Crystal growth, structure, and superconducting properties of the $\beta$-pyrochlore $\mathrm{K}{\mathrm{Os}}_2{\mathrm{O}}_6$

Single crystals of $\mathrm{K}{\mathrm{Os}}_2{\mathrm{O}}_6$ have been grown in a sealed quartz ampoule. Detailed single crystal x-ray diffraction studies at room temperature show Bragg peaks that violate $Fd\overline{3}m$ symmetry. With a comparative structure refinement the structure is identified as noncentrosymmetric $\left(F\overline{4}3m\right)$. Compared to the ideal $\beta$-pyrochlore lattice $\left(Fd\overline{3}m\right)$, both Os tetrahedral and O octahedral networks exhibit breathing mode like volume changes accompanied by strong anisotropic character of the K channels. The crystals show metallic conductivity and a sharp transition to the superconducting state at $T_c=9.65\mathrm{K}$. Superconducting properties have been investigated by magnetization measurements performed in a temperature range from $2\text{to}12\mathrm{K}$ and in magnetic fields from $0\text{to}60\mathrm{kOe}$. The temperature dependence of the upper critical field $H_{c2}\left(T\right)$ has been determined and the initial slope ${(d{H}_{c2}∕dT)}_{Tc}=-33.3\mathrm{kOe}∕\mathrm{K}$ has been obtained near $T_c$. The upper critical field at zero temperature was estimated to be $H_{c2}\left(0\right)\cong 230\mathrm{kOe}$, which is a value close to the Pauli paramagnetic limiting field $H_p\left(0\right)\cong 250\mathrm{kOe}$. Then, the Ginzburg–Landau (GL) coherence length ${\xi }_{\mathrm{GL}}\left(0\right)\approx 3.8\mathrm{nm}$ was calculated, and the Maki parameter $\alpha \approx \surd 2$ was obtained, suggesting the possibility that $\mathrm{K}{\mathrm{Os}}_2{\mathrm{O}}_6$ might behave unconventionally at low temperatures and high magnetic fields.

Figure 1

(Color online) The $\alpha$-pyrochlore (left) and $\beta$-pyrochlore (right) structures shown as a projection along [110]. The $\beta$-pyrochlore structure ${◻}_2{\mathrm{B}}_2{\mathrm{O}}_6{\mathrm{A}}^{\prime }$ ($\mathrm{B}=\mathrm{Os}$; ${\mathrm{A}}^{\prime }=\mathrm{K}$,Rb,Cs) is derived from the $\alpha$-pyrochlore structure ${\mathrm{A}}_2{\mathrm{B}}_2{\mathrm{O}}_6{\mathrm{O}}^{\prime }$.

Figure 2

(Color online) Single crystals of $\mathrm{K}{\mathrm{Os}}_2{\mathrm{O}}_6$ grown in a quartz ampoule. The edge of the picture is about $1\mathrm{mm}$.

Figure 3

(Color online) Reciprocal space scan of the (0 0 6) Bragg peak violating the condition of systematic absences for the $Fd\overline{3}m$ space group symmetry (00l: $1\ne 4n$). The crystal of $\mathrm{K}{\mathrm{Os}}_2{\mathrm{O}}_6$ was measured with the $P4$ diffractometer at room temperature [200 steps with $100\mathrm{s}$ per step, Gaussian fit of $K{\alpha }_1$ and $K{\alpha }_2$ with half width at half maximum (HWHM) and amplitude constraint: ${\mathrm{HWHM}}_{K{\alpha }_1}={\mathrm{HWHM}}_{K{\alpha }_2}$ and ${\mathrm{A}}_{K{\alpha }_2}=0.5\bullet {\mathrm{A}}_{K{\alpha }_1}$].

