Search for violation of fundamental time-reversal and space-reflection symmetries in solid-state experiments

The electric dipole moment (EDM) of a particle violates both time-reversal (T) and space-reflection (P) symmetries. There have been recent suggestions to investigate the electron EDM using solid-state experiments. These experiments could improve the sensitivity compared to present atomic and molecular experiments by several orders of magnitude. In the present paper we calculate the expected effect. We also suggest that this kind of experiment is sensitive to T,P violation in nuclear forces and calculate the effects caused by the nuclear Schiff moment. The compounds under consideration contain magnetic ${\mathrm{Gd}}^{3+}$ ions and oxygen ${\mathrm{O}}^{2-}$ ions. We demonstrate that the main mechanism for the T,P-odd effects is related to the penetration of the oxygen $2p$ electrons into the Gd core. All the effects are related to the deformation of the crystal lattice.