We study theoretically and experimentally the dependence of the electron-phonon interaction in Na$_x$CoO$_2$ on the sodium concentration $x$. For the two oxygen phonon modes found in Raman experiments, $A_{1g}$ and $E_{1g}$, we calculate the matrix elements of the electron-phonon interaction. Analyzing the feedback effect of the conduction electrons on the phonon frequency we compare the calculated and experimentally observed doping dependence of the $A_{1g}$ mode. Furthermore, due to the momentum dependence of the electron-phonon coupling for the $E_{1g}$ symmetry we find no renormalization of the corresponding phonon frequency which agrees with experiment. Our results shed light on the possible importance of the electron-phonon interaction in this system.
We systematically analyze the influence of the superconducting gap symmetry and the electronic structure on the dynamical spin susceptibility in superconducting Na_xCoO_2$\cdot y$H_2O within a three different models: the single a_{1g}-band model with nearest-neighbor hoppings, the realistic three-band t_{2g}-model with, and without e'_g pockets present at the Fermi surface. We show that the magnetic response in the normal state is dominated by the incommensurate antiferromagnetic spin density wave fluctuations at large momenta in agreement with experimental temperature dependence of the spin-l…
Recently the unusual metallic state with a substantially non-uniform distribution of a charge and mag\-ne\-tic density in CoO$_2$ planes was found experimentally in the Na$_x$CoO$_2$ compound with $x>0.6$. We have investigated an origin of such electron disproportionation in the lamellar sodium cobaltates by calculating the ion states as a function of a strength of the electron correlations in the $d$(Co)-shells within the GGA+U approximation for the system with a realistic crystal structure. It was found that the nonuniformity of spin and charge densities are induced by an ordering of the sod…
The single-layer perovskite cobaltates have attracted enormous attention due to the recent observation of hour-glass shaped magnetic excitation spectra which resemble the ones of the famous high-temperature superconducting cuprates. Here, we present an overview of our most recent studies of the spin and charge correlations in floating-zone grown cobaltate single crystals. We find that frustration and a novel kind of electronic and magnetic nano phase separation are intimately connected to the appearance of the hour-glass shaped spin excitation spectra. We also point out the difference between …
Layered misfit cobaltate [Ca$_2$CoO$_3$]$_{0.62}$[CoO$_2$], which emerged as an important thermoelectric material~[A. C. Masset et al. Phys. Rev. B, 62, 166 (2000)], has been explored extensively in the last decade for the exact mechanism behind its high Seebeck coefficient. Its complex crystal and electronic structures have inhibited consensus among such investigations. This situation has arisen mainly due to difficulties in accurate identification of the chemical state, spin state, and site symmetries in its two subsystems (rocksalt [Ca$_2$CoO$_3$] and triangular [CoO$_2$]). By employing res…
We have grown single crystals of Na$_x$Ca$_y$CoO$_2$ and determined their superstructures as a function of composition using neutron and x-ray diffraction. Inclusion of Ca$^{2+}$ stabilises a single superstructure across a wide range of temperatures and concentrations. The superstructure in the Na$^+$ layers is based on arrays of divacancy clusters with Ca$^{2+}$ ions occupying the central site, and it has an ideal concentration Na$_{4/7}$Ca$_{1/7}$CoO$_2$. Previous measurements of the thermoelectric properties on this system are discussed in light of this superstructure. Na$_{4/7}$Ca$_{1/7}$C…
We propose that unconventional superconductivity in hydrated sodium cobaltate $Na_xCoO_2$ results from an interplay of electronic correlations and electron-phonon interactions. On the basis of the $t-V$ model plus phonons we found evidences for a) unconventional superconductivity, b) realistic values of $T_c$ and c) the dome shape existing near $x \sim 0.35$. This picture is obtained for $V$ close to the critical Coulomb repulsion $V_c$ which separates the uniform Fermi liquid from $\sqrt{3} \times \sqrt{3}$ CDW ordered phase.
