Spin-polarized Fermi Liquids Research Articles

Detecting fractionalization in critical spin liquids using color centers

Quantum spin liquids are highly entangled ground states of insulating spin systems, in which magnetic ordering is prevented down to the lowest temperatures due to quantum fluctuations. One of the most extraordinary characteristics of quantum spin liquid phases is their ability to support fractionalized, low-energy quasiparticles known as spinons, which carry spin-1/2 but bear no charge. Relaxometry based on color centers in crystalline materials—of which nitrogen-vacancy (NV) centers in diamond are a well-explored example—provides an exciting new platform to probe the spin spectral functions of magnetic materials with both energy and momentum resolution and to search for signatures of these elusive, fractionalized excitations. In this work, we theoretically investigate the color-center relaxometry of two archetypal quantum spin liquids: the two-dimensional U(1) quantum spin liquid with a spinon Fermi surface and the spin-1/2 antiferromagnetic spin chain. The former is characterized by a metallic, spin-split ground state of mobile, interacting spinons, which closely resembles a spin-polarized Fermi liquid ground state but with neutral quasiparticles. We show that the observation of the Stoner continuum and the collective spin wave mode in the spin spectral function would provide a strong evidence for the existence of spinons and fractionalization. In one dimension, mobile spinons form a Luttinger liquid ground state. We show that the spin spectral function exhibits strong features representing the collective density and spin-wave modes, which are broadened in an algebraic fashion with an exponent characterized by the Luttinger parameter. The possibilities of measuring these collective modes and detecting the power-law decay of the spectral weight using NV relaxometry are discussed. We also examine how the transition rates are modified by marginally irrelevant operators in the Heisenberg limit. Published by the American Physical Society 2024

Superconductivity of highly spin-polarized electrons in FeSe probed by Se77 NMR

A number of recent experiments indicate that the iron-chalcogenide FeSe provides the long-sought possibility to study bulk superconductivity in the cross-over regime between the weakly coupled Bardeen-Cooper-Schrieffer (BCS) pairing and the strongly coupled Bose-Einstein condensation (BEC). We report on $^{77}\mathrm{Se}$ nuclear magnetic resonance experiments of FeSe, focused on the superconducting phase for strong magnetic fields applied along the $c$ axis, where a distinct state with large spin polarization was reported. We determine this high-field state as bulk superconducting with high spatial homogeneity of the low-energy spin fluctuations. Further, we find that the static spin susceptibility becomes unusually small at temperatures approaching the superconducting state, despite the presence of pronounced spin fluctuations. Taken together, our results clearly indicate that FeSe indeed features an unusual field-induced superconducting state of a highly spin-polarized Fermi liquid in the BCS-BEC crossover regime.

Zeeman-limited superconductivity in crystalline Al films

We report the evolution of the Zeeman-mediated superconducting phase diagram (PD) in ultrathin crystalline Al films. Parallel critical field measurements, down to 50 mK, were made across the superconducting tricritical point of films ranging in thickness from 7 to 30 ML. The resulting phase boundaries were compared with the quasiclassical theory of a Zeeman-mediated transition between a homogeneous BCS condensate and a spin-polarized Fermi liquid. Films thicker than $\ensuremath{\sim}20\phantom{\rule{0.16em}{0ex}}\mathrm{ML}$ showed good agreement with theory, but thinner films exhibited an anomalous PD that cannot be reconciled within a homogeneous BCS framework.

Spin dependence of electron effective masses in InGaAs/InAlAs quantum well

The effective masses for spin-up and spin-down electrons of a partially spin-polarized Fermi liquid are theoretically expected to be different. We extract the spin-up and spin-down effective masses from magnetotransport measurements at different temperatures for a two-dimensional electron gas in an In0.65Ga0.35As/In0.52Al0.48As quantum well exhibiting zero-field spin splitting. We apply two analytical methods, one involving the simultaneous fitting of fast Fourier transform (FFT) spectra and the other involving inverse FFT analysis. Both methods confirm that the effective masses for spin-up and spin-down are different, consistent with theoretical expectations.

