1. Magnetoelectric effect of Cr2O3 measured by SQUID-magnetometry
magnetoelectric coefficient
magnetic moment vs. electric 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

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

3. 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

4.  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

5.  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