Magneto-electric interactions probed by x-ray optical activity

Xray Optical Activity (XOA) is caused mainly by E1E2 interference terms in systems with odd space Parity (P). Extra emphasis is put below on nonreciprocal XOA effects in Magneto-Electric (ME) solids in which both Parity and Time-reversal (Θ) symmetries are broken whereas the magnetic structure remains invariant in the product PΘ. Two types of dichroism related to non-reciprocal XOA have been observed experimentally: (i) The x-ray Magnetochiral dichroism (XMχD) detected in the antiferromagnetic (AFM) phase of Cr₂O₃ is associated with the (unpolarized) Stokes component S₀; (ii) A non-reciprocal x-ray Magnetic Linear Dichroism (XMLD) was also observed in the low temperature AFM phase a (V_1−xCr_x)₂O₃ single crystal and is associated with the Stokes components S₁ or S₂. Edge selective XOA sum rules were derived recently which give a unique access to a whole family of spherical ME operators mixing orbitals of different parities in what is assumed to be the ground state. It is proved that the orbital anapole moment Ω₀⁽¹⁾ is primarily responsible for the XMχD signal measured both with a single crystal or a powdered sample of Cr₂O₃. It is suggested that the nonreciprocal XOA in both Cr₂O₃ and (V_1−xCr_x)₂O₃ is due to partially unquenched angular moments that had a different quantization axis from the spins.