Neutrino mean free paths in spin-polarized neutron Fermi liquids

Neutrino mean free paths in magnetized neutron matter are calculated using the Hartree-Fock approximation with effective Skyrme and Gogny forces in the framework of the Landau Fermi Liquid Theory. It is shown that describing nuclear interaction with Skyrme forces and for magnetic field strengths $log_{10} B(G) \gtrsim 17$, the neutrino mean free paths stay almost unchanged at intermediate densities but they largely increase at high densities when they are compared to the field-free case results. However the description with Gogny forces differs from the previous and mean free paths stay almonst unchanged or decrease at densities $[1-2]\rho_0$. This different behaviour can be explained due to the combination of common mild variation of the Landau parameters with both types of forces and the values of the nucleon effective mass and induced magnetization of matter under presence of a strong magnetic field as described with the two parametrizations of the nuclear interaction.

Giant Viscosity Enhancement in a Spin-Polarized Fermi Liquid

The viscosity is measured for a Fermi liquid, a dilute 3He-4He mixture, under extremely high magnetic field/temperature conditions (B<or=14.8 T, T>or=1.5 mK). The spin-splitting energy microB is substantially greater than the Fermi energy kBTF; as a consequence the polarization tends to unity and s-wave quasiparticle scattering is suppressed for T<<TF. Using a novel composite vibrating-wire viscometer an enhancement of the viscosity is observed by a factor of more than 500 over its low-field value. Good agreement is found between the measured viscosity and theoretical predictions based upon a t-matrix formalism.

Zero-temperature spin-wave damping in a spin-polarized Fermi liquid

We have measured the temperature and polarization dependence of the spin-wave damping and spin diffusion coefficient in a saturated $^{3}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}$ mixture with a concentration of 9.4% at a pressure of $8\phantom{\rule{0.3em}{0ex}}\text{bars}$. A Leiden dilution refrigerator has been used to enhance the nuclear polarization and to cool the mixture to temperatures in the range $10--15\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$. The maximum polarization is 3.4 times higher than the equilibrium value of 2.7% in an external magnetic field of $11.36\phantom{\rule{0.3em}{0ex}}\mathrm{T}$. The effects of the dipolar interactions and the radiation damping have been taken into account in the analysis of the spin-wave spectra. We observe that the polarization dependence of the spin-wave damping is proportional to ${T}^{2}+{\mathcal{A}}^{2}{T}_{a0}^{2}$ where $T$ is the temperature, $\mathcal{A}$ is the polarization enhancement factor, and ${T}_{a0}$ is the anisotropy temperature for the mixture at equilibrium in the external field. Our result ${T}_{a0}=3.66\ifmmode\pm\else\textpm\fi{}0.14\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$ is 30% higher than the theoretical prediction for very dilute mixtures and is evidence for the existence of polarization-induced relaxation of transverse spin currents.

Spin-Independent Effective Mass in a Valley-Degenerate Electron System

In a generic spin-polarized Fermi liquid, the masses of spin-up and spin-down electrons are expected to be different and to depend on the degree of polarization. This expectation is not confirmed by the experiments on two-dimensional heterostructures. We consider a model of an N-fold degenerate electron gas. It is shown that in the large- limit, the mass is enhanced via a polaronic mechanism of emission or absorption of virtual plasmons. As plasmons are classical collective excitations, the resulting mass does not depend on , and thus on polarization, to the leading order in 1/N. We evaluate the 1/N corrections and show that they are small even for N = 2.

Vortex matter in the charged Bose liquid at absolute zero

The Gross-Pitaevskii-type equation is solved for the charge Bose liquid in an external magnetic field at zero temperature. There is a vortex lattice with locally broken charge neutrality. Remarkably, there is no upper critical field at zero temperature, so the density of single flux-quantum vortices monotonously increases with the magnetic field up to $B=\ensuremath{\infty}$ and no indication of a phase transition. The size of each vortex core decreases at about ${B}^{\ensuremath{-}1∕2}$ keeping the system globally charge neutral. If bosons are composed of two fermions, a phase transition to a spin-polarized Fermi liquid at some magnetic field larger than the pair-breaking field is predicted.

