Tuning the structural and antiferromagnetic phase transitions in ${\mathrm{UCr}}_2{\mathrm{Si}}_2$: Hydrostatic pressure and chemical substitution

Structural phase transitions in $f$-electron materials have attracted sustained attention both for practical and basic science reasons, including the fact that they offer an environment to directly investigate relationships between structure and the $f$-state. Here we present results for ${\mathrm{UCr}}_2{\mathrm{Si}}_2,$ where structural (tetragonal $\to$ monoclinic) and antiferromagnetic phase transitions are seen at $T_{\mathrm{S}}=205$ K and $T_{\mathrm{N}}=25$ K, respectively. We also provide evidence for an additional second-order phase transition at $T_{\mathrm{X}}=280$ K. We show that $T_{\mathrm{X}},$ $T_{\mathrm{S}},$ and $T_{\mathrm{N}}$ respond in distinct ways to the application of hydrostatic pressure and $\mathrm{Cr}\to \mathrm{Ru}$ chemical substitution. In particular, hydrostatic compression increases the structural ordering temperature, eventually causes it to merge with $T_{\mathrm{X}},$ and destroys the antiferromagnetism. In contrast, chemical substitution in the series ${\mathrm{UCr}}_{2-x}{\mathrm{Ru}}_x{\mathrm{Si}}_2$ suppresses both $T_{\mathrm{S}}$ and $T_{\mathrm{N}}$, causing them to approach zero temperature near $x\approx 0.16$ and 0.08, respectively. The distinct $T\text{−}P$ and $T\text{−}x$ phase diagrams are related to the evolution of the rigid Cr-Si and Si-Si substructures, where applied pressure semiuniformly compresses the unit cell, and $\mathrm{Cr}\to \mathrm{Ru}$ substitution results in uniaxial lattice compression along the tetragonal $c$-axis and an expansion in the $ab$-plane. These results provide insights into an interesting class of strongly correlated quantum materials in which degrees of freedom associated with $f$-electron magnetism, strong electronic correlations, and structural instabilities are readily controlled.

Figure 1

(a) Electrical resistance divided by the room-temperature value $R/R_{300\text{K}}$ vs temperature $T$ for ${\mathrm{UCr}}_2{\mathrm{Si}}_2$ under applied pressure. The anomaly at $T_{\mathrm{X}}$, the structural phase transition $T_{\mathrm{S}}$, and the antiferromagnetic phase transition $T_{\mathrm{N}}$ are indicated by arrows. For clarity, the curves are vertically offset by the value $\mathrm{\Delta }=0.1$. (b) The derivative of $R/R_{300\text{K}}$ with respect to $T\partial R/\partial T$ vs $T$ for ${\mathrm{UCr}}_2{\mathrm{Si}}_2$ under applied pressure. Curves are offset by constant values.

Figure 2

(a) Electrical resistance divided by the room-temperature value $R/R_{300\text{K}}$ vs temperature $T$ for ${\mathrm{UCr}}_{2-x}{\mathrm{Ru}}_x{\mathrm{Si}}_2$. For clarity, the curves are vertically offset by the value $\mathrm{\Delta }=0.1$. Inset: Zoom of $R\left(T\right)$ for $x=0$ showing the features at $T_{\mathrm{X}}$ and $T_{\mathrm{S}}$. (b) The derivative of $R/R_{300\text{K}}$ with respect to $T\partial R/\partial T$ vs $T$ for ${\mathrm{UCr}}_{2-x}{\mathrm{Ru}}_x{\mathrm{Si}}_2$. Curves are offset by the constant value $\mathrm{\Delta }=0.01$. The anomalies $T_{\mathrm{S}}$ and $T_{\mathrm{N}}$ are labeled.

