Multiferroic quantum criticality in (Eu,Ba,Sr)TiO₃ system

The existence of multiferroic quantum criticality was theoretically predicted in (Eu,Ba,Sr)TiO₃ solid solution.¹ Since pure BaTiO₃ is a ferroelectric (below ≈ 400 K), SrTiO₃ is a quantum paraelectric, and incipient ferroelectric EuTiO₃ is an antiferromagnet below ≈ 5 K, the Eu_0.3Ba_0.1Sr_0.6TiO₃ should exhibit both magnetic and ferroelectric quantum criticality¹, and consequently an unconventional low-temperature scaling (power dependence) of its physical properties (e.g. electric and magnetic susceptibility).

Within our research, (Eu,Ba,Sr)TiO₃ ceramics, as well as a single crystal, with compositions close to the Eu_0.3Ba_0.1Sr_0.6TiO₃, were prepared. All samples were examined in terms of low-frequency dielectric permittivity, magnetization, magnetic susceptibility and heat capacity in temperature range 0.3-300 K. Since the phase transition temperature generally depends on many physical conditions, the samples were studied in an external electric field of ≈ 2.5 kV/cm, magnetic field of up to ≈ 10 T and hydrostatic pressure of up to 2.73 GPa (see Fig.).

The temperature dependence of dielectric permittivity shows the presence of ferroelectric quantum criticality (as quantum paraelectrics SrTiO₃ or KTaO₃). Reciprocal magnetic susceptibility, however, follows a linear Curie-Weiss dependence (at least down to 2 K) with antiferromagnetic Curie temperature of ≈ 0.8 K. At similar temperature (0.7 K), a peak in magnetization occurs, which corresponds to the antiferromagnetic phase transition. In fact, its temperature also coincides with a Schottky anomaly existing on Eu²⁺ magnetic ions which was revealed by the heat capacity measurement performed at various external magnetic fields.

¹Narayan, A., et al. Nature Mater. 18, 223 (2019).

Fig.: Temperature dependence of dielectric permittivity of Eu_0.25Ba_0.1Sr_0.65TiO₃ ceramics measured at various hydrostatic pressures.