Pressure dependence of antiferromagnetic and superconducting phases in U2Rh1−xPtxC2

We report temperature ($T$)- and pressure ($P$)-dependent resistivity measurements on the isostructural compounds ${\mathrm{U}}_{2}\mathrm{R}{\mathrm{h}}_{1\ensuremath{-}x}\mathrm{P}{\mathrm{t}}_{x}{\mathrm{C}}_{2}$ ($x=0$, 0.5, and 0.9) from which we construct a $T\ensuremath{-}P\ensuremath{-}x$ phase diagram. Compounds with $x=0$ and $x=0.5$ are antiferromagnets below 22.1 and 9.4 K, respectively, and their N\'eel temperature $({T}_{N})$ decreases under applied pressure. For $x=0$, the critical pressure ${P}_{c}$ required to suppress ${T}_{N}$ to zero temperature is projected to be about 8.8 GPa, but ${P}_{c}$ for $x=0.5$ is between 1.6 and 2.1 GPa. At atmospheric pressure, increasing Pt concentration in ${\mathrm{U}}_{2}\mathrm{R}{\mathrm{h}}_{(1\ensuremath{-}x)}\mathrm{P}{\mathrm{t}}_{x}{\mathrm{C}}_{2}$ tunes magnetic transition temperatures to zero at a critical value of ${x}_{c}\ensuremath{\approx}0.7$, and, consequently, we surmise the existence of a quantum-phase boundary in the $P\ensuremath{-}x$ plane at $T=0$ K that extends from ($P=0, x={x}_{c}$) to (${P}_{c}\ensuremath{\approx}8.8\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}, x=0$). For $x=0.9$, superconductivity appears at ${T}_{\mathrm{c}}=1.09\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, which decreases at a rate of $\ensuremath{\approx}\ensuremath{-}1\phantom{\rule{0.16em}{0ex}}\mathrm{K}/\mathrm{GPa}$ that is nearly twice that found for ${\mathrm{U}}_{2}\mathrm{Pt}{\mathrm{C}}_{2}$ whose ${T}_{\mathrm{c}}$ is 1.47 K. Together, these results indicate that domes of magnetism and superconductivity formed with $T\ensuremath{-}P\ensuremath{-}x$ variations are detached and that the two broken symmetries are independent of each other. Fluctuations in average composition produce rare regions that play an important role in determining physical properties of materials with noninteger $x$.