Superconducting and normal-state properties of the $\ensuremath{\beta}$-pyrochlore oxide $\mathrm{K}{\mathrm{Os}}_{2}{\mathrm{O}}_{6}$ are studied by means of thermodynamic and transport measurements. It is shown that the superconductivity is of conventional $s$-wave type and lies in the extremely strong-coupling regime. Specific heat and resistivity measurements reveal that there are characteristic low-energy phonons that give rise to unusual scattering of carriers due to strong electron-phonon interactions. The entity of the low-energy phonons is ascribed to the heavy rattling of the K ion confined in an oversized cage made of $\mathrm{Os}{\mathrm{O}}_{6}$ octahedra. It is suggested that this electron-rattler coupling mediates the Cooper pairing, resulting in the extremely strong-coupling superconductivity.

Extremely strong-coupling superconductivity and anomalous lattice properties in the β -pyrochlore oxide K Os 2 O 6

The crystal structures of NaxCoO2 phases based on three-layer NaCoO2, with x=0.32, 0.51, 0.60, 0.75, and 0.92, determined by powder neutron diffraction, are reported. The structures have triangular CoO2 layers interleaved by sodium ions, and evolve with variation in Na content in a more complex way than has been observed in the two-layer NaxCoO2 system. The phases with highest and lowest Na content studied x=0.92 and 0.32 are trigonal, with three CoO2 layers per cell and octahedral Na ion coordination. The intermediate compositions have monoclinic structures. The x=0.75 compound has one CoO2 layer per cell, with Na in octahedral coordination and an incommensurate superlattice. The x=0.6 and 0.51 phases are also single layer, but the Na is found in trigonal prismatic coordination. The magnetic behavior of the phases is similar to that observed in the two-layer system. Both the susceptibility and the electronic contribution to the specific heat are largest for x=0.6.

/pdf/crystal-structure-and-elementary-properties-of-naxcoo2-x-0-3tn29sxh6c.pdf

Crystal structure and elementary properties of NaxCoO2 ( x=0.32 , 0.51, 0.6, 0.75, and 0.92) in the three-layer NaCoO2 family

The superconducting properties of two β-pyrochlore oxides, CsOs 2 O 6 and RbOs 2 O 6 , are studied by thermodynamic and transport measurements using high-quality single crystals. It is shown that the character of superconductivity changes systematically from weak coupling for CsOs 2 O 6 to moderately strong coupling for RbOs 2 O 6 , and finally to extremely strong coupling with BCS-type superconductivity for KOs 2 O 6 , with increasing T c . Strong-coupling correction analyses of the superconducting properties reveal that a low-energy rattling mode of the alkali metal ions is responsible for the mechanism of the superconductivity in each compound. The large enhancement of T c from Cs to K is attributed to the increase in the electron–rattler coupling with decreasing characteristic energy of the rattling and with increasing anharmonicity. The existence of weak anisotropy in the superconducting gap or in the electron–rattler interactions is found for the Cs and Rb compounds.

/pdf/rattling-induced-superconductiviy-in-the-b-pyrochlore-oxides-4pm1xf3vw9.pdf

Rattling-Induced Superconductiviy in the β-Pyrochlore Oxides AOs2O6

The superconducting properties of two beta-pyrochlore oxides, CsOs2O6 and RbOs2O6, are studied by thermodynamic and transport measurements using high-quality single crystals. It is shown that the character of superconductivity changes systematically from weak coupling for CsOs2O6 to moderately strong coupling for RbOs2O6, and finally to extremely strong coupling with BCS-type superconductivity for KOs2O6, with increasing Tc. Strong-coupling correction analyses of the superconducting properties reveal that a low-energy rattling mode of the alkali metal ions is responsible for the mechanism of the superconductivity in each compound. The large enhancement of Tc from Cs to K is attributed to the increase in the electron-rattler coupling with decreasing characteristic energy of the rattling and with increasing anharmonicity. The existence of weak anisotropy in the superconducting gap or in the electron-rattler interactions is found for the Cs and Rb compounds.

