90
3 Giant Magnetoresistance (GMR)
multilayer. In this case, the conduction electrons could be subjected to spin–
orbit interaction due to such impurities. Consequently, spin orientations of these
electrons, scattered by such impurity, may be reversed/changed.
3.5.2 How Does Mott Model Describe GMR?
In an attempt to explain GMR, there are two main points, mentioned below, as
proposed by Mott:
(i) As per general consensus, in ferromagnetic metals the probability of spinconserved spin-dependent scattering process is higher compared to that of
spin-flip scattering process. Consequently, the identity of up-spin and downspin electrons would be retained and would not get mixed over long distances.
Hence, electrical conductivity in ferromagnetic metals takes place in parallel
in two largely independent conduction channels, namely, up-spin and downspin channels. It is well understood that the up- or down-spin orientations of
electrons are defined as per projection of the spins along the quantization axis.
(ii) Ferromagnetic metals have exchange-splitting of its band structure, i.e., spindependent band structure, where at the Fermi energy the density of states are
not the same for the two spin species of electrons. Quite intuitively, scattering
rates are expected to be proportional to the density of states. Therefore, in
ferromagnetic metals the up-spin and down-spin electrons scattering rates are
quite different, irrespective of the nature of the scattering centres. Hence, the
resistivities corresponding to the up-spin
ρ
↑
and down-spin
ρ
↓
electrons
are different, i.e., ρ
↑
= ρ
↓ .
3.5.3 Explanation of Negative MR of Ferromagnetic
Transition Metal, Considering Spin Scattering
Mechanisms
As a prelude, let us explain the negative MR of any ferromagnetic transition metal,
considering the above discussed spin scattering mechanisms. At temperatures very
less than ferromagnetic Curie temperature, i.e., T T C , spin-flip scattering is not
supposed to be a major spin scattering mechanism. As already mentioned, in case of
a ferromagnet the conduction phenomenon can be nicely approximated by the twocurrent model, where currents set up by the ↑ and ↓ spin electrons can be considered
to be an independent process. Now, in the presence of magnetic field, which decides
the quantization axis of the ferromagnet, ↓ spin electrons are scattered more strongly
than the ↑ spin electrons. This results in different resistivity for each spin state, which
in turn leads to negative MR in ferromagnetic metal. At high temperatures, the spinflip scattering of conduction electrons takes place due to collisions with spin waves.
This in turn leads to spin mixing, which diminishes the distinction between the two
3 Giant Magnetoresistance (GMR)
multilayer. In this case, the conduction electrons could be subjected to spin–
orbit interaction due to such impurities. Consequently, spin orientations of these
electrons, scattered by such impurity, may be reversed/changed.
3.5.2 How Does Mott Model Describe GMR?
In an attempt to explain GMR, there are two main points, mentioned below, as
proposed by Mott:
(i) As per general consensus, in ferromagnetic metals the probability of spinconserved spin-dependent scattering process is higher compared to that of
spin-flip scattering process. Consequently, the identity of up-spin and downspin electrons would be retained and would not get mixed over long distances.
Hence, electrical conductivity in ferromagnetic metals takes place in parallel
in two largely independent conduction channels, namely, up-spin and downspin channels. It is well understood that the up- or down-spin orientations of
electrons are defined as per projection of the spins along the quantization axis.
(ii) Ferromagnetic metals have exchange-splitting of its band structure, i.e., spindependent band structure, where at the Fermi energy the density of states are
not the same for the two spin species of electrons. Quite intuitively, scattering
rates are expected to be proportional to the density of states. Therefore, in
ferromagnetic metals the up-spin and down-spin electrons scattering rates are
quite different, irrespective of the nature of the scattering centres. Hence, the
resistivities corresponding to the up-spin
ρ
↑
and down-spin
ρ
↓
electrons
are different, i.e., ρ
↑
= ρ
↓ .
3.5.3 Explanation of Negative MR of Ferromagnetic
Transition Metal, Considering Spin Scattering
Mechanisms
As a prelude, let us explain the negative MR of any ferromagnetic transition metal,
considering the above discussed spin scattering mechanisms. At temperatures very
less than ferromagnetic Curie temperature, i.e., T T C , spin-flip scattering is not
supposed to be a major spin scattering mechanism. As already mentioned, in case of
a ferromagnet the conduction phenomenon can be nicely approximated by the twocurrent model, where currents set up by the ↑ and ↓ spin electrons can be considered
to be an independent process. Now, in the presence of magnetic field, which decides
the quantization axis of the ferromagnet, ↓ spin electrons are scattered more strongly
than the ↑ spin electrons. This results in different resistivity for each spin state, which
in turn leads to negative MR in ferromagnetic metal. At high temperatures, the spinflip scattering of conduction electrons takes place due to collisions with spin waves.
This in turn leads to spin mixing, which diminishes the distinction between the two