94
3 Giant Magnetoresistance (GMR)
ρ =
m
ne 2 τ
(3.10)
ρ is clearly found to depend on the electron density, n and on the mean free
time, τ. It is straightforward to understand that τ should be inversely proportional
to the scattering probability. In case of magnetic multilayers films, probability of
scattering is governed by the following two factors: (i) strength of the potential
related to scattering and (ii) density of states available for scattering at the vicinity
of E F . The first factor is governed by the interfacial spin-dependent scattering in
multilayers structure. The second factor results in bulk spin-dependent scattering,
which is basically the well-known Mott mechanism.
Bulk spin-dependent scattering
Let us first focus on the bulk spin-dependent scattering process. If we consider, ρ FM =
total resistivity of the bulk ferromagnetic materials, thus considering two independent
spin channels, we can write
1
ρ F M
=
1
ρ
↑
F M
+
1
ρ
↓
F M
(3.11)
where ρ
↑
F M =
2ρ F M
1+β
, ρ
↓
F M =
2ρ F M
1−β
and β =
ρ
↓
F M −ρ
↑
F M
ρ
↓
F M +ρ
↑
F M
= bulk scattering asymmetry.
Interfacial spin-dependent scattering
Magnetic multilayers consist of thin interfacial layers, which constitute spindependent potential barriers at the interface of a ferromagnet and a non-magnet. As a
result, the corresponding resistivity of the concerned interface is spin-dependent.
Hence, similar to the bulk spin-dependent scattering, an interfacial scattering
asymmetry, γ can also be introduced, which is defined by
ρ
↑
F M−N M =
2ρ F N−N M
1 + γ
, ρ
↓
F M−N M =
2ρ F N−N M
1 − γ
where ρ FM–NM is the total resistivity of the interfacial layer, ρ
↑/↓
F M−N M = interfacial
resistivity corresponding to ↑/↓ spin channel.
3.7.1.1 Periodic Superlattice Structure
Before going into the details of the calculation of GMR, let us introduce the concept
of Periodic Superlattice. Actually, GMR devices are nothing but an extension of
spin valves. The idea behind the forming of a ‘spin-valve-superlattice structure’, as
depicted in Fig. 3.12, is to accrue any advantage by increasing the number of layers
in the basic unit cell of a spin valve, while keeping the width of each layer a few
nanometres thick. A superlattice structure, which is periodic in nature, composed of
3 Giant Magnetoresistance (GMR)
ρ =
m
ne 2 τ
(3.10)
ρ is clearly found to depend on the electron density, n and on the mean free
time, τ. It is straightforward to understand that τ should be inversely proportional
to the scattering probability. In case of magnetic multilayers films, probability of
scattering is governed by the following two factors: (i) strength of the potential
related to scattering and (ii) density of states available for scattering at the vicinity
of E F . The first factor is governed by the interfacial spin-dependent scattering in
multilayers structure. The second factor results in bulk spin-dependent scattering,
which is basically the well-known Mott mechanism.
Bulk spin-dependent scattering
Let us first focus on the bulk spin-dependent scattering process. If we consider, ρ FM =
total resistivity of the bulk ferromagnetic materials, thus considering two independent
spin channels, we can write
1
ρ F M
=
1
ρ
↑
F M
+
1
ρ
↓
F M
(3.11)
where ρ
↑
F M =
2ρ F M
1+β
, ρ
↓
F M =
2ρ F M
1−β
and β =
ρ
↓
F M −ρ
↑
F M
ρ
↓
F M +ρ
↑
F M
= bulk scattering asymmetry.
Interfacial spin-dependent scattering
Magnetic multilayers consist of thin interfacial layers, which constitute spindependent potential barriers at the interface of a ferromagnet and a non-magnet. As a
result, the corresponding resistivity of the concerned interface is spin-dependent.
Hence, similar to the bulk spin-dependent scattering, an interfacial scattering
asymmetry, γ can also be introduced, which is defined by
ρ
↑
F M−N M =
2ρ F N−N M
1 + γ
, ρ
↓
F M−N M =
2ρ F N−N M
1 − γ
where ρ FM–NM is the total resistivity of the interfacial layer, ρ
↑/↓
F M−N M = interfacial
resistivity corresponding to ↑/↓ spin channel.
3.7.1.1 Periodic Superlattice Structure
Before going into the details of the calculation of GMR, let us introduce the concept
of Periodic Superlattice. Actually, GMR devices are nothing but an extension of
spin valves. The idea behind the forming of a ‘spin-valve-superlattice structure’, as
depicted in Fig. 3.12, is to accrue any advantage by increasing the number of layers
in the basic unit cell of a spin valve, while keeping the width of each layer a few
nanometres thick. A superlattice structure, which is periodic in nature, composed of