Rattling-Induced Superconductiviy in the Beta-Pyrochlore Oxides AOs2O6

The results of the $\mathrm{LSDA}+U$ calculations for pyroxenes with diverse magnetic properties $(\mathrm{Li},\mathrm{Na})\mathrm{TM}{(\mathrm{Si},\mathrm{Ge})}_{2}{\mathrm{O}}_{6}$, where TM is the transition metal ion (Ti, V, Cr, Mn, Fe), are presented. We show that the anisotropic orbital ordering results in the spin-gap formation in $\mathrm{Na}\mathrm{Ti}{\mathrm{Si}}_{2}{\mathrm{O}}_{6}$. The detailed analysis of different contributions to the intrachain exchange interactions for pyroxenes is performed both analytically using perturbation theory and basing on the results of the band structure calculations. The antiferromagnetic ${t}_{2g}\ensuremath{-}{t}_{2g}$ exchange is found to decrease gradually in going from Ti to Fe. It turns out to be nearly compensated by ferromagnetic interaction between half-filled ${t}_{2g}$ and empty ${e}_{g}$ orbitals in Cr-based pyroxenes. The fine tuning of the interaction parameters by the crystal structure results in the ferromagnetism for $\mathrm{Na}\mathrm{Cr}{\mathrm{Ge}}_{2}{\mathrm{O}}_{6}$. Further increase of the total number of electrons and occupation of ${e}_{g}$ subshell makes the ${t}_{2g}\ensuremath{-}{e}_{g}$ contribution and total exchange interaction antiferromagnetic for Mn- and Fe-based pyroxenes. Strong oxygen polarization was found in Fe-based pyroxenes. It is shown that this effect leads to a considerable reduction of antiferromagnetic intrachain exchange. The obtained results may serve as a basis for the analysis of diverse magnetic properties of pyroxenes, including those with recently discovered multiferroic behavior.

Electronic structure and magnetic properties of pyroxenes ( Li , Na ) TM ( Si , Ge ) 2 O 6 : Low-dimensional magnets with 90° bonds

We present the results of measurements of the dc-magnetic susceptibility $\ensuremath{\chi}(T)$ and the ${}^{23}\mathrm{Na}$-NMR response of ${\mathrm{Na}}_{0.70}{\mathrm{CoO}}_{2}$ at temperatures between 50 and 340 K. The $\ensuremath{\chi}(T)$ data suggest that for $Tg75\mathrm{K},$ the Co ions adopt an effective configuration of ${\mathrm{Co}}^{3.4+}.$ The ${}^{23}\mathrm{Na}$-NMR response reveals pronounced anomalies near 250 and 295 K, but no evidence for magnetic phase transitions is found in $\ensuremath{\chi}(T).$ Our data suggest the onset of a dramatic change in the Co $3d$-electron spin dynamics at 295 K. This process is completed at 230 K. Our results may be interpreted as evidence for either a tendency to electron localization or an unconventional charge-density-wave phenomenon within the Co $3d$ electron system near room temperature.

Unconventional charge ordering in Na0.70CoO2 below 300 K

We report the results of $^{87}\mathrm{Rb}$ NMR measurements on ${\mathrm{RbOs}}_{2}{\mathrm{O}}_{6}$, a member of the family of the superconducting pyrochlore-type oxides with a critical temperature ${T}_{c}=6.4\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. In the normal state, the nuclear spin-lattice relaxation time ${T}_{1}$ obeys the Korringa-type relation ${T}_{1}T=\mathrm{const}$ and the Knight shift is independent of temperature, indicating the absence of strong magnetic correlations. In the superconducting state, ${T}_{1}^{\ensuremath{-}1}(T)$ exhibits a tiny coherence enhancement just below ${T}_{c}$, and decreases exponentially with further decreasing temperatures. The value of the corresponding energy gap is close to that predicted by the conventional weak-coupling BCS theory. Our results indicate that ${\mathrm{RbOs}}_{2}{\mathrm{O}}_{6}$ is a conventional $s$-wave-type superconductor.