Recently discovered class of cobaltate superconductors (Na0.3CoO2.nH2O) is a novel realization of interacting quantum electron systems in a triangular network with low-energy degrees of freedom. We employ angle-resolved photoemission spectroscopy to uncover the nature of microscopic electron motion in the parent superconductors for the first time. Results reveal a large hole-like Fermi surface (consistent with Luttinger theorem) generated by the crossing of super-heavy quasiparticles. The measured quasiparticle parameters collectively suggest a two orders of magnitude departure from the conven…
We observe quasi-static incommensurate magnetic peaks in neutron scattering experiments on layered cobalt oxides La2-xSrxCoO4 with high Co oxidation states that have been reported to be paramagnetic. This enables us to measure the magnetic excitations in this highly hole-doped incommensurate regime and compare our results with those found in the low-doped incommensurate regime that exhibit hourglass magnetic spectra. The hourglass shape of magnetic excitations completely disappears given a high Sr doping. Moreover, broad low-energy excitations are found, which are not centered at the incommens…
K$_x$CoO$_2$ shares many similarities with Na$_x$CoO$_2$, as well as some important differences (no hydration-induced superconductivity has been reported). At $T_{c2}$=20 K, K$_{0.5}$CoO$_2$ becomes an insulator with a tiny optical gap as happens in Na$_{0.5}$CoO$_2$ at 52 K. This similarity, with a known common structure, enables direct comparisons to be made. Using the K-zigzag structure recently reported and the local density approximation, we compare and contrast these cobaltates at x=0.5. Although the electronic structures are quite similar as expected, substantial differences are observe…
Puzzling properties of sodium cobaltates Na${}_x$CoO${}_2$ become an issue of numerous recent theoretical and experimental investigations because of very high thermopower and intricate phase diagram of this material. Experiments indicated Na${}_{2/3}$CoO${}_2$ to have a kagome-like cobalt sublattice, which implies additional complexity of this strongly correlated system. In the present work we have employed the ab-initio GGA+U modeling method to investigate spin states of Na${}_{2/3}$CoO${}_2$, using an exact crystal cell established in the experiment. Stability of sodium imprint for concentra…
Within the charge-spin separation fermion-spin theory, we have shown that the mechanism of superconductivity in the electron doped cobaltate Na$_{x}$CoO$_{2}\cdot y$H$_{2}$O is ascribed to its kinetic energy. The dressed fermions interact occurring directly through the kinetic energy by exchanging magnetic excitations. This interaction leads to a net attractive force between dressed fermions, then the electron Cooper pairs originating from the dressed fermion pairing state are due to the charge-spin recombination, and their condensation reveals the superconducting ground state. The superconduc…
In this study, we synthesized single crystals of Na$_{x}$CoO$_{2}$ with $x\sim0.8$ using the optical floating zone technique. A thorough electrochemical treatment of the samples permitted us to control the de-intercalation of Na to obtain single crystal samples of stable Na ordered phases with $x=0.5-0.8$. Comparisons of the bulk magnetic properties with those observed in the Na ordered powder samples confirmed the high quality of these single crystal phases. The ab plane resistivity was measured for the Na ordered samples and it was quite reproducible for different sample batches. The data we…
Within the t-J model, the heat transport of electron-doped cobaltates is studied based on the fermion-spin theory. It is shown that the temperature dependent thermal conductivity is characterized by the low temperature peak located at a finite temperature. The thermal conductivity increases monotonously with increasing temperature at low temperatures T $<$ 0.1$J$, and then decreases with increasing temperature for higher temperatures T $>$ 0.1$J$, in qualitative agreement with experimental result observed from Na$_{x}$CoO$_{2}$ .
