3.5 Physical Origin of GMR: Qualitative Explanation
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Now, we will bring ‘spin’ in this discussion. In case of ferromagnetic transitional metallic elements, one need to consider that ↑ and ↓ spin energy band, corresponding to 3d orbitals are almost rigidly shifted with respect to each other along
the energy axis by the ferromagnetic exchange interaction (discussed in Chap. 1).
Consequently, in case of a ferromagnetic metal, the potentials experienced by ↑ and ↓
spin electrons are different. This constitutes the basis of spin-dependent scattering in
a ferromagnetic metal. In addition, in case of a multilayer structure, electrons flowing
into the ferromagnetic layer from its underneath/adjacent non-magnetic spacer layer
encounter a spin-dependent potential barrier. This in turn distinctly reflects ↑ and ↓
spin electrons. It has been found that electrons with spin magnetic moment antiparallel (minority spin electrons) to the magnetization (M) of the ferromagnetic layer
are scattered more strongly than electrons with their spin magnetic moment parallel
(majority spin electrons) to M. This means that in case of electronic conduction in
a ferromagnetic material, majority spin electrons are more easily transmitted than
minority spin electrons. Now this feature can be explained as follows: We note that
there is more empty density of states available for minority spin electrons to scatter
into than for majority spin electrons. As a result, the minority spin electrons encounter
larger scattering than that of majority spin electrons. This spin-dependent scattering,
in effect, causes GMR.
II. Spin-flip scattering
As already discussed, spin-flip scattering of an electron is characterized by changing
or flipping of electron spin orientation. Several sources have been identified as
responsible for spin-flip scattering:
1. Magnetic impurity at non-magnetic (NM) spacer layer—During the fabrication process, due to top ferromagnetic layer deposition on non-magnetic spacer
layer, diffusion of some magnetic atoms may take place into the non-magnetic
spacer layer. Such ferromagnetic inclusions eventually form magnetic impurities in the non-magnetic spacer layer. If these magnetic impurities are located
considerably far away from the ferromagnetic/non-magnetic interface, then the
coupling of the spin magnetic moment associated with these impurities and that
of the ferromagnetic layers is quite weak. As a result, spins associated with
these impurities rotate freely. In this case, when there is scattering between an
electron and magnetic impurity, interchanging of spins of the electron and that
of the impurity may take place.
2. Spin waves in FM layer—Spin waves can also be a source of scattering of
electrons in ferromagnetic layers. Spin waves are quasi-particles with spin one.
Therefore, creation or annihilation of a spin wave, as the case may be, due to
scattering with an electron leads to a spin flipping of that electron. Since it
involves the spin wave energy, this is an inelastic process which is important
only at elevated temperatures.
3. Spin–orbit interaction due to gold (Au) impurity—Let us consider the presence
of impurities, offering strong spin–orbit coupling, such as gold (Au) in the
89
Now, we will bring ‘spin’ in this discussion. In case of ferromagnetic transitional metallic elements, one need to consider that ↑ and ↓ spin energy band, corresponding to 3d orbitals are almost rigidly shifted with respect to each other along
the energy axis by the ferromagnetic exchange interaction (discussed in Chap. 1).
Consequently, in case of a ferromagnetic metal, the potentials experienced by ↑ and ↓
spin electrons are different. This constitutes the basis of spin-dependent scattering in
a ferromagnetic metal. In addition, in case of a multilayer structure, electrons flowing
into the ferromagnetic layer from its underneath/adjacent non-magnetic spacer layer
encounter a spin-dependent potential barrier. This in turn distinctly reflects ↑ and ↓
spin electrons. It has been found that electrons with spin magnetic moment antiparallel (minority spin electrons) to the magnetization (M) of the ferromagnetic layer
are scattered more strongly than electrons with their spin magnetic moment parallel
(majority spin electrons) to M. This means that in case of electronic conduction in
a ferromagnetic material, majority spin electrons are more easily transmitted than
minority spin electrons. Now this feature can be explained as follows: We note that
there is more empty density of states available for minority spin electrons to scatter
into than for majority spin electrons. As a result, the minority spin electrons encounter
larger scattering than that of majority spin electrons. This spin-dependent scattering,
in effect, causes GMR.
II. Spin-flip scattering
As already discussed, spin-flip scattering of an electron is characterized by changing
or flipping of electron spin orientation. Several sources have been identified as
responsible for spin-flip scattering:
1. Magnetic impurity at non-magnetic (NM) spacer layer—During the fabrication process, due to top ferromagnetic layer deposition on non-magnetic spacer
layer, diffusion of some magnetic atoms may take place into the non-magnetic
spacer layer. Such ferromagnetic inclusions eventually form magnetic impurities in the non-magnetic spacer layer. If these magnetic impurities are located
considerably far away from the ferromagnetic/non-magnetic interface, then the
coupling of the spin magnetic moment associated with these impurities and that
of the ferromagnetic layers is quite weak. As a result, spins associated with
these impurities rotate freely. In this case, when there is scattering between an
electron and magnetic impurity, interchanging of spins of the electron and that
of the impurity may take place.
2. Spin waves in FM layer—Spin waves can also be a source of scattering of
electrons in ferromagnetic layers. Spin waves are quasi-particles with spin one.
Therefore, creation or annihilation of a spin wave, as the case may be, due to
scattering with an electron leads to a spin flipping of that electron. Since it
involves the spin wave energy, this is an inelastic process which is important
only at elevated temperatures.
3. Spin–orbit interaction due to gold (Au) impurity—Let us consider the presence
of impurities, offering strong spin–orbit coupling, such as gold (Au) in the