<s>
Giant	B-General_Concept
magnetoresistance	I-General_Concept
(	O
GMR	B-General_Concept
)	O
is	O
a	O
quantum	O
mechanical	O
magnetoresistance	O
effect	O
observed	O
in	O
multilayers	O
composed	O
of	O
alternating	O
ferromagnetic	O
and	O
non-magnetic	O
conductive	O
layers	O
.	O
</s>
<s>
The	O
2007	O
Nobel	O
Prize	O
in	O
Physics	O
was	O
awarded	O
to	O
Albert	O
Fert	O
and	O
Peter	O
Grünberg	O
for	O
the	O
discovery	O
of	O
GMR	B-General_Concept
.	O
</s>
<s>
The	O
main	O
application	O
of	O
GMR	B-General_Concept
is	O
in	O
magnetic	O
field	O
sensors	O
,	O
which	O
are	O
used	O
to	O
read	O
data	O
in	O
hard	B-Device
disk	I-Device
drives	I-Device
,	O
biosensors	O
,	O
microelectromechanical	B-Architecture
systems	I-Architecture
(	O
MEMS	B-Architecture
)	O
and	O
other	O
devices	O
.	O
</s>
<s>
GMR	B-General_Concept
multilayer	O
structures	O
are	O
also	O
used	O
in	O
magnetoresistive	B-General_Concept
random-access	I-General_Concept
memory	I-General_Concept
(	O
MRAM	B-General_Concept
)	O
as	O
cells	O
that	O
store	O
one	O
bit	O
of	O
information	O
.	O
</s>
<s>
In	O
literature	O
,	O
the	O
term	O
giant	B-General_Concept
magnetoresistance	I-General_Concept
is	O
sometimes	O
confused	O
with	O
colossal	O
magnetoresistance	O
of	O
ferromagnetic	O
and	O
antiferromagnetic	O
semiconductors	O
,	O
which	O
is	O
not	O
related	O
to	O
a	O
multilayer	O
structure	O
.	O
</s>
<s>
The	O
term	O
"	O
giant	B-General_Concept
magnetoresistance	I-General_Concept
"	O
indicates	O
that	O
the	O
value	O
δH	O
for	O
multilayer	O
structures	O
significantly	O
exceeds	O
the	O
anisotropic	O
magnetoresistance	O
,	O
which	O
has	O
a	O
typical	O
value	O
within	O
a	O
few	O
percent	O
.	O
</s>
<s>
GMR	B-General_Concept
was	O
discovered	O
in	O
1988	O
independently	O
by	O
the	O
groups	O
of	O
Albert	O
Fert	O
of	O
the	O
University	O
of	O
Paris-Sud	O
,	O
France	O
,	O
and	O
Peter	O
Grünberg	O
of	O
Forschungszentrum	O
Jülich	O
,	O
Germany	O
.	O
</s>
<s>
The	O
enhancement	O
of	O
δH	O
became	O
possible	O
with	O
the	O
advent	O
of	O
sample	O
preparation	O
techniques	O
such	O
as	O
molecular	B-Algorithm
beam	I-Algorithm
epitaxy	I-Algorithm
,	O
which	O
allows	O
manufacturing	O
multilayer	O
thin	O
films	O
with	O
a	O
thickness	O
of	O
several	O
nanometers	O
.	O
</s>
<s>
The	O
GMR	B-General_Concept
discovery	O
work	O
was	O
carried	O
out	O
by	O
the	O
two	O
groups	O
on	O
slightly	O
different	O
samples	O
.	O
</s>
<s>
Electrical	O
resistance	O
changed	O
by	O
up	O
to	O
50%	O
with	O
the	O
external	O
magnetic	O
field	O
at	O
4.2	O
K	O
.	O
Fert	O
named	O
the	O
new	O
effect	O
giant	B-General_Concept
magnetoresistance	I-General_Concept
,	O
to	O
highlight	O
its	O
difference	O
with	O
the	O
anisotropic	O
magnetoresistance	O
.	O
</s>
<s>
The	O
theory	O
of	O
GMR	B-General_Concept
for	O
different	O
directions	O
of	O
the	O
current	O
was	O
developed	O
in	O
the	O
next	O
few	O
years	O
.	O