$^{59}$Co NMR spectra in oriented powders of Na$_{0.35}$CoO$_{2}$ and in its hydrated superconducting phase (HSC) Na$_{0.35}$CoO$_{2}$,1.3H$_{2}$O reveal a single electronic Co state with identical $T$ independent NMR shift tensor. These phases differ markedly from Na$_{0.7}$CoO$_{2}$, in which we resolve 3 types of Co sites. The large T variation of their spin susceptibilities $χ^{s}$ and the anisotropy of the orbital susceptibility $χ^{orb}$ allow us to conclude that charge disproportionation occurs, in a non magnetic Co$^{3+}$ and two magnetic sites with about 0.3 and 0.7 holes in the $t_{2…
[Ca$_2$CoO$_3$]$_{0.62}$[CoO$_2$], a two dimensional misfit metallic compound, is famous for its rich phases accessed by temperature, $i.e.$ high temperature spin-state transition, metal-insulator transition (MIT) at intermediate temperature ($\sim$ 100 K) and low temperature spin density wave (SDW). It enters into SDW phase below T$_{MIT}$ which becomes long range at 27 K. Information on the independent role of misfit layers (rocksalt/Ca$_2$CoO$_3$ \& triangular/CoO$_2$) in these phases is scarce. By combining a set of complementary macroscopic (DC magnetization and resistivity) and microscop…
We present X-ray spectroscopic evidence for the evolution of valence-specific spin states and tetragonal distortions in single-layer cobaltates. Measurements of Co $L_3$-edge resonant inelastic X-ray scattering reveal the $t_{2g}$ electronic structure of Co for hole-doped La$_{2-x}$Sr$_x$CoO$_4$ ($x$ = 0.5, 0.7 and 0.8). As the Sr-doping $x$ increases, the tetragonal splitting of the $t_{2g}$ states of high-spin Co$^{2+}$ decreases, whereas that of low-spin Co$^{3+}$ increases and the fraction of high-spin Co$^{3+}$ increases. The results enable us to clarify the origin of the change of magnet…
Co nuclear-quadrupole-resonance (NQR) measurements were performed on various bilayered hydrate cobaltate Na_x(H_3O)_zCoO_2\cdot yH_2O with different values of the superconducting and magnetic-ordering temperatures, T_c and T_M, respectively. From measurements of the temperature and sample dependence of the NQR frequency, it was revealed that the NQR frequency is changed by the change of the electric field gradient (EFG) along the c axis ν_{zz} rather than the asymmetry of EFG within the ab-plane. In addition, it is considered that the change of ν_{zz} is gaverned mainly by the trigonal distort…
The CoO$_{2}$ layers in sodium-cobaltates Na$_{x}$CoO$_{2}$ may be viewed as a spin $S=1/2$ triangular-lattice doped with charge carriers. The underlying physics of the cobaltates is very similar to that of the high $T_{c}$ cuprates. We will present unequivocal $^{59}$Co NMR evidence that below $T_{CO}\sim51 K$, the insulating ground state of the itinerant antiferromagnet Na$_{0.5}$CoO$_{2}$ ($T_{N}\sim 86 K$) is induced by charge ordering.
We have synthesized and characterized different stable phases of sodium cobaltates Na$_{x}$CoO$_{2}$ with sodium content $0.65<x<0.80$. We demonstrate that $^{23}$Na NMR allows to determine the difference in the susceptibility of the phases and reveals the presence of Na order in each phase. $^{59}$Co NMR experiments give clear evidence that Co charge disproportionation is a dominant feature of Na cobaltates. Only a small fraction ($\approx$ 25%) of cobalts are in a non-magnetic Co$^{3+}$ charge state whereas electrons delocalize on the other cobalts. The magnetic and charge properties of the …
Engineered $Na_{0.75}CoO_2$ is considered a prime candidate to achieve high-efficiency thermoelectric systems to regenerate electricity from waste heat. In this work, three elements with outmost electronic configurations, (1) an open d shell (Ni), (2) a closed d shell (Zn), and (3) a half filled f shell (Eu) with maximum unpaired electrons, were selected to outline the dopants' effects on electronic and crystallographic structures of $Na_{0.75}CoO_2$. Systematic $ab$ $initio$ density functional calculations with $DMOL^3$ package showed that the Ni and Zn were more stable when substituting Co w…
