Pressure study on the interplay between magnetic order and valence-change crossover in EuPd$_2$(Si$_{1-x}$Ge$_x$)$_2$

We present results of the magnetic susceptibility on high-quality single crystals of EuPd$_2$(Si$_{1-x}$Ge$_x$)$_2$ for Ge concentrations 0 $\leq x \leq$ 0.105 performed under varying hydrostatic (He-gas) pressure 0 $\leq p \leq$ 0.5 GPa. The work extends on recent studies at ambient pressure demonstrating the drastic change in the magnetic response from valence-change-crossover behavior for $x$ = 0 and 0.058, to long-range antiferromagnetic (afm) order below $T_{\text{N}}$ = 47 K for $x$ = 0.105. The valence-change-crossover temperature $T'_{\text{V}}$ shows an extraordinarily strong pressure dependence of d$T'_{\text{V}}$/d$p$ = +(80 $\pm$ 10) K/GPa. In contrast, a very small pressure dependence of d$T_{\text{N}}$/d$p \leq$ +(1 $\pm$ 0.5) K/GPa is found for the afm order upon pressurizing the $x$ = 0.105 crystal from $p$ = 0 to 0.05 GPa. Remarkably, by further increasing the pressure to 0.1 GPa, a drastic change in the ground state from afm order to valence-change-crossover behavior is observed. Estimates of the electronic entropy, derived from analyzing susceptibility data at varying pressures, indicate that the boundary between afm order and valence-change crossover represents a first-order phase transition. Our results suggest a particular type of second-order critical endpoint of the first-order transition for $x$ = 0.105 at $p_{\text{cr}} \approx$ 0.06 GPa and $T_{\text{cr}} \approx$ 45 K where intriguing strong-coupling effects between fluctuating charge-, spin- and lattice degrees of freedom can be expected.