Session Y31: Focus Session: Sodium Cobaltites

Charge order and anomalous magnetism in the Na cobaltates

The layered Na cobaltates have some analogies with the cuprates~as 2D conductivity occurs in the CoO$_{2}$ planes and doping can be modified by changing the Na content. Also ordered magnetic phases have been evidenced, but unexpectedly for large values of $x$ for which one would expect a hole doping of the band insulator NaCoO$_{2}$. Indeed, in the high crystal field on the Co sites in these compounds, an ionic picture for the Co states would correspond to low spin configurations Co$^{3+}$, S=0 or Co$^{4+}$, S=1/2. We shall present SQUID and $^{23}$Na and $^{59}$Co NMR data [1] taken on samples synthetized and characterized by X ray cristallography in LLB, Saclay. We evidence that the Co charge is uniform for $x$=0.35 as in the hydrated superconducting phase. For high Na contents the samples are found to display ordered Na structures or mixtures of those, with different $x$ values. In pure phases isolated for specific $x$ values, we evidence a charge disproportionation into non magnetic Co$^{3+}$ and more magnetic Co sites with an average charge of about Co$^{3.5+}$, except for $x$=0.5 [2]. This hole delocalization and charge order occur both for paramagnetic and AF phases [3]. NMR investigations of the dynamic susceptibilities allow us to characterize the nature of the in plane electronic correlations in most parts of the phase diagram. Contrary to the case of most cuprates for which dopant disorder is quite influential, the hole doping achieved in cobaltate samples is associated with the insertion of well ordered Na planar structures. They have to be taken into account to explain theoretically the metallicity, the magnetic properties and their evolution with doping. \newline [1] \textit{I. Mukhamedchine, H. Alloul, G. Collin et N. Blanchard, Phys. Rev. Letters, }\textbf{\textit{ 94}}\textit{, 247602 (2005). } \newline [2] http://arxiv.org/find/cond-mat/1/au:+Bobroff\_J/0/1/0/all/0/1, J. Bobroff; http://arxiv.org/find/cond-mat/1/au:+Lang\_G/0/1/0/all/0/1, G. Lang; http://arxiv.org/find/cond-mat/1/au:+Alloul\_H/0/1/0/all/0/1, H. Alloul; http://arxiv.org/find/cond-mat/1/au:+Blanchard\_N/0/1/0/all/0/1, N. Blanchard and http://arxiv.org/find/cond-mat/1/au:+Collin\_G/0/1/0/all/0/1, G. Collin, \textit{Phys. Rev. Letters \textbf{\textit{96}}, 107201 (2006) .} \newline [3] \textit{I. Mukhamedchine, H. Alloul, G. Collin et N. Blanchard, condmat /0703561. }   

Sodium Ordering Phase Transition in Sodium Cobaltate

Na$_{x}$CoO$_{2}$ has emerged as a system of fundamental scientific interest because of its highly unusual electrical and magnetic properties. Using neutron and x-ray diffraction we have detected long-range 3D ordering of Na$^{+}$ ions in single crystals, and demonstrate a kaleidoscope of Na$^{+}$ ion patterns as a function of concentration and temperature [1]. Large scale numerical simulations reveal the ordering principle for this system, the formation of tri-vacancy charged droplets that then order long range, and the structure factors from these defect clusters are in good agreement with the observed neutron diffraction intensities. Superstructure transitions are observed in the diffraction data which are explained by a change from a stripe structure of tri-vacancies. The results readily explain many of the observed electrical and magnetic properties, including the formation of ferromagnetic sheets in the CoO$_{2}$ layers over this composition range, and the 3D nature of the magnetic excitations. [1] M. Roger et al. Nature 445, 631 (2007)   

New magnetic states in Na$_{x}$CoO$_{2}$ induced by controlled Na order.

We prove the direct link between low temperature magnetism and high-temperature Na$^{+}$ ordering in Na$_{x}$CoO$_{2}$ using the example of a so far unreported magnetic transition at 8K . The new magnetic state carries a weak ferromagnetic moment parallel to the CoO$_{2}$ layers. The 8K feature has been characterized in detail and its dependence on a diffusive Na+ rearrangement around 200K is demonstrated. The diffusive process is found to slow down around 200K, and the characteristic time scale reaches several hours at 195K. Applying muons as local probes this process is shown to result in a reversible phase separation into distinct magnetic phases that can be controlled by specific cooling protocols. Thus the impact of ordered Na+ Coulomb potential on the itinerant electrons in the CoO$_{2}$ layers is evident, and new ways to experimentally revisit the Na$_{x}$CoO$_{2}$ phase diagram are discussed.   

