Correlated electron state in ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$ controlled through Si to P substitution

${\mathrm{CeCu}}_2{\mathrm{Si}}_2$ is an exemplary correlated electron metal that features two domes of unconventional superconductivity in its temperature-pressure phase diagram. The first dome surrounds an antiferromagnetic quantum critical point, whereas the more exotic second dome may span the termination point of a line of $f\text{-electron}$ valence transitions. This behavior has received intense interest, but what has been missing are ways to access the high pressure behavior under milder conditions. Here we study Si $\to$ P chemical substitution, which compresses the unit cell volume but simultaneously weakens the hybridization between the $f$- and conduction electron states and encourages complex magnetism. At concentrations that show magnetism, applied pressure suppresses the magnetic ordering temperature and superconductivity is recovered for samples with low disorder. These results reveal that the electronic behavior in this system is controlled by a nontrivial combination of effects from unit cell volume and electronic shell filling. Guided by this topography, we discuss prospects for uncovering a valence fluctuation quantum phase transition in the broader family of Ce-based ${\mathrm{ThCr}}_2{\mathrm{Si}}_2$-type materials through chemical substitution.

Figure 1

(a) Comparison between the measured phosphorous concentration $x_{\mathrm{meas}}$ and the nominal concentration $x_{\mathrm{nom}}$, where $x_{\mathrm{meas}}$ was determined using energy dispersive spectrometer analysis. Throughout the paper we use $x_{\mathrm{meas}}=x$ unless otherwise specified. (b) The lattice constants $a\left(x\right)$ (left axis) and $c\left(x\right)$ (right axis). (c) The unit cell volume $V\left(x\right)$ (left axis) and chemical pressure $P_{\mathrm{ch}}$ (right axis), calculated using the Burch-Murnaghan equation, where $B_0=110$ GPa [27]. (d) The ratio $c/a$ vs $x$.

Figure 2

(a) Magnetic susceptibility $\chi =M/H$ collected in a magnetic field $H=5$ kOe applied $\parallel$ to the $c$ axis of ${\mathrm{CeCu}}_2{\left({\mathrm{Si}}_{1\text{−}x}{\mathrm{P}}_x\right)}_2$ for $x=0$–0.1. (b) The inverse magnetic susceptibility ${\chi }^{-1}$ vs $T$ for $H\parallel c$ at concentrations $x=0$, 0.043, and 0.098. The dotted lines are Curie-Weiss fits to the data using the expression $\chi \left(T\right)=C/(T-\theta )$. (c) The Curie-Weiss temperature $\theta$ extracted from fits to $\chi \left(T\right)$ vs $x$. (d) Magnetic susceptibility $\chi$ vs temperature $T$ for ${\mathrm{CeCu}}_2{\left({\mathrm{Si}}_{1\text{−}x}{\mathrm{P}}_x\right)}_2$ at select concentrations $x=0$ and 0.098 for magnetic fields $H$ applied parallel $\parallel$ (solid line) and perpendicular $\perp$ (dotted line) to the $c$ axis. (e) The ratio of the magnetic susceptibilities for $H\parallel$ and $\perp$ to the $c$ axis at $T=2$ and 10 K vs $x$.

Figure 3

(a) Heat capacity $C$ divided by temperature $T$ vs $T$ of ${\mathrm{CeCu}}_2{\left({\mathrm{Si}}_{1\text{−}x}{\mathrm{P}}_x\right)}_2$ for $x=0$–0.1. (b) $C/T$ vs $T$ for ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$ and ${\mathrm{LaCu}}_2{\mathrm{Si}}_2$. Also shown is the $4f$ contribution to the heat capacity of ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$ (blue circles) $C_{4f}/T$, which was acquired by subtracting the La contribution from that of the Ce compound. (c) The $4f$ contribution to the entropy $S_{4f}$ vs $T$ for ${\mathrm{CeCu}}_2{\left({\mathrm{Si}}_{1\text{−}x}{\mathrm{P}}_x\right)}_2$. $S_{4f}$ was acquired as described in the text. (d) The electrical resistivity $\rho$ vs $T$ for $0<x<0.043$. (e) $\rho$ vs $T$ for $0.056<x<0.098$. (f) Residual resistivity ${\rho }_0$ vs $x$.