Transverse spin dynamics in a spin-polarized Fermi liquid

The linear equations for transverse spin dynamics in weakly polarised degenerate Fermi liquid with arbitrary relationship between temperature and polarization 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 waves 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.

New evidence for zero-temperature relaxation in a spin-polarized fermi liquid.

Spin-echo experiments are reported for 3He-4He solutions under extremely high B/T conditions, B=14.75 T and T>or=1.73 mK. The 3He concentration x(3) was adjusted close to the value x(c) approximately 3.8% at which the spin-rotation parameter muM0 vanishes. In this way the transverse and longitudinal spin-diffusion coefficients D( perpendicular ),D( parallel ) were measured while keeping |muM(0)|<1. It is found that the temperature dependence of D( perpendicular ) deviates strongly from 1/T(2), with anisotropy temperature T(a)=4.26(+0.18)(-0.44) mK. This value is close to the theoretical prediction for dilute solutions and suggests that spin current relaxation remains finite as the temperature tends to zero.

Approximate Energy Expression for Spin-Polarized Fermi Liquids

An approximate energy expression is proposed for arbitrarily spin-polarized Fermi liquids with central two-body forces. It is explicitly expressed as a functional of spin-dependent radial distribution functions and can be used conveniently in the variational method. It includes the potential energies completely and the kinetic energies up to main parts of the three-body cluster terms. This approximation is similar to that used previously for spinunpolarized and fully polarized matter. A notable feature of this expression is that it guarantees the necessary conditions on arbitrarily spin-polarized structure functions automatically. The Euler-Lagrange equations are derived from this energy expression and are numerically solved for arbitrarily spin-polarized liquid 3 He. The results for liquid 3 He with the HFDHE2 potential are consistent with the nearly ferromagnetic property.

Zero-Temperature Relaxation in Pure Fermi Liquids and Ferromagnetic Metals

We discuss the effect of the zero-temperature transverse attenuation in spin-polarized Fermi liquids on related phenomena in helium and electron systems. In helium Fermi liquids, the magnetic dipole-dipole interaction leads to a transfer of transverse attenuation to longitudinal processes resulting in finite sound attenuation and effective viscosity even at zero temperature. In Heisenberg ferromagnetic metals, this Fermi-liquid effect affects the attenuation of ferromagnetic magnons as a result of exchange coupling between spins of ferromagnetic and conduction electrons.

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.

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.

Zero-temperature attenuation and transverse spin dynamics in fermi liquids. III. Low spin polarizations

This is the third in a series of papers on microscopic theory of transverse dynamics in spin-polarized Fermi liquids. In the lowest order in polarization our exact general theory of Ref. 1 reproduces the conventional Landau-Silin-Leggett theory of Fermi liquids. The next term in polarization expansion contains a zero-temperature attenuation with the magnitude that does not depend on polarization. This attenuation results in a finite relaxation time in transverse spin dynamics at zero temperature and is responsible for anomalous temperature behavior of spin diffusion. The zero-temperature attenuation is determined by two angular harmonics of the derivatives of the mass operators and the irreducible vertex in off-shell directions, and cannot be expressed via standard Fermi liquid harmonics. At high polarizations, the parameters of transverse spin dynamics are calculated as an expansion in polarization. The expansion involves complex values of interaction function and energy on a set of isoenergetic surfaces with the radii between the Fermi momenta for up and down spins,p↓ andp↑. The results explain recent experimental data on spin diffusion in spin-polarized liquid3He↑ and3He↑-4He mixtures. The comparison with experimental data indicates that the superfluid transition temperature for3He in3He-4He mixtures may be much lower than the current estimates.

Anomalous spin dynamics and relaxation in Fermi liquids.

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.

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.

Effects of high spin polarization in 3He↑- 4He mixtures

We apply a generalized microscopic Landau theory of spin-polarized Fermi liquids to 3He↑- 4He mixtures. We describe spin dynamics, a zero temperature relaxation, and thermodynamic parameters including the retardation caused by the phonon part of 3He- 3He 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.