Static Local Field Research Articles

Exchange and correlation effect on spin Coulomb drag in a quasi-two-dimensional electron system

We investigate the effect of many-body electronic correlations on spin Coulomb drag (SCD) beyond the random phase approximation (RPA). We make use of the fully spin-resolved static and dynamical many-body local field factors of the two-dimensional electron gas (2DEG) to improve the calculations of the particle-hole and plasmon-mediated contributions to the SCD. Also, we incorporate in our calculations the transverse thickness of the quantum well in which the 2DEG resides. In contrast to the conventional charge Coulomb drag, in the SCD the effect of layer thickness is significant even at relatively high temperature and densities. The final outcome of our study is that the enhancement of the spin drag caused by many-body local field effects largely compensates the reduction of the effect coming from the finite well thickness, restoring good agreement with the experimental observations by C.P. Weber et al., Nature 437 (2005) 1330.

Exchange and correlation effects on plasmon dispersions and Coulomb drag in low-density electron bilayers

We investigate the effect of exchange and correlation (xc) on the plasmon spectrum and the Coulomb drag between spatially separated low-density two-dimensional electron layers. We adopt a new approach, which employs dynamic xc kernels in the calculation of the bi-layer plasmon spectra and of the plasmon-mediated drag, and static many-body local field factors in the calculation of the particle-hole contribution to the drag. The spectrum of bi-layer plasmons and the drag resistivity are calculated in a broad range of temperatures taking into account both intra- and inter-layer correlation effects. We observe that both plasmon modes are strongly affected by xc corrections. After the inclusion of the complex dynamic xc kernels, a decrease of the electron density induces shifts of the plasmon branches in opposite directions. And this is in stark contrast to the tendency obtained within the RPA that both optical and acoustical plasmons move away from the boundary of the particle-hole continuum with a decrease in the electron density. We find that the introduction of xc corrections results in a significant enhancement of the transresistivity and qualitative changes in its temperature dependence. In particular, the large high-temperature plasmon peak that is present in the random phase approximation is found to disappear when the xc corrections are included. Our numerical results at low temperatures are in good agreement with the results of recent experiments by M. Kellogg {\it et al.}, Solid State Commun. \textbf{123}, 515 (2002).

Proton NMR measurements of the local magnetic field in the paramagnetic metal and antiferromagnetic insulator phases ofλ−(BETS)2FeCl4

Measurements of the $^{1}$H-NMR spectrum of a small ($\sim$ 4 $\mu$g) single crystal of the organic conductor $\lambda$-(BETS)$_{2}$FeCl$_{4}$ are reported with an applied magnetic field $\bf{B}$$_{0}$ = 9 T parallel to the a-axis in the $ac$-plane over a temperature $(T)$ range 2.0 $-$ 180 K. They provide the distribution of the static local magnetic field at the proton sites in the paramagnetic metal (PM) and antiferromagnetic insulator (AFI) phases, along with the changes that occur at the PM$-$AFI phase transition. The spectra have six main peaks that are significantly broadened and shifted at low $T$. The origin of these features is attributed to the large dipolar field from the 3d Fe$^{3+}$ ion moments (spin $S_{\rm{d}}$ = 5/2). Their amplitude and $T-$dependence are modeled using a modified Brillouin function that includes a mean field approximation for the total exchange interaction ($J_{0}$) between one Fe$^{3+}$ ion and its two nearest neighbors. A good fit is obtained using $J_{0}$ = $-$ 1.7 K. At temperatures below the PM$-$AFI transition temperature $T_{MI}$ = 3.5 K, an extra peak appears on the high frequency side of the spectrum and the details of the spectrum become smeared. Also, the rms linewidth and the frequency shift of the spectral distribution are discontinuous, consistent with the transition being first-order. These measurements verify that the dominant local magnetic field contribution is from the Fe$^{3+}$ ions and indicate that there is a significant change in the static local magnetic field distribution at the proton sites on traversing the PM to AFI phase transition.