https://arxiv.org/pdf/cond-mat/0409169.pdf

Evidence for s -wave superconductivity in the β -pyrochlore oxide RbOs 2 O 6

We report results of susceptibility χ and 7Li NMR measurements on LiVSi2O6. The temperature dependence of the magnetic susceptibility χ(T) exhibits a broad maximum, typical for low-dimensional magnetic systems. Quantitatively it is in agreement with the expectation for an S=1 spin chain, represented by the structural arrangement of V ions.
The NMR results indicate antiferromagnetic ordering below TN=24 K. The intra- and interchain coupling J and Jp for LiVSi2O6, and also for its sister compounds LiVGe2O6, NaVSi2O6 and NaVGe2O6, are obtained via a modified random phase approximation which takes into account results of quantum Monte Carlo calculations. While Jp is almost constant across the series, J varies by a factor of 5, decreasing with increasing lattice constant along the chain direction. The comparison between experimental and theoretical susceptibility data suggests the presence of an easy-axis magnetic anisotropy, which explains the formation of an energy gap in the magnetic excitation spectrum below TN, indicated by the variation of the NMR spin-lattice relaxation rate at T≪TN.

/pdf/quenching-of-the-haldane-gap-in-livsi2o6-and-related-50w8904riy.pdf

Quenching of the Haldane gap in LiVSi2O6 and related compounds

Based on experimental $^{59}\mathrm{Co}$-NMR data in the temperature range between 0.1 and $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, we address the problem of the character of the Co $3d$-electron based magnetism in ${\mathrm{Na}}_{0.7}\mathrm{Co}{\mathrm{O}}_{2}$. Temperature-dependent $^{59}\mathrm{Co}$-NMR spectra reveal different Co environments below $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and their differentiation increases with decreasing temperature. We show that the $^{23}\mathrm{Na}$- and $^{59}\mathrm{Co}$-NMR data may consistently be interpreted by assuming that below room temperature the Co $3d$ electrons are itinerant. We also argue that the $^{59}\mathrm{Co}$-NMR response is inconsistent with well-defined local magnetic moments on the Co sites. We identify a substantial orbital contribution ${\ensuremath{\chi}}^{\mathrm{orb}}$ to the $d$-electron susceptibility. At low temperatures ${\ensuremath{\chi}}^{\mathrm{orb}}$ seems to acquire some temperature dependence, suggesting an increasing influence of spin-orbit coupling. The temperature dependence of the spin-lattice relaxation rate ${T}_{1}^{\ensuremath{-}1}(T)$ confirms significant variations in the dynamics of this electronic subsystem between 250 and $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, as previously suggested. Below $100\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, ${\mathrm{Na}}_{0.7}\mathrm{Co}{\mathrm{O}}_{2}$ may be viewed as a weak antiferromagnet with ${T}_{N}$ below $1\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, but this scenario still leaves a number of open questions.

/pdf/localized-versus-itinerant-magnetic-moments-in-na0-7coo2-7mlhuik5ba.pdf

Localized versus itinerant magnetic moments in Na0.7CoO2

We report the results of measurements of the dc magnetic susceptibility $\ensuremath{\chi}$ and of the $^{23}\mathrm{Na}$ nuclear magnetic resonance (NMR) response of ${\mathrm{NaVGe}}_{2}{\mathrm{O}}_{6}$, a material in which the $\mathrm{V}$ ions form a network of interacting one-dimensional spin $S=1$ chains. The experiments were made at temperatures between 2.5 and $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The $\ensuremath{\chi}(T)$ data suggest that the formation of the expected low-temperature Haldane phase is intercepted by an antiferromagnetic phase transition at ${T}_{N}=18\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The transition is also reflected in the $^{23}\mathrm{Na}$ NMR spectra and the corresponding spin-lattice relaxation rate ${T}_{1}^{\phantom{\rule{0.2em}{0ex}}\ensuremath{-}1}(T)$. In the ordered phase, ${T}_{1}^{\phantom{\rule{0.2em}{0ex}}\ensuremath{-}1}(T)$ decreases by orders of magnitude with decreasing temperature, indicating the formation of a gap of the order of $12\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ in the magnetic excitation spectrum.

B. Pedrini

Papers

Unconventional charge ordering in Na0.70CoO2 below 300 K

Evidence for s -wave superconductivity in the β -pyrochlore oxide RbOs 2 O 6

Quenching of the Haldane gap in LiVSi2O6 and related compounds

Localized versus itinerant magnetic moments in Na0.7CoO2

NMR and dc susceptibility studies of NaVGe 2 O 6