Multiferroic quantum criticality in a (Eu,Ba,Sr)${\mathrm{TiO}}_3$ solid solution

Based on the earlier published theory [A. Narayan, Nat. Mater. 18, 223 (2019)], a comprehensive experimental investigation of multiferroic quantum critical behavior of (Eu,Ba,Sr)${\mathrm{TiO}}_3$ polycrystalline and single-crystal samples was performed. The presence of the displacive ferroelectric quantum criticality is revealed through nonclassical ($T^2$) temperature scaling of inverse dielectric susceptibility up to 60 K. With increasing hydrostatic pressure, this ferroelectric quantum criticality is gradually suppressed. Inverse magnetic susceptibility follows classical Curie-Weiss law down to 4 K, but quantum fluctuations belonging to an antiferromagnetic phase transition ($T_N<0.8$ K) change its scaling below 3 K to $T^{(1.7\pm 0.1)}$ and $T^{(2.1\pm 0.2)}$ for samples containing 29% and 25% of ${\mathrm{Eu}}^{2+}$ ions, respectively. Experimental indications of the coexisting ferroelectric and antiferromagnetic, i.e., multiferroic, quantum fluctuations and qualitative explanation of why they could be seen only in the immediate proximity of $T_N$ is given.