<s>
Superexchange	B-General_Concept
,	O
or	O
Kramers	O
–	O
Anderson	O
superexchange	B-General_Concept
,	O
is	O
the	O
strong	O
(	O
usually	O
)	O
antiferromagnetic	O
coupling	O
between	O
two	O
next-to-nearest	O
neighbour	O
cations	O
through	O
a	O
non-magnetic	O
anion	O
.	O
</s>
<s>
Superexchange	B-General_Concept
is	O
a	O
result	O
of	O
the	O
electrons	O
having	O
come	O
from	O
the	O
same	O
donor	O
atom	O
and	O
being	O
coupled	O
with	O
the	O
receiving	O
ions	O
 '	O
spins	O
.	O
</s>
<s>
Superexchange	B-General_Concept
was	O
proposed	O
by	O
Hendrik	O
Kramers	O
in	O
1934	O
,	O
when	O
he	O
noticed	O
that	O
in	O
crystals	O
like	O
MnO	O
,	O
there	O
are	O
Mn	O
atoms	O
that	O
interact	O
with	O
one	O
another	O
despite	O
having	O
nonmagnetic	O
oxygen	O
atoms	O
between	O
them	O
.	O
</s>
<s>
O2−	O
)	O
,	O
the	O
superexchange	B-General_Concept
will	O
be	O
strongly	O
anti-ferromagnetic	O
while	O
the	O
coupling	O
between	O
an	O
ion	O
with	O
a	O
filled	O
orbital	O
and	O
one	O
with	O
a	O
half-filled	O
orbital	O
will	O
be	O
ferromagnetic	O
.	O
</s>
<s>
Complications	O
begin	O
to	O
arise	O
in	O
various	O
situations	O
:	O
1	O
)	O
when	O
direct	O
exchange	O
and	O
superexchange	B-General_Concept
mechanisms	O
compete	O
with	O
one	O
another	O
;	O
2	O
)	O
when	O
the	O
cation	O
–	O
anion	O
–	O
cation	O
bond	O
angle	O
deviates	O
away	O
from	O
180°	O
;	O
3	O
)	O
when	O
the	O
electron	O
occupancy	O
of	O
the	O
orbitals	O
is	O
non-static	O
,	O
or	O
dynamical	O
;	O
and	O
4	O
)	O
when	O
spin	O
–	O
orbit	O
coupling	O
becomes	O
important	O
.	O
</s>
<s>
It	O
differs	O
from	O
superexchange	B-General_Concept
in	O
the	O
following	O
manner	O
:	O
in	O
superexchange	B-General_Concept
,	O
the	O
occupancy	O
of	O
the	O
d-shell	O
of	O
the	O
two	O
metal	O
ions	O
is	O
the	O
same	O
or	O
differs	O
by	O
two	O
,	O
and	O
the	O
electrons	O
are	O
localized	O
.	O
</s>
<s>
where	O
tMn	O
,	O
O	O
is	O
the	O
so-called	O
hopping	O
energy	O
between	O
a	O
Mn	O
3d	O
and	O
the	O
oxygen	O
p	O
orbitals	O
,	O
while	O
U	O
is	O
a	O
so-called	O
Hubbard	B-Algorithm
energy	O
for	O
Mn	O
.	O
</s>
