Thermal expansion of the heavy-fermion superconductor ${\mathrm{PuCoGa}}_5$

We have performed high-resolution powder x-ray-diffraction measurements on a sample of ${}^{242}\mathrm{PuCoGa}_5$, the heavy-fermion superconductor with the highest critical temperature of $T_c=18.7\mathrm{K}$. The results show that the tetragonal symmetry of its crystallographic lattice is preserved down to 2 K. Marginal evidence is obtained for an anomalous behavior below $T_c$ of the $a$ and $c$ lattice parameters. The observed thermal expansion is isotropic down to 150 K and becomes anisotropic for lower temperatures. This gives a $c/a$ ratio that decreases with increasing temperature to become almost constant above $\sim 150\mathrm{K}$. The volume thermal expansion coefficient ${\alpha }_V$ has a jump at $T_c$, a factor $\sim 20$ larger than the change predicted by the Ehrenfest relation for a second-order phase transition. The volume expansion deviates from the curve expected for the conventional anharmonic behavior described by a simple Grüneisen-Einstein model. The observed differences are about ten times larger than the statistical error bars but are too small to be taken as an indication for the proximity of the system to a valence instability that is avoided by the superconducting state.

Figure 1

X-ray-diffraction pattern recorded for ${\mathrm{PuCoGa}}_5$ at 5 K; the blue points are the experimental data, the red line is the refined Rietveld profile ($R_{wp}=8.77\%,R_{wp}/R_{exp}=1.2$). The residual is given by the black line at the bottom; vertical ticks represent the angular position of Bragg peaks. No impurity phases were detected. The left inset: crystallographic unit cell (space-group $P4/mmm$, No. 123). Pu atoms (blue spheres) occupy the $1a$ Wyckoff position, Co atoms (red spheres) are located at the $1b$ position, halfway between the Pu atoms along the $c$ direction, and the Ga atoms sit on two crystallographic positions, one (orange spheres) in the center of the basal planes ($1c$) and the other ($4i$) in the rectangular faces of the unit cell (yellow spheres) with the position (0, 1/2, $z$). The refined value of the $z$ parameter at 5 K is $z=0.3075\left(2\right)$. The right inset: temperature dependence of the magnetic susceptibility measured under zero-field cooling (closed brown circles) and field cooling conditions (open red circles, applied field of ${10}^{-3}\mathrm{T}$), providing a $T_c$ of 18.7 K.

Figure 2

The (020) Bragg peak measured at 5 K (black circles) and 21 K (red dashed line). Neither splitting nor broadening of the line shape is observable, indicating that the tetragonal symmetry is preserved in the superconducting phase.

Figure 3

Thermal expansion of the ${\mathrm{PuCoGa}}_5$ lattice parameters and unit-cell volume. The solid lines represent a fit to a Grüneisen-Einstein model as explained in the text. The vertical bars give the statistical error multiplied by a factor of 5. If not visible, the error bars are smaller than the symbol sizes.

Figure 4

Top panel: temperature dependence of the $c/a$ ratio for ${\mathrm{PuCoGa}}_5$. The inset shows the temperature dependence of the linear thermal expansion coefficients along the $a$ (triangles) and $c$ (circles) crystallographic directions. Bottom panel: Thermal expansion coefficient for the unit-cell volume (in an expanded scale around $T_c$ in the inset). Error bars are estimated as five times the statistical error provided by the Rietveld refinement and are smaller than the symbol size if not shown. The solid lines are guides to the eye.