Structural and superconducting properties of $\mathrm{Rb}{\mathrm{Os}}_2{\mathrm{O}}_6$ single crystals

Single crystals of $\mathrm{Rb}{\mathrm{Os}}_2{\mathrm{O}}_6$ have been grown from ${\mathrm{Rb}}_2\mathrm{O}$ and Os in sealed quartz ampoules. The crystal structure has been identified at room temperature as cubic with the lattice constant $a=10.1242\left(12\right)\mathrm{\AA }$. The anisotropy of the tetrahedral and octahedral networks is lower and the displacement parameters of alkali metal atoms are smaller than those for $\mathrm{K}{\mathrm{Os}}_2{\mathrm{O}}_6$, so the “rattling” of the alkali atoms in $\mathrm{Rb}{\mathrm{Os}}_2{\mathrm{O}}_6$ is less pronounced. The superconducting properties of $\mathrm{Rb}{\mathrm{Os}}_2{\mathrm{O}}_6$ in the mixed state have been described well within the London approach and the Ginzburg–Landau parameter $\kappa \left(0\right)\cong 31$ has been derived from the reversible magnetization. This parameter is field dependent and changes at low temperatures from $\kappa \cong 22$ (low fields) to $\kappa \cong 31$ at $H_{c2}$. The thermodynamic critical field $H_c\left(0\right)=1.3\mathrm{kOe}$ and the superconducting gap $2{\Delta }_o∕k_B{T}_c\cong 3.2$ have been estimated. These results, together with the slightly different $H_{c2}\left(T\right)$ dependence obtained for crystals and polycrystalline $\mathrm{Rb}{\mathrm{Os}}_2{\mathrm{O}}_6$, evidently prove that this compound is a weak-coupling BCS-type superconductor close to the dirty limit.

Figure 1

(Color online) Single crystals of $\mathrm{Rb}{\mathrm{Os}}_2{\mathrm{O}}_6$ grown in quartz ampoules. The edge of each individual picture is about $1\mathrm{mm}$.

Figure 2

Structural details of $\mathrm{Rb}{\mathrm{Os}}_2{\mathrm{O}}_6$ at room temperature ($F\overline{4}3m$ space group) showing the anisotropic nature of the rubidium channels (structure projected along the $[-110]$ direction). Interatomic distances Rb1-O2 and Rb2-O1 are shorter $\left(3.1081\mathrm{\AA }\right)$ and longer $\left(3.1395\mathrm{\AA }\right)$, respectively, compared to the $\beta$-pyrochlore structure with $\overline{3}m$ symmetry $[\mathrm{Rb}\text{−}\mathrm{O}=3.125\left(7\right)\mathrm{\AA }]$. The O2 displacement ellipsoid is elongated toward the Rb1 atom whereas the O1 displacement ellipsoid does not point to the Rb2 atom. The displacement ellipsoids are drawn at the 50% probability level.

Figure 3

Magnetic moment vs temperature at constant fields $H=0.2\mathrm{kOe}$ and $4\mathrm{kOe}$ (inset) for the $\mathrm{Rb}{\mathrm{Os}}_2{\mathrm{O}}_6$ single crystal with $T_c=6.25\mathrm{K}$ at $5\mathrm{Oe}$. The superconducting transition temperature $T_c$ and the transition onset temperature $T_{co}$ are marked by arrows. For $H=4\mathrm{kOe}$, $T_{co}\approx T_c=5.76\mathrm{K}$, indicative of a bulk transition to the superconducting state.

Figure 4

Magnetic moment vs temperature at constant fields $H=500\mathrm{Oe}$ and $5\mathrm{Oe}$ (inset) for the $\mathrm{Rb}{\mathrm{Os}}_2{\mathrm{O}}_6$ single crystal with $T_c=6.18\mathrm{K}$ at $5\mathrm{Oe}$. The results are obtained upon heating from the ZFC state and upon cooling (FC). The superconducting transition temperature $T_c$ and the irreversibility temperature $T_{\mathit{irr}}$ are marked by arrows. The beginning of the irreversible $m\left(T\right)$ properties at $T_{\mathit{irr}}$ is not visible in this scale.

