Crystallographic and superconducting properties of filled skutterudite ${\mathrm{SrOs}}_4{\mathrm{P}}_{12}$

The crystallographic and physical properties of the recently discovered filled skutterudite superconductor ${\mathrm{SrOs}}_4{\mathrm{P}}_{12}$, synthesized by a high-pressure and -temperature technique, are studied by measuring electrical resistivity, specific heat, and magnetization, and by performing electronic band calculations. X-ray powder diffraction with Rietveld refinement indicates that the lattice parameter of ${\mathrm{SrOs}}_4{\mathrm{P}}_{12}$ is 8.093(2) Å and that fractional coordinates of the P site are [0, 0.3607(9), 0.1450(9)], which is also confirmed by calculations based on density functional theory. The electrical resistivity indicates a metallic nature of ${\mathrm{SrOs}}_4{\mathrm{P}}_{12}$, which is consistent with the density of states at Fermi energy with 7.5 (states/eV)/f.u. deduced from the electronic band calculations. The Sommerfeld coefficient $\gamma$ and Einstein temperature $\theta {}_{\mathrm{E}}$ of ${\mathrm{SrOs}}_4{\mathrm{P}}_{12}$ are deduced as $\gamma \sim 26\mathrm{mJ}/{\mathrm{mol}\mathrm{K}}^2$ and $\theta {}_{\mathrm{E}}\sim 150$ K, respectively. A larger isotropic atomic displacement parameter $U_{\mathrm{eq}}$ of Sr compared to other atomic species as obtained from a Rietveld analysis and a specific heat anomaly around 30 K refers to anharmonic lattice vibrations of Sr in ${\mathrm{SrOs}}_4{\mathrm{P}}_{12}$. ${\mathrm{SrOs}}_4{\mathrm{P}}_{12}$ exhibits two superconducting transitions at $T_{\mathrm{c}1}=1.6$ K and $T_{\mathrm{c}2}=1.0$ K. Specific-heat data indicate that the observed superconductivity is of bulk nature with approximate volume fractions of $27\%$ and $38\%$ for superconductivity at $T_{\mathrm{c}1}$ and $T_{\mathrm{c}2}$, respectively. The electrical resistivity under field and pressure as well as the specific heat under field indicate that $T_{\mathrm{c}1}$ is sensitive to the magnetic field and $T_{\mathrm{c}2}$ is sensitive to pressure. The results show that ${\mathrm{SrOs}}_4{\mathrm{P}}_{12}$ is an $s$-wave weakly coupled superconductor with an electron-phonon mass enhancement ${\lambda }_{\text{ep}}\sim 0.47$.

Figure 1

Elemental mapping for Sr (left top), Os (right top), P (left bottom), and secondary electron image (right bottom) of ${\mathrm{SrOs}}_4{\mathrm{P}}_{12}$ obtained by EPMA. Point analysis was also performed to the points numbered.

Figure 2

Main panel: XRD pattern of ${\mathrm{SrOs}}_4{\mathrm{P}}_{12}$ (filled circles). The solid black line behind the XRD pattern is the calculated profile. The vertical marks show the positions of allowed reflections. The differences between the observed and calculated patterns are shown at the bottom. Inset: Pressure dependence of $V/V_0$. The solid line indicates the fitting line according to the Birch-Murnaghan equation of state. The dashed-dotted line and the dotted line indicate the fitting line from DFT calculations and the fitting line by fixing $B_1=4.7$, respectively (see the text for details).

Figure 3

Temperature dependence of resistivity at a pressure of 0 GPa (triangles), 0.8 GPa (squares), 1.4 GPa (inverted triangles), and 1.9 GPa (circles) without magnetic field (open symbols) and exposed to a field of ${\mu }_{0}H=0.5$ T (solid symbols). The inset shows the pressure dependence of $T_{\mathrm{c}}$ without a magnetic field (open circles) and with a field of 0.5 T (solid circles).

Figure 4

Main panel: Specific heat as a function of temperature $C\left(T\right)$ of ${\mathrm{SrOs}}_4{\mathrm{P}}_{12}$ in the presence of an applied magnetic field. Top inset: Phonon contribution of the specific heat as a function of temperature $(C-\gamma T)/T^3$ ($T$) above 10 K. Bottom inset: Electronic contribution to the specific heat divided by temperature as a function of temperature $C_e/T$ ($T$) below 2 K.

Figure 5

Main panel: Isothermal magnetization curve of ${\mathrm{SrOs}}_4{\mathrm{P}}_{12}$. The magnetization from the normal conducting state is subtracted. Bottom inset: Low-field magnification of the isothermal magnetization curve. Top inset: Temperature dependence of magnetic susceptibility $4\pi \chi$ at 2 mT in the process of FC (triangle) and ZFC (filled circle) and at 0.5 mT in the process of ZFC (open circle).

Figure 6

(a) Temperature dependence of ${\mu }_0{H}_{\mathrm{c}2}$ deduced from resistivity (circle), specific heat (square for SC1 and triangle for SC2), and from magnetization (diamond) of ${\mathrm{SrOs}}_4{\mathrm{P}}_{12}$. Temperature-dependent ${\mu }_0{H}_{\mathrm{c}}$ deduced from specific heat (solid line) and ${\mu }_0{H}_{\mathrm{c}1}$ deduced from magnetization (inverted triangle) is multiplied by 10 for clarity. (b) ${\mu }_0{H}_{\mathrm{c}2}$ vs $T$ deduced from resistivity at various pressures. The dotted lines are intended to guide the eyes in both figures. See the text for details.

Figure 7

Electronic density of states of ${\mathrm{SrO}}_4{\mathrm{P}}_{12}$ together with the partial densities of state for each atomic species. The inset shows the site-projected electronic density of states of Sr, Os, and P below $-5$ eV.

Figure 8

Band structure for ${\mathrm{SrOs}}_4{\mathrm{P}}_{12}$ as calculated by the GGA method. The Fermi level is set to be energy zero.