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The electric dipole moment (EDM) of a particle violates both time reversal(T) and space reflection (P) symmetries. There have been recent suggestions forsearches of the electron EDM using solid state experiments [1,2]. Theseexperiments could improve the sensitivity compared to present atomic andmolecular experiments by several orders of magnitude. In the present paper wecalculate the expected effect. We also suggest that this kind of experiment issensitive to T,P-violation in nuclear forces and calculate effects caused bythe nuclear Schiff moment.  The compounds under consideration contain magnetic Gd$^{3+}$ ions and oxygenO$^{2-}$ ions. We demonstrate that the main mechanism for the T,P-odd effectsis related to the penetration of the Oxygen 2p-electrons to the Gd core. Allthe effects are related to the deformation of the crystal lattice.Comment: 13 pages, 6 figure

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