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In-Depth Information
2.1 Magnetoresistance
The MTJs are conductive to electrical current. Interestingly their electrical resis-
tance across the free and fixed layer is dependent on the relative magnetization
angle
θ
between the two layers. The resistance, which is the inverse of the con-
ductance
G
(
θ
), can be calculated from Eq.
4
.
G
(
θ
)=
1
2
(
G
P
+
G
AP
)+
1
2
(
G
P
+
G
AP
)
· cos θ
(4)
where,
G
P
and
G
AP
are the conductances of the MTJ for
θ
=0
ⓦ
and
θ
= 180
ⓦ
respectively. The
θ
=0
ⓦ
is also known as the parallel state and is commonly used
in STT-MRAM to represent logic 0. The
θ
= 180
ⓦ
is known as the antiparallel
state and is used to represent logic 1 (see Fig.
1
b). Note,
G
p
>G
AP
.Fora
quantum mechanical explanation of the angular dependence of MTJ resistance,
readers are encouraged to refer [
8
,
9
]. In STT-MRAM the MTJ resistance is used
to read its state.
It should be evident that greater the difference between the resistances of 0
and 1 state, the easier it is to read the MTJ. A parameter that represents this
resistive difference is the Magnetoresistance (MR) defined by Eq.
5
. This MR is
an important parameter since it defines the ease and reliability for MTJ read.
Higher the MR, higher is the read distinguishibility and lower are the read based
errors for MTJs [
3
].
MR
=
G
P
−
G
AP
G
AP
(5)
Before we move on to the next property, we would like to briefly men-
tion that the MR phenomenon was discovered as early as 1856 [
10
]. However,
it was not until 1975 that Julliere in his seminal work defined the first MR
model on a Fe/Ge/Co multilayer [
11
]. Since then various material combinations
and fabrication steps has been explored to improve the MR at room temper-
ature. Today a MR as high as 410 % is reported at room temperature with a
Co(001)/MgO(001)/Co(001) material stack [
12
]. Interested readers may refer
to [
9
] for a chronological description of MR developments.
2.2 Spin Transfer Torque
When spin conduction electrons interact with the localized magnetic moment of
a ferromagnet, they transfer a part of their angular momentum to the magnet.
This results in a torque on the magnet. When this torque is suciently strong,
it can excite the magnetization in the material. This torque is called the spin
transfer torque and is dependent on the magnitude and direction of the current.
When electrons flow from the fixed to the free layer within the MTJ, the spin
transfer torque and the damping act together to switch the free layer to logic
0 state (see Fig.
2
). For electrons flowing in the reverse direction, the torque
and the damping acts against each other. When the torque exceeds a critical
magnitude, the MTJ switches to logic 1 state (see Fig.
2
).
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