Limit on the Electron Electric Dipole Moment Using Paramagnetic Ferroelectric ${\mathrm{Eu}}_{0.5}{\mathrm{Ba}}_{0.5}{\mathrm{TiO}}_3$

We report on the results of a search for the electron electric dipole moment $d_e$ using paramagnetic ferroelectric ${\mathrm{Eu}}_{0.5}{\mathrm{Ba}}_{0.5}{\mathrm{TiO}}_3$. The electric polarization creates an effective electric field that makes it energetically favorable for the spins of the seven unpaired $4f$ electrons of the ${\mathrm{Eu}}^{2+}$ to orient along the polarization, provided that $d_e\ne 0$. 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 $d_e=(-1.07\pm {3.06}_{\mathrm{stat}}\pm {1.74}_{\mathrm{syst}})\times {10}^{-25}e\mathrm{cm}$, implying an upper limit of $|d_e|<6.05\times {10}^{-25}e\mathrm{cm}$ (90% confidence).

Figure 1

A cut-through schematic of the $e\mathrm{EDM}$ experiment. Note the coordinate system in the bottom of the figure.

Figure 2

The procedure for measuring the $e\mathrm{EDM}$. Electric field pulses (top) of duration $t_p$ are applied a time $\tau$ apart. Each subsequent pulse reverses the polarization of the sample. The current flow through the samples (second from the top) is numerically integrated to obtain the polarization of the samples (second from the bottom). The SQUID signal (bottom) is averaged after each pulse between times $t_s$ and $\tau$, where $t_s$ is generally $0.8\tau$. Shown on the right are typical orders of magnitude for the various applied fields and measured quantities. If $d_e\approx {10}^{-27}e\mathrm{cm}$, the size of the SQUID signal would be of order $1\mathrm{n}{\Phi }_0$.

Figure 3

Example of the difference of the heating decay transient. The blue dashed lines show the applied electric field pulses and the red solid lines show the resulting SQUID signal. The large features in the SQUID signal seen during the electric field pulses are caused by the current that flows during the polarization reversal. After the reversal, the heated sample returns to equilibrium with the LHe bath, which can be seen as the decay after the pulse. These data were taken in the presence of an $H_x$ field (top panel) and an $H_z$ field (bottom panel), each approximately 1 mG.

Figure 4

Final best fit $e\mathrm{EDM}$ values with statistical error bars. Data were recorded at reversal frequencies of 0.25 Hz (violet, upward triangles), 0.167 Hz (red squares), 0.125 Hz (green, downward triangles), and 0.1 Hz (blue circles). The annotations show which sample(s) were driven. The solid cyan line shows the best fit mean, and the dashed cyan lines show its $1\sigma$ statistical error.