Many particle aspects of a semiconductor quantum wire within an improved random phaseapproximation

The structure factor, pair distribution function, screened impurity potential, density ofscreening charge, and exchange and screened exchange energies have been theoreticallyinvestigated for a semiconductor quantum wire using an improved random phaseapproximation that takes into account the local field corrections within the Hubbardapproximation. Our approach enabled us to obtain approximate analytical results on someof the aspects and to greatly simplify the computation task on others. However,computed results from our simple approach show very good agreement with thoseobtained by performing cumbersome numerical solutions for the structure factor,density–density response function and the static local field corrections, within theSingwi–Tosi–Land–Sjölander approximation. Our investigations suggest that: (i) themagnitude of the screened impurity potential and the average distribution ofelectrons about an electron at larger distances are enhanced on reducing the width ofquantum wire, and (ii) the exchange interactions strengthen on narrowing thequantum wire and on increasing the carrier density. Friedel oscillations are seenin both our computed screened potential and the density of screening charge.

Static Local Field Factor and Ground State Properties of Interacting Electron Gas

In the most general case, the calculation of the static local field factor G(q) for the unpolarised electron gas requires the knowledge of exchange-correlation energy functionals for both the parallel and antiparallel relative spin orientations of the electron gas system. Accurate density interpolation formulae using the quantum Monte Carlo data of Ceperley–Alder for the correlation energy of electron gas in both the “para” and “ferro” states, respectively, in the given density range are used for the calculation of G(q). Fulfilment of relevant consistency criteria is ensured and the local field factor so obtained renders significant improvement of ab initio pseudopotential calculation of effective interaction of Al. The Levin like interpolant of the correlation energy Ceperley–Alder data has been further used to study the ground state properties of the electron gas. It is also noted that a better understanding of the interacting electron gas properties requires a more accurate spin interpolation formula for the correlation energy than the existing ones.

Local field in LiD polarized target material

We have experimentally studied the first and the second moments of D, 6 Li and 7 Li (I> 1 2 ) NMR lines in a granulated LiD-target material as a function of nuclear polarizations and the data has been compared with a theory elaborated by Abragam, Roinel and Bouffard for monocrystalline samples. The experiments were carried out in the large COMPASS twin-target at CERN. The static local magnetic field of the polarized nuclei was measured by frequency shift between the NMR-signals in the two oppositely polarized cells and lead to the first moment, whereas the investigation of the second moment was done through Gaussian approximation. The average field magnitude in granulated material was estimated 20% larger than the value given by the calculations for monocrystalline samples of cylindrical shape. The second moment shows a qualitative agreement with the theory but it is slightly larger at the negative than at the positive polarization. In a polarized mode, the moments depend on the saturated microwave field.

Local-field factors in a polarized two-dimensional electron gas

We derive approximate expressions for the static local field factors of a spin polarized two-dimensional electron gas which smoothly interpolate between their small- and large-wavevector asymptotic limits. For the unpolarized electron gas, the proposed analytical expressions reproduce recent diffusion Monte Carlo data. We find that the degree of spin polarization produces important modifications to the local factors of the minority spins, while the local field functions of the majority spins are less affected.

Dynamic form factor of two-component plasmas beyond the static local field approximation

The spectrum of ion density fluctuations in a strongly coupled plasma is described both within the static G(k, 0) and high-frequency G(k, ∞) local field approximation. By a direct comparison with molecular dynamics data, we find that for large coupling, G(k, 0) is inadequate. Based on this result, we employ the Zwanzig–Mori memory function approach to model the Thomson scattering cross section, i.e. the electron dynamic form factor See(k, ω) of a dense two-component plasma. We show the sensitivity of See(k, ω) to three approximations for G(k, ω).

Dynamical local field, compressibility, and frequency sum rules for quasiparticles

The finite temperature dynamical response function including the dynamical local field is derived within a quasiparticle picture for interacting one-, two-, and three-dimensional Fermi systems. The correlations are assumed to be given by a density-dependent effective mass, quasiparticle energy shift, and relaxation time. The latter one describes disorder or collisional effects. This parametrization of correlations includes local-density functionals as a special case and is therefore applicable for density-functional theories. With a single static local field, the third-order frequency sum rule can be fulfilled simultaneously with the compressibility sum rule by relating the effective mass and quasiparticle energy shift to the structure function or pair-correlation function. Consequently, solely local-density functionals without taking into account effective masses cannot fulfill both sum rules simultaneously with a static local field. The comparison to the Monte Carlo data seems to support such a quasiparticle picture.

