Relativistic nature of a magnetoelectric modulus of Cr₂O₃-crystals: a new 4-dimensional pseudoscalar and its measurement

Earlier, the magnetoelectric effect of chromium sesquioxide Cr_2O_3 has been determined experimentally as a function of temperature. One measures the electric field-induced magnetization on Cr_2O_3 crystals or the magnetic field-induced polarization. From the magnetoelectric moduli of Cr_2O_3 we extract a 4-dimensional relativistic invariant pseudoscalar $\widetilde{\alpha}$. It is temperature dependent and of the order of 10^{-4}/Z_0, with Z_0 as vacuum impedance. We show that the new pseudoscalar is odd under parity transformation and odd under time inversion. Moreover, $\widetilde{\alpha}$ is for Cr_2O_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.