Figure 3

Powder x-ray diffraction data for ${\mathrm{UCr}}_{2-x}{\mathrm{Ru}}_x{\mathrm{Si}}_2$ spanning concentrations $0<x<0.256$ and at temperatures $T$ (a) 300 K and (b) 40 K. Results at $T=10$ K are similar to those seen at 40 K. The transition from the tetragonal to the monoclinic structure is evidenced by the splitting of peaks between 300 and 40 K, as highlighted by the shaded box in panel (b).

Figure 4

Summary of structural quantities determined from analysis of powder x-ray diffraction measurements of ${\mathrm{UCr}}_{2-x}{\mathrm{Ru}}_x{\mathrm{Si}}_2$ at temperatures of 300 K [panels (a)–(c)], 40 K, and 10 K [panels (d)–(g)]. The dashed lines are guides to the eye. (a) The lattice constants $a\left(x\right)$ (left axis) and $c\left(x\right)$ (right axis) for the 300 K tetragonal structure. (b) The $c/a$ ratio for the 300 K tetragonal structure. (c) The unit-cell volume $V\left(x\right)$ for the 300 K tetragonal structure. (d) Lattice constants $a(x$), $b(x$), and $c(x$) for the low-temperature monoclinic structure. (e) The monoclinic distortion angle $\beta (x$) for the low-temperature monoclinic structure. (f) The unit-cell volume $V\left(x\right)$ for the low-temperature monoclinic structure. (g) The interlayer U-U spacing for the monoclinic structure. Above $x=0.16$, the U-U spacing is considered as $c/2$ from the tetragonal structure at low temperature.

Figure 5

(a) The magnetic susceptibility $\chi$ vs temperature $T$ for measurement in an applied magnetic field $H=0.5$ T for select concentrations spanning the ${\mathrm{UCr}}_{2-x}{\mathrm{Ru}}_x{\mathrm{Si}}_2$ chemical substitution series. The antiferromagnetic ordering temperatures are indicated by arrows as $T_{\mathrm{N}}$. (b) The inverse magnetic susceptibility ${\chi }^{-1}$ vs temperature $T$ for measurement in an applied magnetic field $H=0.5$ T for select concentrations spanning the ${\mathrm{UCr}}_{2-x}{\mathrm{Ru}}_x{\mathrm{Si}}_2$ chemical substitution series. The structural ordering temperatures are indicated by arrows as $T_{\mathrm{S}}$.

Figure 6

(a) The heat capacity divided by temperature $C$/$T$ vs $T$ for ${\mathrm{UCr}}_{2-x}{\mathrm{Ru}}_x{\mathrm{Si}}_2$ emphasizing the structural phase transition at $T_{\mathrm{S}}$. (b) Low-temperature $C$/$T$ for selected concentrations showing both the antiferromagnetic phase transition at $T_{\mathrm{N}}$ and the low-temperature upturn that are described in the text. (c),(d) Relaxation curves around the structural phase transition temperature for $x=0$ and 0.16. In panel (c) the arrow indicates the kink in the heating curve due to the latent heat of the first-order phase transition. A similar feature is not detected for $x=0.16$. (e) The entropy associated with the structural phase transition for selected $x$, which was determined as described in the text.

Figure 7

(a) Temperature $T$ vs pressure $P$ phase diagram for ${\mathrm{UCr}}_2{\mathrm{Si}}_2$ constructed from electrical resistance $R$ measurements under applied pressure. The unidentified phase transition at $T_{\mathrm{X}}$, the structural phase transition at $T_{\mathrm{S}}$, and the antiferromagnetic phase transition at $T_{\mathrm{N}}$ are shown. (b) Temperature $T$ vs concentration $x$ phase diagram for ${\mathrm{UCr}}_{2-x}{\mathrm{Ru}}_x{\mathrm{Si}}_2$ for $x=0$–0.26 constructed from electrical resistance $R$, powder x-ray diffraction, magnetic susceptibility $\chi$, and heat capacity $C$ measurements. The arrows represent results from XRD measurements where the tetragonal phase persists down to $T=10$ K. At these same concentrations, $R$ and $C$ measurements show that there are no phase transitions for $T>500$ mK.