Spin Transfer Torque Magnetoresistive Random Access Memory
51
zation. The resultant angular dependence of AMR can be expressed in the following
form [44, 45]:
ρ(θ) = ρ ⊥ + (ρ || − ρ ⊥ ) cos
2
θ,
(1)
where ρ is the resistivity, θ is the angle between M and the current and the subscripts
|| and ⊥ refers to the parallel and perpendicular component respectively. Therefore,
the resistance is at its maximum when the electric current is aligned with the magnetization M, which can be controlled using an externally applied magnetic field H ext .
Here, the magnetoresistive coefficient
ρ || −ρ ⊥
ρ
=
ρ
ρ
is the key figure of merit to
evaluate the AMR effect. The relatively large magnetoresistive coefficient and small
magneostriction effect for Ni 81 Fe 19 leads to a shift from inductive head technology
towards MR-based read heads [46, 47, 48]. Note that in the absence of H ext , the
average resistivity of a demagnetized sample would be ρ = ρ average =
1
3
ρ || +
2
3
ρ ⊥ .
For Giant Magnetoresistance (GMR) effect, we begin by considering the density
of states (DOS) of a single ferromagnetic electrode. It is well known from quantum
mechanics that the 3d-orbital bands in ferromagnetic materials (e.g. Fe, Co, Ni) are
exchange-split, resulting in non-zero magnetization as the two bands are not filled
equally at the Fermi energy level. We denote electrons with spin parallel to the overall
magnetization as majority carriers, also known as spin-up electrons, while electrons
with their spin anti-parallel to the overall magnetization as minority carriers, or spindown electrons. Due to the heavier effective mass of 3d electrons that are more
tightly bounded to the nucleus, electrical conductivity is mainly due to the 4s electrons. Scattering of electrons from 4s-3d states will result in larger resistivity, which
will be less common in the majority channel due to the lack of available DOS. The
two-current model proposed by Mott can then provide a qualitatively understanding
of spin-dependent conduction in ferromagnetic materials, which consider a ferromagnetic material having two independent current channels parallel to each other
[49]. Assuming no spin-flip processes, the resistivity ρ for a ferromagnetic measured
at a temperature lower than the Curie temperature T c can be expressed as:
1
ρ
=
1
ρ ↑ +
1
ρ ↓ ,
(2)
where the superscripts ↑ and ↓ refers to the majority and minority carriers, respectively. Due to the difference in resistivity experienced by the majority and minority
carriers, a net balance of majority charge carriers will prevail, resulting in a spin
polarized current.
If the model is extended to the scenario where an ultra-thin non-magnetic metal
is sandwiched between two ferromagnetic electrodes, two resistance states can be
obtained depending on the magnetization orientation of the two ferromagnetic electrodes as shown in Fig. 4. Since the electrons will spend half of the time on average
within each ferromagnetic electrode, the resistance is split into two components,
where r and R refers to the resistance encountered by the itinerant electrons in the
51
zation. The resultant angular dependence of AMR can be expressed in the following
form [44, 45]:
ρ(θ) = ρ ⊥ + (ρ || − ρ ⊥ ) cos
2
θ,
(1)
where ρ is the resistivity, θ is the angle between M and the current and the subscripts
|| and ⊥ refers to the parallel and perpendicular component respectively. Therefore,
the resistance is at its maximum when the electric current is aligned with the magnetization M, which can be controlled using an externally applied magnetic field H ext .
Here, the magnetoresistive coefficient
ρ || −ρ ⊥
ρ
=
ρ
ρ
is the key figure of merit to
evaluate the AMR effect. The relatively large magnetoresistive coefficient and small
magneostriction effect for Ni 81 Fe 19 leads to a shift from inductive head technology
towards MR-based read heads [46, 47, 48]. Note that in the absence of H ext , the
average resistivity of a demagnetized sample would be ρ = ρ average =
1
3
ρ || +
2
3
ρ ⊥ .
For Giant Magnetoresistance (GMR) effect, we begin by considering the density
of states (DOS) of a single ferromagnetic electrode. It is well known from quantum
mechanics that the 3d-orbital bands in ferromagnetic materials (e.g. Fe, Co, Ni) are
exchange-split, resulting in non-zero magnetization as the two bands are not filled
equally at the Fermi energy level. We denote electrons with spin parallel to the overall
magnetization as majority carriers, also known as spin-up electrons, while electrons
with their spin anti-parallel to the overall magnetization as minority carriers, or spindown electrons. Due to the heavier effective mass of 3d electrons that are more
tightly bounded to the nucleus, electrical conductivity is mainly due to the 4s electrons. Scattering of electrons from 4s-3d states will result in larger resistivity, which
will be less common in the majority channel due to the lack of available DOS. The
two-current model proposed by Mott can then provide a qualitatively understanding
of spin-dependent conduction in ferromagnetic materials, which consider a ferromagnetic material having two independent current channels parallel to each other
[49]. Assuming no spin-flip processes, the resistivity ρ for a ferromagnetic measured
at a temperature lower than the Curie temperature T c can be expressed as:
1
ρ
=
1
ρ ↑ +
1
ρ ↓ ,
(2)
where the superscripts ↑ and ↓ refers to the majority and minority carriers, respectively. Due to the difference in resistivity experienced by the majority and minority
carriers, a net balance of majority charge carriers will prevail, resulting in a spin
polarized current.
If the model is extended to the scenario where an ultra-thin non-magnetic metal
is sandwiched between two ferromagnetic electrodes, two resistance states can be
obtained depending on the magnetization orientation of the two ferromagnetic electrodes as shown in Fig. 4. Since the electrons will spend half of the time on average
within each ferromagnetic electrode, the resistance is split into two components,
where r and R refers to the resistance encountered by the itinerant electrons in the