</s>
<s>
The	O
theory	O
of	O
the	O
GMR	B-General_Concept
for	O
the	O
current	O
perpendicular	O
to	O
the	O
layers	O
(	O
current	O
perpendicular	O
to	O
the	O
plane	O
or	O
CPP	O
geometry	O
)	O
,	O
known	O
as	O
the	O
Valet-Fert	O
theory	O
,	O
was	O
reported	O
in	O
1993	O
.	O
</s>
<s>
In	O
ferromagnets	O
,	O
the	O
dependence	O
of	O
electron-atom	O
scattering	O
on	O
the	O
orientation	O
of	O
their	O
magnetic	O
moments	O
is	O
related	O
to	O
the	O
filling	O
of	O
the	O
band	O
responsible	O
for	O
the	O
magnetic	O
properties	O
of	O
the	O
metal	O
,	O
e.g.	O
,	O
3d	O
band	O
for	O
iron	O
,	O
nickel	O
or	O
cobalt	B-Algorithm
.	O
</s>
<s>
The	O
hybridized	O
spd	O
band	O
has	O
a	O
high	O
density	O
of	O
states	O
,	O
which	O
results	O
in	O
stronger	O
scattering	O
and	O
thus	O
shorter	O
mean	B-Algorithm
free	I-Algorithm
path	I-Algorithm
λ	O
for	O
minority-spin	O
than	O
majority-spin	O
electrons	O
.	O
</s>
<s>
In	O
cobalt-doped	O
nickel	O
,	O
the	O
ratio	O
λ	O
↑	O
/λ	O
↓	O
can	O
reach	O
20	O
.	O
</s>
<s>
Electrons	O
"	O
remember	O
"	O
the	O
direction	O
of	O
spin	O
within	O
the	O
so-called	O
spin	O
relaxation	O
length	O
(	O
or	O
spin	O
diffusion	O
length	O
)	O
,	O
which	O
can	O
significantly	O
exceed	O
the	O
mean	B-Algorithm
free	I-Algorithm
path	I-Algorithm
.	O
</s>
<s>
A	O
combination	O
of	O
both	O
types	O
of	O
materials	O
can	O
result	O
in	O
a	O
so-called	O
inverse	O
GMR	B-General_Concept
effect	O
.	O
</s>
<s>
The	O
CPP	O
geometry	O
results	O
in	O
more	O
than	O
twice	O
higher	O
GMR	B-General_Concept
,	O
but	O
is	O
more	O
difficult	O
to	O
realize	O
in	O
practice	O
than	O
the	O
CIP	O
configuration	O
.	O
</s>
<s>
Applications	O
of	O
the	O
GMR	B-General_Concept
effect	O
require	O
dynamic	O
switching	O
between	O
the	O
parallel	O
and	O
antiparallel	O
magnetization	O
of	O
the	O
layers	O
in	O
a	O
superlattice	O
.	O
</s>
<s>
where	O
R0	O
is	O
the	O
resistance	O
of	O
ferromagnetic	O
superlattice	O
,	O
ΔR	O
is	O
the	O
GMR	B-General_Concept
increment	O
and	O
θ	O
is	O
the	O
angle	O
between	O
the	O
magnetizations	O
of	O
adjacent	O
layers	O
.	O
</s>
<s>
The	O
GMR	B-General_Concept
phenomenon	O
can	O
be	O
described	O
using	O
two	O
spin-related	O
conductivity	O
channels	O
corresponding	O
to	O
the	O
conduction	O
of	O
electrons	O
,	O
for	O
which	O
the	O
resistance	O
is	O
minimum	O
or	O
maximum	O
.	O
</s>
<s>
Therefore	O
,	O
the	O
equivalent	O
circuit	O
of	O
the	O
GMR	B-General_Concept
structure	O
consists	O
of	O
two	O
parallel	O
connections	O
corresponding	O
to	O
each	O
of	O
the	O
channels	O
.	O
</s>
<s>
Such	O
a	O
device	O
,	O
with	O
resistance	O
depending	O
on	O
the	O
orientation	O
of	O
electron	O
spin	O
,	O
is	O
called	O
a	O
spin	B-General_Concept
valve	I-General_Concept
.	O
</s>
<s>
In	O
1993	O
,	O
Thierry	O
Valet	O
and	O
Albert	O
Fert	O
presented	O
a	O
model	O
for	O
the	O
giant	B-General_Concept
magnetoresistance	I-General_Concept
