Elastic, structural and magnetic properties of EuTi$_{\mathrm{1-x}}$A$_{\mathrm{x}}$O$_{3}$ (A$=$Zr, Nb)

The elastic moduli as a function of temperature (280-380 K) and magnetic field (0-9T) for single crystal EuTiO$_{3}$ have been measured using resonant ultrasound spectroscopy (RUS). All the moduli show a sharp step-like softening upon the cubic-to-tetragonal transition at around 288K. We also present low-temperature XRD, magnetic susceptibility, and RUS results on polycrystalline EuTi$_{\mathrm{1-x}}$Zr$_{\mathrm{x}}$O$_{3}$ and EuTi$_{\mathrm{1-x}}$Nb$_{\mathrm{x}}$O$_{3}$ (x$=$0.015, 0.03 and 0.05). All of the compositions investigated present a cubic-to-tetragonal structural transition as temperature is lowered. Our results indicate that the transition temperature of the structural instability increases to higher temperatures with increasing Zr and Nb concentration in both solid-solutions, accompanied by the decrease of the antiferromagnetic transition temperature T$_{\mathrm{N}}$. While the structural distortion in EuTi$_{\mathrm{1-x}}$Zr$_{\mathrm{x}}$O$_{3}$ is suppressed with increasing Zr doping, the magnitude of the structural distortion in EuTi$_{\mathrm{1-x}}$Nb$_{\mathrm{x}}$O$_{3}$ is not affected by Nb-doping. The differences between Zr and Nb as dopants are discussed.