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Register a new userPhase Diagram of Na$_x$CoO$_2$ Studied by Gutzwiller Density Functional Theory
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The ground states of Na$_x$CoO$_2$ ($0.0<x<1.0$) is studied by the LDA+Gutzwiller approach, where charge transfer and orbital fluctuations are all self-consistently treated {it ab-initio}. In contrast to previous studies, which are parameter-dependent, we characterized the phase diagram as: (1) Stoner magnetic metal for $x>0.6$ due to $a_{1g}$ van-Hove singularity near band top; (2) correlated non-magnetic metal without $e_g^{prime}$ pockets for $0.3<x<0.6$; (3) $e_g^{prime}$ pockets appear for $x<0.3$, and additional magnetic instability involves. Experimental quasi-particle properties is well explained, and the $a_{1g}$-$e_g^{prime}$ anti-crossing is attributed to spin-orbital coupling.
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We propose a minimal model resolving a puzzle of enigmatic correlations observed in sodium-rich Na$_x$CoO$_2$ where one expects a simple, free motion of the dilute $S=1/2$ holes doped into a band insulator NaCoO$_2$. The model also predicts singlet superconductivity at experimentally observed compositions. The model is based on a key property of cobalt oxides -- the spin-state quasidegeneracy of CoO$_6$ octahedral complex -- leading to an unusual physics of, {it e.g.}, LaCoO$_3$. We show that correlated hopping between $t_{2g}$ and $e_g$ states leads to the spin-polaron physics at $xsim 1$, and to an extended s-wave pairing at larger doping when coherent fermionic bands are formed.
We report on first investigation of the lattice dynamics in the novel superconducting material Na$_{0.35}$CoO$_2$$cdot$1.3H$_2$O and the non-hydrated parent compound Na$_{0.7}$CoO$_2$ by inelastic x-ray scattering. The measured phonon dispersion along the $Gamma-M$ direction show a marked softening with hole doping of two optical phonon branches close to the Brillouin zone boundary. The phonon spectra, dispersion, and softening are well reproduced by first-principle calculations. The calculations indicates that the soft branches are mainly composed of Co-vibration modes. The estimation of the critical temperature based on electron-phonon coupling mechanism undisputedly points to a non-conventional superconducting state in this material.
Magnetism of layered cobaltites Na$_x$CoO$_2$ with $x$ = 0.6 and 0.9 has been investigated by a positive muon spin rotation and relaxation ($mu^+$SR) spectroscopy together with magnetic susceptibility and specific heat measurements, using single crystal samples in the temperature range between 250 and 1.8 K. Zero-field (ZF-) $mu^+$SR measurements on Na$_{0.9}$CoO$_2$ indicates a transition from a paramagnetic to an incommensurate spin density wave state at 19 K(=$T_{sf SDW}$). The anisotropic ZF-$mu^+$SR spectra suggest that the oscillating moments of the {sf IC-SDW} directs along the c-axis. Since Na$_{0.6}$CoO$_2$ is paramagnetic down to 1.8 K, the magnitude of $T_{sf SDW}$ is found to strongly depend on $x$.This behavior is well explained using the Hubbard model within a mean field approximation on two-dimensional triangle lattice in the CoO$_2$ plane. Also, both the appearance of the {sf IC-SDW} state by the change in $x$ and the magnitude of the electronic specific heat parameter of Na$_{0.6}$CoO$_2$ indicate that Na$_x$CoO$_2$ is unlikely to be a typical strongly correlated electron system.
We use the Gutzwiller Density Functional Theory to calculate ground-state properties and bandstructures of iron in its body-centered-cubic (bcc) and hexagonal-close-packed (hcp) phases. For a Hubbard interaction $U=9, {rm eV}$ and Hunds-rule coupling $J=0.54, {rm eV}$ we reproduce the lattice parameter, magnetic moment, and bulk modulus of bcc iron. For these parameters, bcc is the ground-state lattice structure at ambient pressure up to a pressure of $p_{rm c}=41, {rm GPa}$ where a transition to the non-magnetic hcp structure is predicted, in qualitative agreement with experiment ($p_{rm c}^{rm exp}=10ldots 15, {rm GPa}$). The calculated bandstructure for bcc iron is in good agreement with ARPES measurements. The agreement improves when we perturbatively include the spin-orbit coupling.
Band structure of metallic sodium cobaltate Na$_x$CoO$_2$ ($x$=0.33, 0.48, 0.61 0.72) has been investigated by local density approximation+Hubbard $U$ (LDA+$U$) method and within Gutzwiller approximation for the Co-$t_{2g}$ manifold. Correlation effects being taken into account results in suppression of the $e_g$ hole pockets at the Fermi surface in agreement with recent angle-resolved photo-emission spectroscopy (ARPES) experiments. In the Gutzwiller approximation the bilayer splitting is significantly reduced due to the correlation effects. The formation of high spin (HS) state in Co $d$-shell was shown to be very improbable.
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