Figure 4

(Color online) Structural details of $\beta$-pyrochlore $\mathrm{K}{\mathrm{Os}}_2{\mathrm{O}}_6$ at room temperature with $F\overline{4}3m$ space group symmetry showing the anisotropic nature of the potassium channels. Interatomic distances $\mathrm{O}2–\mathrm{K}1=3.141\mathrm{\AA }$ and $\mathrm{O}1–\mathrm{K}2=3.059\mathrm{\AA }$ are longer and shorter, respectively, compared to the ideal $\beta$-pyrochlore structure with $Fd\overline{3}m$ symmetry $(\mathrm{O}\text{–}\mathrm{K}=3.099\mathrm{\AA }$). Shown is the structure projected along the [110] direction (a) and along the $[-110]$ direction (b). Spheres represent K (large size), Os (medium size), and O (small size).

Figure 5

(Color online) Structural details of $\beta$-pyrochlore $\mathrm{K}{\mathrm{Os}}_2{\mathrm{O}}_6$ at room temperature with $F\overline{4}3m$ space group symmetry (middle) compared to $\alpha$-pyrochlore ${\mathrm{Cd}}_2{\mathrm{Re}}_2{\mathrm{O}}_7$ at $298\mathrm{K}$ (left) and $13\mathrm{K}$ (right). Atomic parameters for ${\mathrm{Cd}}_2{\mathrm{Re}}_2{\mathrm{O}}_7$ were taken from Weller et al.[17] For $\mathrm{K}{\mathrm{Os}}_2{\mathrm{O}}_6$, the O–O interatomic distances are shown in the octahedral network: the length $\mathrm{O}1–\mathrm{O}1=2.82\mathrm{\AA }$ is longer and the length $\mathrm{O}2–\mathrm{O}2=2.70\mathrm{\AA }$ is shorter than the distance $\mathrm{O}\text{–}\mathrm{O}=2.76\mathrm{\AA }$ for the ideal $\beta$-pyrochlore structure $\left(Fd\overline{3}m\right)$. Large spheres represent Os, small spheres signify O.

Figure 6

(Color online) Tetrahedral network of the Os atoms (spheres) in $\beta$-pyrochlore $\mathrm{K}{\mathrm{Os}}_2{\mathrm{O}}_6$ with $F\overline{4}3m$ space group symmetry. Two different Os tetrahedra are shown which exhibit breathing mode like behavior: tetrahedra with increased Os–Os length $\left(3.592\mathrm{\AA }\right)$ and tetrahedra with decreased Os–Os length $\left(3.548\mathrm{\AA }\right)$, compared to the ideal $\beta$-pyrochlore structure with $Fd\overline{3}m$ symmetry $(\mathrm{Os}\text{–}\mathrm{Os}=3.570\mathrm{\AA })$.

Figure 7

Magnetization $\left(M\right)$ vs temperature at constant field $H=500\mathrm{Oe}$ for a set of 28 $\mathrm{K}{\mathrm{Os}}_2{\mathrm{O}}_6$ crystals. The results are obtained upon heating from zero-field-cooled (ZFC) state and upon cooling (FC). The superconducting transition temperature $T_c$ and the irreversibility temperature $T_{\mathrm{irr}}$ are marked by arrows. The inset shows $M\left(T\right)$ reduced to $M$ at $5\mathrm{K}$ for an individual $\mathrm{K}{\mathrm{Os}}_2{\mathrm{O}}_6$ crystal in a field of $10\mathrm{Oe}$.

Figure 8

Upper critical field $H_{c2}$ close to the zero-field superconducting transition temperature $T_c=9.65\mathrm{K}$ for the $\mathrm{K}{\mathrm{Os}}_2{\mathrm{O}}_6$ crystals. The orbital critical field at zero temperature $H_{c2}{}^{*}\left(0\right)=235\mathrm{kOe}$, calculated within the GLAG theory (clean limit), is close to the Pauli limiting field $H_p\left(0\right)\cong 250\mathrm{kOe}$. The dashed line is a fit of experimental points to the formula $H_{c2}\left(T\right)=H_{c2}{}^{*}\left(0\right)(1-t^n)$ with $n=1.5$, where $t=T∕T_c$. The inset shows a low-field part of the virgin magnetization curve obtained at $5\mathrm{K}$ for $H$ swept from zero to $5\mathrm{kOe}$ and then back to zero.