in	O
the	O
CPP	O
geometry	O
,	O
based	O
on	O
the	O
Boltzmann	O
equations	O
.	O
</s>
<s>
Many	O
combinations	O
of	O
materials	O
exhibit	O
GMR	B-General_Concept
,	O
and	O
the	O
most	O
common	O
are	O
the	O
following	O
:	O
</s>
<s>
At	O
a	O
temperature	O
of	O
4.2	O
K	O
and	O
a	O
thickness	O
of	O
cobalt	B-Algorithm
layers	O
of	O
1.5nm	O
,	O
increasing	O
the	O
thickness	O
of	O
copper	O
layers	O
dCu	O
from	O
1	O
to	O
10nm	O
decreased	O
δH	O
from	O
80	O
to	O
10%	O
in	O
the	O
CIP	O
geometry	O
.	O
</s>
<s>
For	O
example	O
,	O
δH	O
up	O
to	O
40%	O
was	O
demonstrated	O
for	O
organic	O
layers	O
at	O
11	O
K	O
.	O
Graphene	O
spin	B-General_Concept
valves	I-General_Concept
of	O
various	O
designs	O
exhibited	O
δH	O
of	O
about	O
12%	O
at	O
7	O
K	O
and	O
10%	O
at	O
300	O
K	O
,	O
far	O
below	O
the	O
theoretical	O
limit	O
of	O
109%	O
.	O
</s>
<s>
The	O
GMR	B-General_Concept
effect	O
can	O
be	O
enhanced	O
by	O
spin	O
filters	O
that	O
select	O
electrons	O
with	O
a	O
certain	O
spin	O
orientation	O
;	O
they	O
are	O
made	O
of	O
metals	O
such	O
as	O
cobalt	B-Algorithm
.	O
</s>
<s>
where	O
ΔGSV	O
is	O
change	O
in	O
the	O
conductivity	O
of	O
the	O
spin	B-General_Concept
valve	I-General_Concept
without	O
the	O
filter	O
,	O
ΔGf	O
is	O
the	O
maximum	O
increase	O
in	O
conductivity	O
with	O
the	O
filter	O
,	O
and	O
β	O
is	O
a	O
parameter	O
of	O
the	O
filter	O
material	O
.	O
</s>
<s>
GMR	B-General_Concept
is	O
often	O
classed	O
by	O
the	O
type	O
of	O
devices	O
which	O
exhibit	O
the	O
effect	O
.	O
</s>
<s>
GMR	B-General_Concept
in	O
films	O
was	O
first	O
observed	O
by	O
Fert	O
and	O
Grünberg	O
in	O
a	O
study	O
of	O
superlattices	O
composed	O
of	O
ferromagnetic	O
and	O
non-magnetic	O
layers	O
.	O
</s>
<s>
Magnetic	O
layers	O
in	O
such	O
structures	O
interact	O
through	O
antiferromagnetic	O
coupling	O
,	O
which	O
results	O
in	O
the	O
oscillating	O
dependence	O
of	O
the	O
GMR	B-General_Concept
on	O
the	O
thickness	O
of	O
the	O
non-magnetic	O
layer	O
.	O
</s>
<s>
In	O
the	O
first	O
magnetic	O
field	O
sensors	O
using	O
antiferromagnetic	O
superlattices	O
,	O
the	O
saturation	O
field	O
was	O
very	O
large	O
,	O
up	O
to	O
tens	O
of	O
thousands	O
of	O
oersteds	O
,	O
due	O
to	O
the	O
strong	O
antiferromagnetic	O
interaction	O
between	O
their	O
layers	O
(	O
made	O
of	O
chromium	O
,	O
iron	O
or	O
cobalt	B-Algorithm
)	O
and	O
the	O
strong	O
anisotropy	O
fields	O
in	O
them	O
.	O
</s>
<s>
In	O
the	O
most	O
successful	O
spin	B-General_Concept
valves	I-General_Concept
the	O
GMR	B-General_Concept
effect	O
originates	O
from	O
exchange	O
bias	O
.	O
</s>
<s>
The	O
main	O
difference	O
of	O
these	O
spin	B-General_Concept
valves	I-General_Concept
from	O
other	O
multilayer	O
GMR	B-General_Concept
devices	O
is	O
the	O
monotonic	O
dependence	O
of	O
the	O
amplitude	O
of	O
the	O
effect	O
on	O
the	O
thickness	O
dN	O
of	O
the	O
non-magnetic	O
layers	O
