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 $17,\rm K$.

💡 Research Summary

In this work the authors report the successful growth of high‑quality single crystals of Eu(Pd₁₋ₓAuₓ)₂Si₂ (0 < x ≤ 0.2) and EuPd₂(Si₁₋ₓGeₓ)₂ (x = 0.2) using a levitating Eu‑rich melt and the Czochralski technique under 20 bar Ar. Structural characterization by powder and low‑temperature X‑ray diffraction confirms that all Au‑substituted samples retain the ThCr₂Si₂ tetragonal structure, while the lattice parameters a and c increase monotonically with nominal Au content. Energy‑dispersive and wavelength‑dispersive X‑ray spectroscopy reveal that only 25–35 % of the Au present in the melt is incorporated into the crystal, leading to a real Au concentration substantially lower than the nominal value. This limited incorporation results in a relatively homogeneous substitution but also explains why the actual chemical pressure is weaker than expected from the nominal composition.

The key physical effect of Au substitution is the application of chemical pressure: even a small amount of Au (nominal x = 0.1) reduces the valence‑crossover temperature T′ᵥ from ≈160 K in the parent EuPd₂Si₂ to ≈110 K, as evidenced by a clear anomaly in the heat‑capacity and a ≈2 % contraction of the a‑axis upon cooling through the transition, while the c‑axis remains essentially unchanged. Importantly, contrary to earlier studies on polycrystalline material, the authors do not observe any signatures of a first‑order valence transition (no hysteresis, no abrupt jump in the Mössbauer isomer shift, and no sharp latent‑heat peak). Likewise, antiferromagnetic (AFM) order, which was reported for higher Au concentrations (x ≈ 0.25), is absent up to the highest Au content studied (nominal x = 0.2). The absence of a first‑order transition in single crystals suggests that the previously reported critical endpoint (CEP) near x ≈ 0.04 may be an artifact of compositional inhomogeneity in polycrystals.

At higher Au loadings (nominal x = 0.2) the authors encounter the formation of a quaternary side phase, identified by powder diffraction as a distinct Eu‑Pd‑Si‑Ge compound. This secondary phase segregates during growth because the residual melt becomes enriched in Eu and Au as the crystal is pulled, leading to cracks upon cooling due to mismatched thermal expansion.

Ge substitution was also explored. Cubic‑millimeter sized EuPd₂(Si₁₋ₓGeₓ)₂ crystals with nominal x = 0.2 were grown. Micro‑XRF mapping shows a slight variation of the actual Ge content (≈0.18–0.22), which is sufficient to shift the valence‑crossover temperature and, in some regions, to induce a transition from intermediate valence to stable Eu²⁺ magnetic order (T_N ≈ 47 K). The authors emphasize that such tiny compositional fluctuations can dramatically alter the crossover temperature and even change the nature of the low‑temperature ground state, making these crystals ideal candidates for pressure‑tuned studies of critical elasticity.

A serendipitous discovery is a new orthorhombic phase with composition EuPd₁.₄₂Si₁.₂₇Ge₀.₃₁, isolated as a side product. Single‑crystal diffraction confirms its orthorhombic symmetry, and magnetic measurements reveal antiferromagnetic ordering below 17 K. This phase expands the known structural landscape of Eu‑Pd‑Si‑Ge compounds and provides a platform to investigate how subtle changes in the Pd‑Si/Ge sublattice affect Eu valence and magnetic interactions.

Overall, the paper delivers several important insights: (i) Au substitution acts as an efficient chemical‑pressure knob that strongly lowers the valence‑crossover temperature even at low concentrations; (ii) the lack of a first‑order transition in high‑quality single crystals challenges earlier phase‑diagram proposals based on polycrystals; (iii) the limited Au incorporation and the emergence of side phases highlight the need for careful control of melt composition and growth parameters; (iv) Ge substitution, despite being isoelectronic, induces comparable effects through lattice contraction, and minute compositional gradients can tip the balance between intermediate valence and magnetic order; (v) the newly identified orthorhombic EuPd₁.₄₂Si₁.₂₇Ge₀.₃₁ phase adds a magnetic member to the Eu‑based 122 family with a distinct crystal symmetry.

These results establish Eu(Pd₁₋ₓAuₓ)₂Si₂ and EuPd₂(Si₁₋ₓGeₓ)₂ single crystals as versatile platforms for studying valence fluctuations, critical elasticity, and the interplay between electronic correlations and lattice degrees of freedom. The clarified phase behavior and the availability of high‑quality crystals open pathways for systematic pressure‑dependent experiments, neutron scattering, and spectroscopic investigations aimed at unraveling the microscopic mechanisms governing valence‑driven quantum criticality in Eu‑based intermetallics.