Magnetoelectric effect of Cr2O3 measured by SQUID-magnetometry magnetoelectric coefficient magnetic moment vs. electric field @ H=0 -rhombohedral corundum type structure -noncentrosymmetric magnetic point group @T<TN=308K  Cr2O3 moments can order in two different 180° domains Cr moments have opposite direction with respect to the arrangement of oxygen ligands

Origin of the magneto-electric effect  Phenomenological theory, Rado (1961) @T>0 magn. field creates magnetization fictitious field, h, such that Ansatz ~sublattice magnetization

E = 0 E = 0 Microscopic view A Cr3+- B  why becomes α negative for T0 ?  what is the microscopic origin of h ? Microscopic view  Hamiltonian of a single Cr3+-Ion in the crystal field single ion terms no interaction with neighbors A B Cr3+- coordination E = 0 E = 0 where

 A u u B A A B B O2- Cr3+,S=3/2 Cr3+  E shifts Cr3+-ions in field direction A B A shifted towards B shifted towards

 Interaction term exchange interaction where mean field approximation  Interaction term for one ion on place A/B where  electric induced exchange and g-shift seem to dominate in Cr2O3