Analytical expressions for the spin-spin local-field factor and the spin-antisymmetric exchange-correlation kernel of a two-dimensional electron gas

We present an analytical expression for the static many-body local field factor $G_{-}(q)$ of a homogeneous two-dimensional electron gas, which reproduces Diffusion Monte Carlo data and embodies the exact asymptotic behaviors at both small and large wave number $q$. This allows us to also provide a closed-form expression for the spin-antisymmetric exchange and correlation kernel $K^{-}_{xc}(r)$ which represents a key input for spin-density functional studies of inhomogeneous electronic systems.

Analytical expressions for the charge-charge local-field factor and the exchange-correlation kernel of a two-dimensional electron gas

We present an analytical expression for the static many-body local field factor ${G}_{+}(q)$ of a homogeneous two-dimensional electron gas, which reproduces diffusion Monte Carlo data and embodies the exact asymptotic behaviors at both small and large wave number q. This allows us to also provide a closed-form expression for the exchange and correlation kernel ${K}_{\mathrm{xc}}(r),$ which represents a key input for density functional studies of inhomogeneous systems.

Location of the superconducting hole condensate in Sr 2YRu 1− uCu uO 6 by μ +SR

The magnetic and superconducting characteristics of sintered Sr 2YRu 1− u Cu u O 6 (for u=0.05, 0.10, 0.15) were probed using transverse- and zero-field muon-spin rotation (μ +SR). Since positive muons are attracted to oxygen ions in the high- T C oxides, Sr 2YRu 1− u Cu u O 6 should (and does) present two types of μ + sites, one in the YRuO 4 layers and the other in the SrO layers. The transverse- and zero-field μSR spectra for all three stoichiometries exhibit magnetic ordering at and below T N ≈ 30 K, with a static local field of ∼3 kG. This transition is marked by a dramatic increase in the μ + spin relaxation rate as the temperature decreases below T N, corresponding to an increased static disordering of the magnetic moments. Above T N no static fields are observed. Instead, the data exhibit a slow dynamic depolarization, presumably due to rapid fluctuation of magnetic moments. Both transverse- and zero-field data also indicate a smaller second component (∼10%) that we associate with the SrO layer, exhibiting superconducting behavior in transverse field with an observed bulk T C≈ T N∼30 K.

Electron correlations in an electron bilayer at finite temperature: Landau damping of the acoustic plasmon

We report angle-resolved Raman scattering observations of the temperature-dependent Landau damping of the acoustic plasmon in an electron bilayer system realized in a GaAs double-quantum-well structure. Corresponding calculations of the charge-density excitation spectrum of the electron bilayer using forms of the random-phase approximation (RPA), and the static local field formalism of Singwi, Tosi, Land and Sjölander (STLS) extended to incorporate non-zero electron temperature Te and phenomenological damping, are also presented. The STLS calculations include details of the temperature dependence of the intra- and inter-layer local field factors and pair correlation functions. Good agreement between experiment and the various theories is obtained for the acoustic plasmon energy and damping for Te TF/2, where TF is the Fermi temperature. However, contrary to current expectations, all of the calculations show significant departures from our experimental data for Te TF/2. From this, we go on to demonstrate unambiguously that real local field factors fail to provide a physically accurate description of exchange correlation behaviour in low-dimensional electron gases. Our results suggest instead that one must resort to a dynamical local field theory, characterized by a complex field factor to provide a more accurate description.

