2.3 Spin Generation and Injection
27
2.3.1 What Is Spin Injection?
In general, when electrons move in a material, it carries both charge (−e) and spin
degrees of freedom (è/2). It is straightforward to state that in case of paramagnets,
conduction electrons do not intrinsically have any net spin polarization. This means
that in a paramagnet the population of two species of electrons, i.e., up-spin and
down-spin electrons, is equal under equilibrium. On the other hand, ferromagnets
have a non-zero spin polarization, i.e., a net spin magnetic moment of electrons under
equilibrium conditions. In order to attain spin transport in a device, as is requisite in
spintronics, the primary condition is to achieve an imbalance in the number of two
species of the spin carriers so that the net spin magnetic moment becomes finite.
It is noteworthy that in spintronics device, often we have to use paramagnetic
metallic or semiconducting component as its part. Thus following the prerequisite
condition of achieving spin transport in such paramagnetic components of spintronics
devices, net spin polarization P [given by Eq. (2.1)] can be generated in a paramagnet
either through electrical spin injection of charge carriers from a ferromagnet. Creation
of such a non-equilibrium situation in a material in terms of spin magnetic moment
of charge carriers is generally termed as ‘spin injection’.
2.3.2 Transport Method
The transport method, i.e., electrical injection of spins, is the most suitable method
for electrical device applications. It requires successfully injecting an imbalance of
spin from a ferromagnet into the paramagnet in the form of a current. It is well known
that the magnetization (M) of the ferromagnet is M ∞ n ↑ –n ↓ , where n ↑ (n ↓ ) are the
populations of the majority (minority) spin electrons. n ↑ (n ↓ ) can be found by taking
integration over the filled states of the up-spin (down-spin) energy band. Accordingly,
in a ferromagnet the electrons at the Fermi level (E F ) possess certain spin polarization.
In a half-metallic ferromagnet the charge carriers are highly spin polarized (P ~
100%). Thus, in the ferromagnetic material the electric current constitutes a net flow
of spins. This spin-polarized electron current in a ferromagnetic material is generally
referred to as ‘spin current’.
Now, let us consider a spin transport experiment, which is all-electrical. In this
case, spin injection into the paramagnet can be obtained by employing contacts,
commonly described as ‘spin injectors’. This ferromagnetic contact could be transition metals, half-metals or diluted magnetic semiconductors. In a paramagnetic/nonmagnetic material (NM), at equilibrium, the spin magnetic moments are aligned
randomly in space. Thus, inside the device the average spin magnetic moment of the
electron spin that ensembles at any position and time would be zero. This in turn
implies that the conduction electrons in a non-magnetic material are unpolarized.
Application of an external bias voltage induces a flow of this unpolarized ensemble
27
2.3.1 What Is Spin Injection?
In general, when electrons move in a material, it carries both charge (−e) and spin
degrees of freedom (è/2). It is straightforward to state that in case of paramagnets,
conduction electrons do not intrinsically have any net spin polarization. This means
that in a paramagnet the population of two species of electrons, i.e., up-spin and
down-spin electrons, is equal under equilibrium. On the other hand, ferromagnets
have a non-zero spin polarization, i.e., a net spin magnetic moment of electrons under
equilibrium conditions. In order to attain spin transport in a device, as is requisite in
spintronics, the primary condition is to achieve an imbalance in the number of two
species of the spin carriers so that the net spin magnetic moment becomes finite.
It is noteworthy that in spintronics device, often we have to use paramagnetic
metallic or semiconducting component as its part. Thus following the prerequisite
condition of achieving spin transport in such paramagnetic components of spintronics
devices, net spin polarization P [given by Eq. (2.1)] can be generated in a paramagnet
either through electrical spin injection of charge carriers from a ferromagnet. Creation
of such a non-equilibrium situation in a material in terms of spin magnetic moment
of charge carriers is generally termed as ‘spin injection’.
2.3.2 Transport Method
The transport method, i.e., electrical injection of spins, is the most suitable method
for electrical device applications. It requires successfully injecting an imbalance of
spin from a ferromagnet into the paramagnet in the form of a current. It is well known
that the magnetization (M) of the ferromagnet is M ∞ n ↑ –n ↓ , where n ↑ (n ↓ ) are the
populations of the majority (minority) spin electrons. n ↑ (n ↓ ) can be found by taking
integration over the filled states of the up-spin (down-spin) energy band. Accordingly,
in a ferromagnet the electrons at the Fermi level (E F ) possess certain spin polarization.
In a half-metallic ferromagnet the charge carriers are highly spin polarized (P ~
100%). Thus, in the ferromagnetic material the electric current constitutes a net flow
of spins. This spin-polarized electron current in a ferromagnetic material is generally
referred to as ‘spin current’.
Now, let us consider a spin transport experiment, which is all-electrical. In this
case, spin injection into the paramagnet can be obtained by employing contacts,
commonly described as ‘spin injectors’. This ferromagnetic contact could be transition metals, half-metals or diluted magnetic semiconductors. In a paramagnetic/nonmagnetic material (NM), at equilibrium, the spin magnetic moments are aligned
randomly in space. Thus, inside the device the average spin magnetic moment of the
electron spin that ensembles at any position and time would be zero. This in turn
implies that the conduction electrons in a non-magnetic material are unpolarized.
Application of an external bias voltage induces a flow of this unpolarized ensemble