Figure 4

Summary of electrical resistivity $\rho$ vs temperature $T$ measurements under applied pressure $P$ for ${\mathrm{CeCu}}_2{\left({\mathrm{Si}}_{1\text{−}x}{\mathrm{P}}_x\right)}_2$ at select concentrations $x=0.015$, 0.043, and 0.098. For clarity, the curves for $x=0.015$ and 0.043 are offset by constant values $\mathrm{\Delta }\rho =10$ $\mu \mathrm{\Omega }\mathrm{cm}$. (a) Temperature-pressure $\left(T\text{−}P\right)$ phase diagram for $x=0.015$ for $P<20$ kbar showing the suppression of $T_{\mathrm{A}}$, the enhancement of $T_{\mathrm{coh},\rho }$, and the appearance of superconductivity at the extrapolated quantum phase transition. Open circles indicate ambiguity in defining $T_{\mathrm{A}}$. (b) $\rho (T)$ for $x=0.015$ for $P<20$ kbar at $0<T<40$ K where the Kondo coherence temperature $T_{\mathrm{coh},\rho }$ appears as a broad hump. (c) $\rho (T)$ for $x=0.015$ for pressures $P<20$ kbar and $0<T<7$ K. (d) $T\text{−}P$ phase diagram for $x=0.043$ for $P<20$ kbar. (e) $\rho (T)$ for $x=0.043$ for $P<20$ kbar at $0<T<40$ K. (f) $\rho (T)$ for $x=0.043$ for pressures $P<20$ kbar at $0<T<7$ K. (g) $T\text{−}P$ phase diagram for $x=0.098$ for several pressures $P<20$ kbar. (h) $\rho (T)$ for $x=0.098$ for several pressures $P$ and $0<T<40$ K. (i) $\rho (T)$ for $x=0.098$ at $P<20$ kbar and $0<T<7$ K.

Figure 5

Summary of thermodynamic and electrical transport results for ${\mathrm{CeCu}}_2{\left({\mathrm{Si}}_{1\text{−}x}{\mathrm{P}}_x\right)}_2$ at concentrations $x=0$–0.1. (a) Unit cell volume $V$ (left axis) and chemical pressure $P_{\mathrm{chem}}$ vs $x$, where $x$ is the measured value. $P_{\mathrm{chem}}$ was obtained using the Birch-Murnaghan equation of state. (b) Temperature-phosphorous concentration $\left(T\text{−}x\right)$ phase diagram for ${\mathrm{CeCu}}_2{\left({\mathrm{Si}}_{1\text{−}x}{\mathrm{P}}_x\right)}_2$ constructed from magnetic susceptibility $\chi$, heat capacity $C$, and electrical resistivity $\rho$ vs $T$ measurements. The magnetic ordering temperatures $T_{\mathrm{A}},T_{\mathrm{N}}$, and $T_{\mathrm{C}}$ and the Kondo coherence temperature $T_{\mathrm{coh},\rho }$ are defined as described in the text.

Figure 6

Phase diagram for the compounds $\mathrm{Ce}{T}_2{X}_2$ $(T$ = transition metal and $X$ = Si, Ge) that crystallize in the ${\mathrm{ThCr}}_2{\mathrm{Si}}_2$-type structure [15, 16]. The axes that define the four quadrants (I–IV) and control the ground state behavior are the difference in unit cell volume $\left(\mathrm{\Delta }V\right)$ from that of ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$ and increasing $d$-shell filling going from the Fe column to the Cu column $\left(x\right)$. The white band that traverses the center of the phase diagram approximately separates the magnetic (left-hand side) and intermediate valence examples (right-hand side). The bars labeled SCI (green) and SCII (dark blue) show the regions where superconductivity is observed for ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$ along the $\mathrm{\Delta }V$ axis [17, 18, 19, 20, 21, 23]. In parentheses are the maximum superconducting transition temperatures that are observed under applied pressure for those compounds with an antiferromagnetic quantum phase transition [20, 21, 28, 29, 30, 31, 32]. In quadrant IV the open circles show the zero temperature magnetic phase boundary resulting from the investigation of the substitution series ${\mathrm{CeCu}}_2{\left({\mathrm{Si}}_{1\text{−}x}{\mathrm{P}}_x\right)}_2$ presented here (see Fig. 5). The closed circles show where applied pressure suppresses magnetic ordering to quantum phase transitions in this series (see Fig. 4).