We study the interplay between superconductivity and antiferromagnetic spin fluctuations in electron-doped cobaltate Na$_{x}$CoO$_{2}\cdot y$H$_{2}$O based on the kinetic energy driven superconductivity mechanism. We show that the superconducting state is governed by both charge carrier pairing and quasiparticle coherent, and displays a common dome-shaped phase diagram in agreement with experimental results. By calculating the dynamical spin structure factor, we theoretically find that the magnetic excitation shows a commensurate resonance peak, which locates at antiferromagnetic wave vector $…
We have performed Co-nuclear quadrupole resonance (NQR) studies on Na$_{x}$CoO$_{2}\cdot y$H$_{2}$O compounds with different Na ($x$) and hydrate ($y$) contents. Two samples with different Na contents but nearly the same $T_c$ values ($x$ = 0.348, $T_c$ = 4.7 K ; $x$ = 0.339, $T_c$ = 4.6 K) were investigated. The spin-lattice relaxation rate $1/T_1$ in the superconducting (SC) and normal states is almost the same for the two samples except just above $T_c$. NQR measurements were also performed on different-hydrate-content samples with different $T_c$ values, which were prepared from the same N…
Using elastic and inelastic neutron scattering, we investigated the evolution of the local atomic structure and lattice dynamics of La(1-x)Sr(x)CoO3 (x=0-0.5) as it crosses over with x from an insulator to a ferromagnetic metal (FMM). Our pair density function analysis indicates that in the paramagnetic insulating (PMI) phase for all x, spin activation of Co3+ ions induces local static Jahn-Teller (JT) distortions. The size of the JT lattice increases almost linearly with x. However, in the FMM phase, static JT distortions are absent for x <= 30 %. This coincides with narrowing of hw=22 and 24…
Measurements of polarization-dependent soft x-ray absorption reveal that the electronic states determining the low-energy excitations of Na$_{x}$CoO$_2$ have predominantly $a_{1g}$ symmetry with significant O $2p$ character. A large transfer of spectral weight observed in O $1s$ x-ray absorption provides spectral evidence for strong electron correlations in the layered cobaltates. Comparing Co $2p$ x-ray absorption with calculations based on a cluster model, we conclude that Na$_{x}$CoO$_2$ exhibits a charge-transfer electronic character rather than a Mott-Hubbard character.
$^{59}$Co NMR experiments have been performed on single crystals of the layered cobaltate Na$_{x}$CoO$_{2}$ with x=0.77 which is an antiferromagnet with Néel temperature $T_{N}=22$~K. In this metallic phase six Co sites are resolved in the NMR spectra, with distinct quadrupole frequencies $ν_{Q}$, magnetic shifts $K_{ZZ}$ and nuclear spin lattice relaxation rates $% 1/T_{1}$. Contrary to the $x=1/2$ or $x=2/3$ phases the 3D stacking of the Na planes is not perfect for $x=0.77$ but this does not influence markedly the electronic properties. We evidence that the magnetic and charge properties of…
Layered cobaltates embody novel realizations of correlated quantum matter on a spin-1/2 triangular lattice. We report a high-resolution systematic photoemission study of the insulating cobaltates (Na1/2CoO2 and K1/2CoO2). Observation of single-particle gap opening and band-folding provides direct evidence of anisotropic particle-hole instability on the Fermi surface due to its unique topology. Kinematic overlap of the measured Fermi surface is observed with the $\sqrt{3}$x$\sqrt{3}$ cobalt charge-order Brillouin zone near x=1/3 but not at x=1/2 where insulating transition is actually observed.…
We show that geometric frustration and strong correlation in the triangular lattice Hubbard model lead a rich and novel phase structure of $\sqrt{3}\times\sqrt{3}$ spin-charge textured electronic states over a wide region of electron doping $0\le x \le 0.40$. In addition to the 120$^\circ$ Néel ordered insulator at half-filling, we found a novel spin-charge ordered insulator at $x=1/3$ with collinear antiferromagnetic (AF) order on the underlying unfrustrated honeycomb lattice. Separating the two insulating phases is a Lifshitz transition between a noncollinear AF ordered metal and one with co…
Temperature-driven sodium-ion dynamical-to-static crossover in the zig-zag ordered phase of Na$_{0.5}$CoO$_2$
Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院人工结构与量子控制教育部重点实验室）；School of Physical Science and Technology, Lanzhou University（兰州大学物理科学与技术学院）；International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院物质科学量子创新中心）；Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所北京凝聚态物理国家实验室）
