<s>
In	O
Physics	O
,	O
antisymmetric	B-General_Concept
exchange	I-General_Concept
,	O
also	O
known	O
as	O
the	O
Dzyaloshinskii	B-General_Concept
–	I-General_Concept
Moriya	I-General_Concept
interaction	I-General_Concept
(	O
DMI	O
)	O
,	O
is	O
a	O
contribution	O
to	O
the	O
total	O
magnetic	O
exchange	B-General_Concept
interaction	I-General_Concept
between	O
two	O
neighboring	O
magnetic	O
spins	O
,	O
and	O
.	O
</s>
<s>
In	O
magnetically	O
ordered	O
systems	O
,	O
it	O
favors	O
a	O
spin	B-General_Concept
canting	I-General_Concept
of	O
otherwise	O
parallel	O
or	O
antiparallel	O
aligned	O
magnetic	O
moments	O
and	O
thus	O
,	O
is	O
a	O
source	O
of	O
weak	O
ferromagnetic	O
behavior	O
in	O
an	O
antiferromagnet	O
.	O
</s>
<s>
The	O
discovery	O
of	O
antisymmetric	B-General_Concept
exchange	I-General_Concept
originated	O
in	O
the	O
early	O
20th	O
century	O
from	O
the	O
controversial	O
observation	O
of	O
weak	O
ferromagnetism	O
in	O
typically	O
antiferromagnetic	O
-FeO	O
crystals	O
.	O
</s>
<s>
In	O
1960	O
,	O
Toru	O
Moriya	O
identified	O
the	O
spin-orbit	O
coupling	O
as	O
the	O
microscopic	O
mechanism	O
of	O
the	O
antisymmetric	B-General_Concept
exchange	I-General_Concept
interaction	O
.	O
</s>
<s>
Moriya	O
referred	O
to	O
this	O
phenomenon	O
specifically	O
as	O
the	O
"	O
antisymmetric	O
part	O
of	O
the	O
anisotropic	O
superexchange	B-General_Concept
interaction.	O
"	O
</s>
<s>
The	O
simplified	O
naming	O
of	O
this	O
phenomenon	O
occurred	O
in	O
1962	O
,	O
when	O
D	O
.	O
Treves	O
and	O
S	O
.	O
Alexander	O
of	O
Bell	O
Telephone	O
Laboratories	O
simply	O
referred	O
to	O
the	O
interaction	O
as	O
antisymmetric	B-General_Concept
exchange	I-General_Concept
.	O
</s>
<s>
Because	O
of	O
their	O
seminal	O
contributions	O
to	O
the	O
field	O
,	O
antisymmetric	B-General_Concept
exchange	I-General_Concept
is	O
sometimes	O
referred	O
to	O
as	O
the	O
Dzyaloshinskii	B-General_Concept
–	I-General_Concept
Moriya	I-General_Concept
interaction	I-General_Concept
.	O
</s>
<s>
The	O
functional	O
form	O
of	O
the	O
DMI	O
can	O
be	O
obtained	O
through	O
a	O
second-order	O
perturbative	O
analysis	O
of	O
the	O
spin-orbit	O
coupling	O
interaction	O
,	O
between	O
ions	O
in	O
Anderson	O
's	O
superexchange	B-General_Concept
formalism	O
.	O
</s>
<s>
Considering	O
the	O
case	O
that	O
the	O
magnetic	O
interaction	O
between	O
two	O
neighboring	O
ions	O
is	O
transferred	O
via	O
a	O
single	O
third	O
ion	O
(	O
ligand	O
)	O
by	O
the	O
superexchange	B-General_Concept
mechanism	O
(	O
see	O
Figure	O
)	O
,	O
the	O
orientation	O
of	O
is	O
obtained	O
by	O
the	O
simple	O
relation	O
.	O
</s>
<s>
The	O
Dzyaloshinskii	B-General_Concept
–	I-General_Concept
Moriya	I-General_Concept
interaction	I-General_Concept
has	O
proven	O
difficult	O
to	O
experimentally	O
measure	O
directly	O
due	O
to	O
its	O
typically	O
weak	O
effects	O
and	O
similarity	O
to	O
other	O
magnetoelectric	O
effects	O
in	O
bulk	O
materials	O
.	O
</s>
<s>
Attempts	O
to	O
quantify	O
the	O
DMI	O
vector	O
have	O
utilized	O
X-ray	O
diffraction	O
interference	O
,	O
Brillouin	B-Algorithm
scattering	I-Algorithm
,	O
electron	O
spin	O
resonance	O
,	O
and	O
neutron	O
scattering	O
.	O
</s>
<s>
It	O
is	O
thus	O
the	O
combination	O
of	O
the	O
distribution	O
of	O
ion	O
spins	O
,	O
the	O
misalignment	O
of	O
the	O
total	O
spin	O
vector	O
,	O
and	O
the	O
resulting	O
antisymmetry	O
of	O
the	O
unit	O
cell	O
that	O
gives	O
rise	O
to	O
the	O
antisymmetric	B-General_Concept
exchange	I-General_Concept
phenomenon	O
seen	O
in	O
these	O
crystal	O
structures	O
.	O
</s>
<s>
They	O
exist	O
in	O
spiral	O
or	O
hedgehog	O
configurations	O
that	O
are	O
stabilized	O
by	O
the	O
Dzyaloshinskii-Moriya	B-General_Concept
interaction	I-General_Concept
.	O
</s>
<s>
Antisymmetric	B-General_Concept
exchange	I-General_Concept
is	O
of	O
importance	O
for	O
the	O
understanding	O
of	O
magnetism	O
induced	O
electric	O
polarization	O
in	O
a	O
recently	O
discovered	O
class	O
of	O
multiferroics	O
.	O
</s>
