-200 -150 -100 -50 0 50 100 150 200

-15

-10

-5

0

5

m [ 1

0-6 e

mu

]

U [V]

T = 50K T = 190K T = 290K

magnetic moment vs. electric field @ H=0

Magnetoelectric effect of Cr2O3 measured by SQUID-magnetometry

Cr2O3 moments can order in

two different 180° domains

Cr moments have opposite direction

with respect to the arrangement

of oxygen ligands

0 50 100 150 200 250 300 350

0

1

2

3

4

5

|| @

0H = 0T

|| @

0H = 0.5T

|| [ 1

0-8 e

mu

/ V

]

T [K]

z zm / Emagnetoelectric coefficient

3 m

-rhombohedral

corundum type

structure

-noncentrosymmetric magnetic point group

@T<TN=308K

Origin of the magneto-electric effect

Phenomenological theory, Rado (1961) M H@T>0 magn. field creates magnetization

M h E fictitious field, h, such that

h

E

Ansatz zh E S

~sublattice magnetization zS

0 2 40,0

0,1

0,2

0,3

0,4

T0 2 4

0,0

0,1

0,2

0,3

0,4

Sz>

T 0 1 20,00

0,03

0,06

S

z>T

20 B z z zH (g g) H S (D D) S

Microscopic view

why becomes α negative for T0 ?

what is the microscopic origin of h ?

Hamiltonian of a single Cr3+-Ion in the crystal field

20 B z z zH g H S D S

single ion terms no interaction with neighbors

E = 0

E = 0

where g

g EE

D

D EE

A

B

Cr3+-coordination

E shifts Cr3+-ions in field direction

O2-

BCr3+

u

u ACr3+,S=3/2

A shifted towards

B shifted towards

g, D

A

B

Interaction term ij ijJ J (E)exchange interaction

z zexchange ij i j

i,j

H J S S zexchange i i

i

H hS

wherez

i ij j z ijj j

h J S S J (E) mean field approximation

Interaction term for one ion on place A/B

z zH K S S E where ijj

K J (E)E

electric induced exchange and g-shift seem to dominate in Cr2O3