{T}^{\ensuremath{-}2}$ for $T\ensuremath{\gg}H$ and $\ensuremath{\xi}\ensuremath{\ll}1$. Our results are qualitatively consistent with the experimental data in weakly spin-polarized $^{3}\mathrm{He}$ and $^{3}\mathrm{He}$- $^{4}\mathrm{He}$ mixtures.

arXiv:cond-mat/9406101Physical Review LettersFeb 27, 199519 citations

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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.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 matterFeb 1, 199311 citations

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Physical Review LettersAug 9, 199391 citations

Spin transport in cold Fermi gases: A pseudogap interpretation of spin diffusion experiments at unitarity

Dan Wulin, Hao Guo, Chih-Chun Chien +1 more

We address recent spin transport experiments in ultracold unitary Fermi gases. We provide a theoretical understanding for how the measured temperature dependence of the spin diffusivity at low $T$ can disagree with the expected behavior of a Fermi liquid (FL), while the spin susceptiblity, following the experimental protocols, is consistent with a FL picture. We show that the experimental protocols for extracting the spin susceptibility implicitly reflect a FL viewpoint; relaxing this leads to consistency within but not proof of a pseudogap-based theory. Our transport calculations yield insight into the observed suppression of the spin diffusion constant at lower $T$ .We address recent spin transport experiments in ultracold unitary Fermi gases. We provide a theoretical understanding for how the measured temperature dependence of the spin diffusivity at low $T$ can disagree with the expected behavior of a Fermi liquid (FL), while the spin susceptiblity, following the experimental protocols, is consistent with a FL picture. We show that the experimental protocols for extracting the spin susceptibility implicitly reflect a FL viewpoint; relaxing this leads to consistency within but not proof of a pseudogap-based theory. Our transport calculations yield insight into the observed suppression of the spin diffusion constant at lower $T$.

arXiv:1102.0997Physical Review AJun 6, 201117 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.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/0507675Physical Review BOct 20, 200523 citations

We explain the anomalous temperature dependence of spin diffusion in liquid

^{3}\mathrm{\ensuremath{\uparrow}}

and

^{3}\mathrm{\ensuremath{-}}^{4}

^{3}\mathrm{He}

^{3}\mathrm{\ensuremath{-}}^{4}

He mixtures is much lower than the current estimates.

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.

H

. While the longitudinal diffusion coefficient displays the conventional Fermi-liquid dependence, ${D}_{\ensuremath{\parallel}}\ensuremath{\propto}{T}^{\ensuremath{-}2}$, the behavior of ${D}_{\ensuremath{\perp}}$ shows three separate regimes: (a) ${D}_{\ensuremath{\perp}}\ensuremath{\sim}{H}^{\ensuremath{-}2}$ for $T\ensuremath{\ll}H$, (b) ${D}_{\ensuremath{\perp}}\ensuremath{\sim}{T}^{\ensuremath{-}2}$, $\frac{{D}_{\ensuremath{\perp}}}{{D}_{\ensuremath{\parallel}}}\ensuremath{\ne}1$ for $T\ensuremath{\gg}H$ and large spin-rotation parameter $\ensuremath{\xi}\ensuremath{\gg}1$, and (c) ${D}_{\ensuremath{\perp}}={D}_{\ensuremath{\parallel}}\ensuremath{\propto}{T}^{\ensuremath{-}2}$ for $T\ensuremath{\gg}H$ and $\ensuremath{\xi}\ensuremath{\ll}1$. Our results are qualitatively consistent with the experimental data in weakly spin-polarized

^{3}\mathrm{He}

and

^{3}\mathrm{He}

^{4}\mathrm{He}

mixtures.

We have studied NMR spin echoes in

^{3}\mathrm{He}

liquid in a magnetic field

{\mathit{B}}_{0}

=8 T for temperatures T\ensuremath{\ge}4.5 mK. The data are analyzed in terms of the Leggett-Rice effect to obtain the transverse spin-diffusion coefficient ${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$(T). For T20 mK we find that ${\mathit{D}}_{\mathrm{\ensuremath{\perp}}}$ is less than measured in earlier experiments at lower

{\mathit{B}}_{0}

. This phenomenon has been predicted for degenerate Fermi systems, due to the phase space created for quasiparticle scattering by spin polarization. The effect we have measured is more pronounced than suggested by scaling a dilute-gas theory result by a Fermi-liquid factor.

We address recent spin transport experiments in ultracold unitary Fermi gases. We provide a theoretical understanding for how the measured temperature dependence of the spin diffusivity at low

T

can disagree with the expected behavior of a Fermi liquid (FL), while the spin susceptiblity, following the experimental protocols, is consistent with a FL picture. We show that the experimental protocols for extracting the spin susceptibility implicitly reflect a FL viewpoint; relaxing this leads to consistency within but not proof of a pseudogap-based theory. Our transport calculations yield insight into the observed suppression of the spin diffusion constant at lower

T

{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.