:	O
</s>
<s>
where	O
δH0	O
is	O
a	O
normalization	O
constant	O
,	O
λN	O
is	O
the	O
mean	B-Algorithm
free	I-Algorithm
path	I-Algorithm
of	O
electrons	O
in	O
the	O
non-magnetic	O
material	O
,	O
d0	O
is	O
effective	O
thickness	O
that	O
includes	O
interaction	O
between	O
layers	O
.	O
</s>
<s>
GMR	B-General_Concept
can	O
also	O
be	O
observed	O
in	O
the	O
absence	O
of	O
antiferromagnetic	O
coupling	O
layers	O
.	O
</s>
<s>
In	O
this	O
case	O
,	O
the	O
magnetoresistance	O
results	O
from	O
the	O
differences	O
in	O
the	O
coercive	O
forces	O
(	O
for	O
example	O
,	O
it	O
is	O
smaller	O
for	O
permalloy	O
than	O
cobalt	B-Algorithm
)	O
.	O
</s>
<s>
The	O
existence	O
of	O
these	O
structures	O
means	O
that	O
GMR	B-General_Concept
does	O
not	O
require	O
interlayer	O
coupling	O
,	O
and	O
can	O
originate	O
from	O
a	O
distribution	O
of	O
the	O
magnetic	O
moments	O
that	O
can	O
be	O
controlled	O
by	O
an	O
external	O
field	O
.	O
</s>
<s>
In	O
the	O
inverse	O
GMR	B-General_Concept
,	O
the	O
resistance	O
is	O
minimum	O
for	O
the	O
antiparallel	O
orientation	O
of	O
the	O
magnetization	O
in	O
the	O
layers	O
.	O
</s>
<s>
Inverse	O
GMR	B-General_Concept
is	O
observed	O
when	O
the	O
magnetic	O
layers	O
are	O
composed	O
of	O
different	O
materials	O
,	O
such	O
as	O
NiCr/Cu/Co/Cu	O
.	O
</s>
<s>
If	O
the	O
NiCr	O
layer	O
is	O
not	O
too	O
thin	O
,	O
its	O
contribution	O
may	O
exceed	O
that	O
of	O
the	O
Co	O
layer	O
,	O
resulting	O
in	O
inverse	O
GMR	B-General_Concept
.	O
</s>
<s>
Note	O
that	O
the	O
GMR	B-General_Concept
inversion	O
depends	O
on	O
the	O
sign	O
of	O
the	O
product	O
of	O
the	O
coefficients	O
β	O
in	O
adjacent	O
ferromagnetic	O
layers	O
,	O
but	O
not	O
on	O
the	O
signs	O
of	O
individual	O
coefficients	O
.	O
</s>
<s>
Inverse	O
GMR	B-General_Concept
is	O
also	O
observed	O
if	O
NiCr	O
alloy	O
is	O
replaced	O
by	O
vanadium-doped	O
nickel	O
,	O
but	O
not	O
for	O
doping	O
of	O
nickel	O
with	O
iron	O
,	O
cobalt	B-Algorithm
,	O
manganese	O
,	O
gold	O
or	O
copper	O
.	O
</s>
<s>
GMR	B-General_Concept
in	O
granular	O
alloys	O
of	O
ferromagnetic	O
and	O
non-magnetic	O
metals	O
was	O
discovered	O
in	O
1992	O
and	O
subsequently	O
explained	O
by	O
the	O
spin-dependent	O
scattering	O
of	O
charge	O
carriers	O
at	O
the	O
surface	O
and	O
in	O
the	O
bulk	O
of	O
the	O
grains	O
.	O
</s>
<s>
A	O
necessary	O
condition	O
for	O
the	O
GMR	B-General_Concept
effect	O
in	O
such	O
structures	O
is	O
poor	O
mutual	O
solubility	O
in	O
its	O
components	O
(	O
e.g.	O
,	O
cobalt	B-Algorithm
and	O
copper	O
)	O
.	O
</s>
<s>
They	O
can	O
also	O
exhibit	O
inverse	O
GMR	B-General_Concept
.	O
</s>
<s>
One	O
of	O
the	O
main	O
applications	O
of	O
GMR	B-General_Concept
materials	O
is	O
in	O
magnetic	O
field	O
sensors	O
,	O
e.g.	O
,	O
in	O
hard	B-Device
disk	I-Device
drives	I-Device
and	O
biosensors	O
,	O
as	O
well	O
as	O
detectors	O
of	O
oscillations	O
