Relativistic analysis of magnetoelectric crystals: extracting a new 4-dimensional P odd and T odd pseudoscalar from Cr₂ O₃ data

Earlier, the linear magnetoelectric effect of chromium sesquioxide Cr_2 O_3 has been determined experimentally as a function of temperature. One measures the electric field-induced magnetization on Cr_2 O_3 crystals or the magnetic field-induced polarization. From the magnetoelectric moduli of Cr_2 O_3 we extract a 4-dimensional relativistic invariant pseudoscalar \tilde\alpha. It is temperature dependent and of the order of ~ 10^{-4} Y_0, with Y_0 as vacuum admittance. We show that the new pseudoscalar \tilde\alpha is odd under parity transformation and odd under time inversion. Moreover, \tilde\alpha is for Cr_2 O_3 what Tellegen's gyrator is for two port theory, the axion field for axion electrodynamics, and the PEMC (perfect electromagnetic conductor) for electrical engineering.