Pressure study on the interplay between magnetic order and valence crossover in EuPd2(Si1−xGex)2

We present results of the magnetic susceptibility on high-quality single crystals of ${\mathrm{EuPd}}_{2}{({\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Ge}}_{x})}_{2}$ for Ge concentrations $0\ensuremath{\le}x\ensuremath{\le}0.105$ performed under varying hydrostatic (He-gas) pressure $0\ensuremath{\le}p\ensuremath{\le}0.5$ GPa. The work extends recent studies at ambient pressure demonstrating the drastic change in the magnetic response from valence-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-crossover temperature ${T}_{\text{V}}^{\ensuremath{'}}$ shows an extraordinarily strong pressure dependence of $d{T}_{\text{V}}^{\ensuremath{'}}/dp=+(80\ifmmode\pm\else\textpm\fi{}10)$ K/GPa. In contrast, a very small pressure dependence of $d{T}_{\text{N}}/dp\ensuremath{\le}+(1\ifmmode\pm\else\textpm\fi{}0.5)$ 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-crossover behavior is observed. Estimates of the electronic entropy related to the Eu $4f$ electrons, derived from analyzing susceptibility data at varying pressures, indicate that the boundary between AFM order and valence crossover represents a first-order phase transition. Our results suggest a particular type of second-order critical end point of the first-order transition for $x=0.105$ at ${p}_{\text{cr}}\ensuremath{\approx}0.06$ GPa and ${T}_{\text{cr}}\ensuremath{\approx}39$ K where intriguing strong-coupling effects between fluctuating charge, spin, and lattice degrees of freedom can be expected.