A limit on the electron electric dipole moment using paramagnetic ferroelectric Eu$_{0.5}$Ba$_{0.5}$TiO$_3$

We report on the results of a search for the electron electric dipole moment $d_e$ using paramagnetic ferroelectric Eu$_{0.5}$Ba$_{0.5}$TiO$_3$. The electric polarization creates an effective electric field that makes it energetically favorable for the spins of the seven unpaired $4f$ electrons of the Eu$^{2+}$ to orient along the polarization, provided that $d_e\neq 0$. This interaction gives rise to sample magnetization, correlated with its electric polarization, and is therefore equivalent to a linear magnetoelectric effect. A SQUID magnetometer is used to search for the resulting magnetization. We obtain $d_e = (-1.07\pm3.06_\text{stat}\pm 1.74_\text{sys})\times10^{-25}\ecm$, implying an upper limit of $|d_e|<6.05\times10^{-25}\ecm$ (90% confidence).