in	O
MEMS	B-Architecture
.	O
</s>
<s>
A	O
typical	O
GMR-based	O
sensor	O
consists	O
of	O
seven	O
layers	O
:	O
</s>
<s>
In	O
the	O
sensing	O
layer	O
,	O
magnetization	O
can	O
be	O
reoriented	O
by	O
the	O
external	O
magnetic	O
field	O
;	O
it	O
is	O
typically	O
made	O
of	O
NiFe	O
or	O
cobalt	B-Algorithm
alloys	O
.	O
</s>
<s>
The	O
fixed	O
layer	O
is	O
made	O
of	O
a	O
magnetic	O
material	O
such	O
as	O
cobalt	B-Algorithm
.	O
</s>
<s>
Spin	B-General_Concept
valves	I-General_Concept
may	O
exhibit	O
anisotropic	O
magnetoresistance	O
,	O
which	O
leads	O
to	O
an	O
asymmetry	O
in	O
the	O
sensitivity	O
curve	O
.	O
</s>
<s>
In	O
hard	B-Device
disk	I-Device
drives	I-Device
(	O
HDDs	O
)	O
,	O
information	O
is	O
encoded	O
using	O
magnetic	O
domains	O
,	O
and	O
a	O
change	O
in	O
the	O
direction	O
of	O
their	O
magnetization	O
is	O
associated	O
with	O
the	O
logical	O
level	O
1	O
while	O
no	O
change	O
represents	O
a	O
logical	O
0	O
.	O
</s>
<s>
A	O
cell	O
of	O
magnetoresistive	B-General_Concept
random-access	I-General_Concept
memory	I-General_Concept
(	O
MRAM	B-General_Concept
)	O
has	O
a	O
structure	O
similar	O
to	O
the	O
spin-valve	B-General_Concept
sensor	O
.	O
</s>
<s>
In	O
a	O
typical	O
GMR-based	O
storage	O
unit	O
,	O
a	O
CIP	O
structure	O
is	O
located	O
between	O
two	O
wires	O
oriented	O
perpendicular	O
to	O
each	O
other	O
.	O
</s>
<s>
Pulses	O
of	O
electric	O
current	O
passing	O
through	O
the	O
lines	O
generate	O
a	O
vortex	O
magnetic	O
field	O
,	O
which	O
affects	O
the	O
GMR	B-General_Concept
structure	O
.	O
</s>
<s>
In	O
the	O
GMR	B-General_Concept
structure	O
,	O
the	O
magnetization	O
is	O
oriented	O
along	O
the	O
line	O
.	O
</s>
<s>
With	O
the	O
simultaneous	O
passage	O
of	O
pulses	O
along	O
the	O
row	O
and	O
column	O
lines	O
,	O
of	O
the	O
total	O
magnetic	O
field	O
at	O
the	O
location	O
of	O
the	O
GMR	B-General_Concept
structure	O
will	O
be	O
directed	O
at	O
an	O
acute	O
angle	O
with	O
respect	O
to	O
one	O
point	O
and	O
an	O
obtuse	O
to	O
others	O
.	O
</s>
<s>
Tunnel	O
magnetoresistance	O
(	O
TMR	O
)	O
is	O
an	O
extension	O
of	O
spin-valve	B-General_Concept
GMR	B-General_Concept
,	O
in	O
which	O
the	O
electrons	O
travel	O
with	O
their	O
spins	O
oriented	O
perpendicularly	O
to	O
the	O
layers	O
across	O
a	O
thin	O
insulating	O
tunnel	O
barrier	O
(	O
replacing	O
the	O
non-ferromagnetic	O
spacer	O
)	O
.	O
</s>
<s>
TMR	O
has	O
now	O
replaced	O
GMR	B-General_Concept
in	O
MRAMs	B-General_Concept
and	O
disk	B-Device
drives	I-Device
,	O
in	O
particular	O
for	O
high	O
area	O
densities	O
and	O
perpendicular	O
recording	O
.	O
</s>
<s>
A	O
Wheatstone	O
bridge	O
of	O
four	O
identical	O
GMR	B-General_Concept
devices	O
is	O
insensitive	O
to	O
a	O
uniform	O
magnetic	O
field	O
and	O
reacts	O
only	O
when	O
the	O
field	O
directions	O
are	O
antiparallel	O
in	O
the	O
neighboring	O
arms	O
of	O
the	O
bridge	O
.	O
</s>
