Single crystal growth and properties of Au- and Ge-substituted EuPd$_2$Si$_2$

We report on the single crystal growth of Eu(Pd$_{1-x}$Au$_x$)$_2$Si$_2$, $0< x\leq 0.2$, from a levitating Eu-rich melt using the Czochralski method. Our structural analysis of the samples confirms the ThCr$_2$Si$_2$-type structure as well as an increase of the room temperature $a$ and $c$ lattice parameters with increasing $x$. Chemical analysis reveals that, depending on the Au concentration, only about 25-35\% of the amount of Au available in the initial melt is incorporated into the crystal structure, resulting in a decreasing substitution level for increasing $x$. Through Au substitution, chemical pressure is applied and large changes in valence crossover temperatures are already observed for low substitution levels $x$. In contrast to previous studies, we do not find any signs of a first-order transition in samples with $x_{\rm nom}=0.1$ or AFM order for higher $x$. Furthermore, we observe the formation of quarternary side phases for a higher amount of Au in the melt. In addition, cubic-mm-sized single crystals of EuPd$_2$(Si$_{1-x}$Ge$_x$)$_2$ with $x_{\rm nom}=0.2$ were grown. The analysis of the X-ray fluorescence revealed that the crystals exhibit a slight variation in the Ge content. Such tiny compositional changes can cause changes in the sample properties concerning variations of the crossover temperature or changes of the type of the transition from crossover to magnetic order. Furthermore, we report on a new orthorhombic phase EuPd$_{1.42}$Si$_{1.27}$Ge$_{0.31}$ that orders antiferromagnetically below $17\,\rm K$.