Precise control of the Na nonstoichiometry in Na$_{x}$CoO$_{2}$

Na$_{x}$CoO$_{2}$ has been attracting great interests in terms of a correlation between its electronic properties and Na nonstoichiometry. Many groups have reported that a Na rich phase ($x \quad \sim $ 0.7) is a Curie-Weiss metal and a poor phase ($x \quad \sim $ 0.3) is a Pauli paramagnetic metal. The origin of this difference, however, has not been confirmed yet, mainly because of difficulty in controlling precisely the Na nonstoichiometry. We succeeded in synthesizing a series of polycrystalline samples of Na$_{x}$CoO$_{2}$ with well-controlled Na content by the solid-state reaction instead of the solution reaction previously used. We prepared polycrystalline Na$_{x}$CoO$_{2}$ (0.58 $\le \quad x \quad \le $ 0.63) by a solid-state reaction of Na$_{0.71}$CoO$_{2}$ and Na$_{0.5}$CoO$_{2}$ at 200$^{\circ}$C. Furthermore, fine tuning of Na content in the range of 0.62 $< \quad x \quad <$ 0.63 was carried out by a solid-state reaction of Na$_{0.62}$CoO$_{2}$ and Na$_{0.63}$CoO$_{2}$. Magnetic susceptibility of Na$_{x}$CoO$_{2}$ exhibited Curie-Weiss behavior at $x \quad \ge $ 0.621 while nearly temperature independent paramagnetism at $x \quad \le $ 0.620. Such a drastic change of magnetism clearly indicates that the magnetic phase boundary is located in an extremely narrow range around $x$ = 0.62. We think that the difference originates from a change of the Fermi surface topology with electron filling probably associated with the dip in the a$_{1g}$ band near the $\Gamma $ point.   

Systematic ARPES study on Na-rich Na$_{x}$CoO$_{2}$ (0.75$<$x$<$1)

The phase diagram of the cobaltite Na$_{x}$CoO$_{2}$, with varying Na concentration x, is very rich and complicated. At the high-doping regime (x$>$0.75), the system was found to be more correlated, with a spin-density-wave state emerging at low temperatures. A stable phase was found with $\sqrt {13} \times \sqrt {13} $ symmetrical superstructure at Na-rich doping cobaltite. We will report our recent ARPES results of the Na-rich Na$_{x}$CoO$_{2}$ (0.75$<$x$<$1) samples.   

Fermi surface pockets in Na$_x$CoO$_2$ for $ x = 0.71$ and $0.84$: Localization effects and emergence of a quantum spin-liquid ground state

Here we report the observation of Fermi surface (FS) pockets via the Shubnikov de Haas effect in Na$_x$CoO$_2$ for $x = 0.71$ and $0.84$, respectively. Our observations indicate that the FS of each compound can intersect their corresponding Brillouin zones, as defined by the previously reported superlattice structures, leading to small reconstructed FS pockets, only if a precise number of holes per unit cell is \emph{localized}. For $0.71 \leq x < 0.75$ the coexistence of itinerant carriers and localized $S =1/2$ spins on a paramagnetic triangular lattice leads, at low temperatures, to the observation of non Fermi-liquid behavior in the electrical transport and heat capacity properties. Namely, an anomalous exponent in the temperature dependence of the resistivity and a logarithmic divergence of the heat capacity divided by temperature as the temperature is lowered. These observations suggest the possibility of a unique quantum spin-liquid ground state resulting from the interplay between itinerant carriers and fluctuating $S=1/2$ spins on a frustrated lattice.   