Figure 5

Upper critical field $H_{c2}$ extracted from the magnetization measurements (circles) for the $\mathrm{Rb}{\mathrm{Os}}_2{\mathrm{O}}_6$ single crystal with a bulk transition temperature $T_c=6.13\mathrm{K}$. The solid line is the power law fit $H_{c2}\left(T\right)=H_{c2}\left(0\right)[1-{(T∕T_c)}^n]$ with an exponent $n=1.2$ and $H_{c2}\left(0\right)=56\mathrm{kOe}$. The dashed line is the fit with $n=1.5$ and $H_{c2}^{*}\left(0\right)=46.5\mathrm{kOe}$ (star), where $H_{c2}^{*}\left(0\right)$ is the GLAG orbital limiting field in the dirty limit. The inset shows the initial $H_{c2}\left(T\right)$ dependence derived with the bulk (circles) and the onset (triangles) transition temperatures. The BCS Pauli limiting field $H_p\left(0\right)=113\mathrm{kOe}$ is much higher than $H_{c2}^{\mathit{lin}}\left(0\right)=67\mathrm{kOe}$ obtained from a linear extrapolation of the initial $H_{c2}\left(T\right)$ dependence.

Figure 6

Magnetization loop $M\left(H\right)$ obtained at $3.4\mathrm{K}$ for $H$ swept from zero to $1.5\mathrm{kOe}$ (closed circles), then to $-1.5\mathrm{kOe}$ (open circles), and then back to zero (closed circles). Inset (a) shows the virgin curve of the $M\left(H\right)$ loop, which was used to determine the first penetration field $H_{\mathit{fp}}$. The first deviation from the linear part of the virgin curve is marked by an arrow. Inset (b) shows the reversible magnetization $M_{\mathrm{rev}}$ calculated from the $M\left(H\right)$ half-loop (see text).

Figure 7

Reversible magnetization as a function of an applied field for $\mathrm{Rb}{\mathrm{Os}}_2{\mathrm{O}}_6$ and $\mathrm{K}{\mathrm{Os}}_2{\mathrm{O}}_6$ single crystals. The data for $\mathrm{K}{\mathrm{Os}}_2{\mathrm{O}}_6$ are shifted with $+0.1\mathrm{emu}∕\mathrm{g}$ for convenience. The inset shows the experimental $M_{\mathit{rev}}\left(H\right)$ data (circles) corrected for demagnetizing effects (see text). The experimental data are compared to the results calculated with Eq. (1) for $\kappa \left(H\right)=\mathrm{const}=22.2$ (solid line) and with Eq. (2) for the same $\kappa$ (dot-dashed line) and for $\kappa$ being field dependent (dashed line). The dashed line has been obtained for $\kappa$ changing gradually from 22.2 $(H\sim 0.2\mathrm{kOe})$ to 26.4 $(H⩾13\mathrm{kOe})$.

Figure 8

Superconducting transition temperature (closed symbols) and an upper critical field at zero temperature (open symbols) versus $U_{\mathit{iso}}$ at $300\mathrm{K}$ of the $A^{\prime }$ atoms of $A^{\prime }{\mathrm{Os}}_2{\mathrm{O}}_6$ for polycrystalline $\mathrm{Cs}{\mathrm{Os}}_2{\mathrm{O}}_6$ (triangles) and single crystals of $\mathrm{Rb}{\mathrm{Os}}_2{\mathrm{O}}_6$ (circles) and $\mathrm{K}{\mathrm{Os}}_2{\mathrm{O}}_6$ (diamonds). Results for $\mathrm{Cs}{\mathrm{Os}}_2{\mathrm{O}}_6$ were taken from Ref. 21. Results for $\mathrm{K}{\mathrm{Os}}_2{\mathrm{O}}_6$ come from our previous work (Ref. 7).