2.2 Spin Filter Effect
25
are having majority population. Therefore, we define electrons having their spin
magnetic moment parallel to magnetization M as majority spin electrons, whereas
electrons having their spin magnetic moment antiparallel to magnetization M as
minority spin electrons.
2.2.1 What Is Spin Filter Effect?
It has been found that majority spin electrons are more easily transmitted through
ferromagnet than minority spin electrons. This phenomenon is known as spin filter
effect (Appelbaum et al. 2007) and is characterized by a parameter called spin
asymmetry ‘A’. Now, spin filtering effect or spin asymmetry arises due to this
spin-dependent scattering and is defined as
A =
I
↑
− I
↓
/
I
↑
+ I
↓
(2.2)
where current contributed by the electrons having spin magnetic moment
parallel/antiparallel to M is denoted by I
↑ /I
↓ .
2.2.2 Physical Interpretation of Spin Asymmetry ‘A’
In an attempt to give physical interpretation of A considering only the intensity of
the transmitted electrons, let us note that the empty states available for minority
spin electrons for scattering into are much more than that for majority spin electrons
(Fig. 2.1a). Thus, minority spin electrons possess a larger absorption coefficient than
that of majority spin electrons. Such difference in absorption coefficients between
majority and minority spin electrons gives rise to spin filtering or A as two branches of
electrons, majority and minority spin electrons, traveling through the ferromagnetic
film.
To summarize, during a passage of electronic current through a ferromagnet,
because of its spin-dependent scattering, both the absorption coefficients and phases
for majority and minority spin electrons within the ferromagnet would be different.
This gives rise to spin filter effect, which plays a very critical role in exhibiting
spintronics effect.
2.2.3 Spin Detection Efficiency
In this context, a quantity named ‘spin detection efficiency’ has been defined. Such
quantity is a measure of how efficiently a ferromagnet can filter spin, i.e., how
selectively it can transmit electrons of a particular spin orientation impinging on it
25
are having majority population. Therefore, we define electrons having their spin
magnetic moment parallel to magnetization M as majority spin electrons, whereas
electrons having their spin magnetic moment antiparallel to magnetization M as
minority spin electrons.
2.2.1 What Is Spin Filter Effect?
It has been found that majority spin electrons are more easily transmitted through
ferromagnet than minority spin electrons. This phenomenon is known as spin filter
effect (Appelbaum et al. 2007) and is characterized by a parameter called spin
asymmetry ‘A’. Now, spin filtering effect or spin asymmetry arises due to this
spin-dependent scattering and is defined as
A =
I
↑
− I
↓
/
I
↑
+ I
↓
(2.2)
where current contributed by the electrons having spin magnetic moment
parallel/antiparallel to M is denoted by I
↑ /I
↓ .
2.2.2 Physical Interpretation of Spin Asymmetry ‘A’
In an attempt to give physical interpretation of A considering only the intensity of
the transmitted electrons, let us note that the empty states available for minority
spin electrons for scattering into are much more than that for majority spin electrons
(Fig. 2.1a). Thus, minority spin electrons possess a larger absorption coefficient than
that of majority spin electrons. Such difference in absorption coefficients between
majority and minority spin electrons gives rise to spin filtering or A as two branches of
electrons, majority and minority spin electrons, traveling through the ferromagnetic
film.
To summarize, during a passage of electronic current through a ferromagnet,
because of its spin-dependent scattering, both the absorption coefficients and phases
for majority and minority spin electrons within the ferromagnet would be different.
This gives rise to spin filter effect, which plays a very critical role in exhibiting
spintronics effect.
2.2.3 Spin Detection Efficiency
In this context, a quantity named ‘spin detection efficiency’ has been defined. Such
quantity is a measure of how efficiently a ferromagnet can filter spin, i.e., how
selectively it can transmit electrons of a particular spin orientation impinging on it