ARPES investigation of the electronic properties of PdCoO$_{2}$

The triangular-lattice layered cobaltates have emerged as an exciting new correlated electron system.~ Although tremendous progress has been made with Sodium Cobaltate (Na$_{x}$CoO$_{2})$ there still remain disputes, most notably, the precise Fermi surface topology.~ In order to gain another perspective, we have studied a related compound, Palladium Cobaltate (PdCoO$_{2})$. This is a chemically stable metallic oxide that can be prepared with very high purity, allowing us to study a clean system that lacks the complications introduced by doping in Na$_{x}$CoO$_{2}$. We present the first ARPES measurements on PdCoO$_{2}$, focusing on determining the Fermi surface topology, comparing observed band structure to theory, and making connections with bulk measurements.   

a$_1g$-e$_g$' splitting and the small Fermi surface pockets in Na$_x$CoO$_2$

Because DFT calculations and ARPES experiments disagree on the existence of six small Fermi surface pockets in NaxCoO2, it has been suggested that correlation effects neglected by the LDA may be responsible for suppressing the eg-derived pockets. Recent DMFT work has shown that such suppression is only possible if the position of the eg' band is lower than that of the a1g band, prior to correlation effects. Here we show that the energy difference between band positions, $\Delta$=$\epsilon_{eg'}$-$\epsilon_{a1g}$ strongly depends on Na content, Na positions, and on whether bands stem from the surface or bulk. We show that the Coulomb field of the Na ions is enough to shift the a1g band beneath the eg band, even though simple crystal field arguments would suggest the opposite.   

Resonant Ultrasound Studies of Quasi-2D Na$_{x}$CoO$_{2}$ (0.7 $\le $ x $\le $ 0.77)

Cobalt-based oxides have been shown to represent a new paradigm for a good thermoelectric material. These materials violate all of the traditional guidelines to help identify a potentially good thermoelectric material. In order to obtain a better understanding of its physical properties, we have initiated the synthesis of layered Na$_{x}$CoO$_{2}$, and started a study of the elastic properties of these materials using Resonant Ultrasound Spectroscopy (RUS). In this work, we discuss our results for sodium cobaltate compounds with 0.7 $\le $ x $\le $ 0.77. Single crystals were successfully grown in a floating-zone furnace, and the elastic constants have been measured as a function of temperature (5-300K) and in magnetic fields up to 5 Tesla. The resulting plots of elasticity vs. temperature clearly reflect a transition below 50 K, which is believed to be associated with rearrangement of the Na-atoms between the CoO$_{2}$ planes.   

Thermo-magnetic effect of cobalt oxides

The cobalt oxide, Na$_x$CoO$_2$, shows not only a large thermoelectric response but also an anomalous high-temperature Hall effect: The Hall coefficient increases linearly as a function of temperature and the magnitude comes to no fewer than 8 times as large as the expected Drude value. On the electron system with the large thermopower and the large Hall coefficient, an interesting behavior is expected in the response to a magnetic field upon a temperature gradient. We have studied the electronic state of the cobalt oxide and found that the electronic structure reflects the nature of the kagom\'e lattice hidden in the CoO$_2$ layer. We will show the importance of the hidden kagom\'e lattice structure in the emergence of the anomalous Hall effect and the close relationship between the Hall and Nernst coefficients.   

Nodal $d+id$ pairing and topological phases on the triangular lattice: unconventional superconducting state of Na$_x$CoO$_2\cdot y$H$_2$O

We show that the finite angular momentum pairing on the triangular lattice has point nodes in the complex gap function. A topological quantum phase transition takes place through a gapless critical state at a specific carrier density $x_c$ where the normal state Fermi surface crosses these isolated nodes. For spin singlet pairing, we show that the second nearest neighbor $d+id$ pairing is the dominate superconducting channel. The gapless critical state appears at $x_c\simeq0.25$ for the sodium cobaltates. It has six Dirac points and is topologically nontrivial with a $T^3$ spin relaxation rate below $T_c$. This theory provides a consistent explanation for the unconventional superconducting state of Na$_x$CoO$_2\cdot y$H$_2$O.   

Unusual Muon Spin Relaxation in Hydrated Cobaltite Superconductors

Muon spin relaxation ($\mu^+$SR) was studied in zero (ZF) and weak transverse magnetic field (TF) in Na$_x$(H$_3$O)$_z$CoO$_2\cdot y$H$_2$O and its deuterated analog. In ZF, the muon relaxes (surprisingly) faster for the deuterated sample. Detectable effects of superconductivity are also surprisingly subtle in both cases.