MUON SPIN ROTATION IN SR2YRU1-UCUUO6

The magnetic and superconducting behaviors of sintered Sr 2 YRu 1-u Cu u O 6 (for u=0.05, 0.10, 0.15) were probed using transverse- and zero-field muon spin rotation (μ+ SR). In general, positive muons are attracted to oxygen ions in the high-T c oxides, and so, Sr 2 YRu 1-u Cu u O 6 should (and does) present two types of μ+ sites, those associated with the oxygen in the YRuO 4 layers and those associated with the SrO-layer oxygen. The tranverse- and zero-field data for all three stoichiometries u exhibit a sudden onset of magnetic structure at TN~30 K, with a static local field of ~3 kG. This transition is marked by a dramatic increase in the relaxation rate as the temperature decreases below TN, corresponding to an increased static disordering of the magnetic moments. Above TN no static fields are observed. Instead the data exhibit a slow dynamic depolarization, presumably due to the rapid fluctuation of paramagnetic moments. Both transverse- and zero-field data also indicate a smaller second component (~10%) which we associate with the SrO layer, exhibiting superconducting behavior in transverse field with an observed T c ≈TN~30 K.

Static local field correction description of acoustic waves in strongly coupling dusty plasmas

The kinetic equations for an interacting dust system with external time-dependent forces is considered from the Born–Bogolyubov–Green–Kirkwood–Yvon equations. A kinetic equation is obtained by writing the two-particle distribution function as a product of two one-particle distribution functions and the equilibrium radial distribution function. It is shown that a Vlasov-like equation is recovered with a collision term which is a functional of the pair correlation function. Wave behavior from the corresponding fluid equations is considered for a dusty plasma. The results are in qualitative agreement with previously obtained dispersion relations based on generalized hydrodynamics and the quasilocalized charge approximation.

Static Local Field Factor for Dielectric Screening Function of Electron Gas at Metallic and Lower Densities

A simple parametric form for the static local field factor G(q) which appears in the dielectric screening theory of an electron gas is proposed. A very accurate fit of Ceperley–Alder data of electron correlation energy in the entire density range using Levin–Weniger interpolant is obtained and used for the calculation of G(q). Both the short- and long- wavelength limits of G(q) are satis ed exactly in the present formulation which ensures fulfilment of a number of other legitimate criteria and produces some interesting results. A comparative study of the various static local eld factors derived so far vis-a-vis the present work is made. Even within the approximations of a static self-consistent theory, reasonable prediction regarding Wigner Crystallization is obtained in the present work.

μSR on an induced-moment spin glass system: Hg 1-x Fe x Se

Zero and longitudinal field μSR have been used to examine the singlet ground state magnetism of the diluted magnetic semiconductor Hg1-xFexSe. For x\geq 0.05\ μSR experiments indicate spin glass behaviour which is limited to sample regions with locally enhanced Fe2+ content. Longitudinal field spectra in the glassy state reveal a static local field \sim 50 mT due to induced moments of Fe2+. These are proposed to originate from a distribution of bound magnetic polaron energies.

Static response and local field factor of the electron gas.

We have evaluated the density-density static response of the electron gas at zero temperature and in the metallic regime by diffusion Monte Carlo. The computed local field factor $G(q)$ smoothly interpolates between the asymptotic small and large $q$ behavior, with a crossover around ${2q}_{F}$. In fact, $G(q)$ appears to be almost completely given by its asymptotes, being accurately reproduced by the local density approximation to density functional theory for $q\ensuremath{\lesssim}{2q}_{F}$. We give a simple formula to reproduce $G(q)$ at relevant values of the wave vector.

Unusual static local field distribution in the spin-frozen state of icosahedral AlMnSi

Zero-field and longitudinal field muon spin relaxation in AlMnSi quasicrystals show the spin glass state remains inhomogeneous down to temperatures of order 1 100 T g . In the frozen-moment regions, the field distribution at the muon site is static but causes monotonic relaxation of the ensemble polarization to the “ 1 3 tail ”.

μSR studies in an I2-doped phenylenediamine polymer

We report μSR studies of the recently synthesized I2-doped phenylenediamine polymer. Longitudinal-field spectra exhibit typical behavior of a spin-glass with a freezing temperatureT g ∼ 100 K and a spontaneous static local field ∼ 500 G at low temperatures. Preliminary magnetization measurements hint of antiferromagnetic spin coupling and hysteretic behavior aroundT g. These features suggest possible spin-glass and/or antiferromagnetic spin freezing with a high transition temperature due to the doped radical spins in this organic polymer.