5.2 Spin-Transfer Torque in Ferromagnetic Layer Structures
129
have larger transmission amplitude through the interface compared to spin-down
electrons. As a result, spin polarization of the transmitted electron across the interface
between the NM metal and the FM layer is supposed to be oriented at a smaller
angle θ with respect to z-axis than its initial incident angle.
Region 2: Ferromagnetic (FM) layer
After entering the FM layer, electron continues to travel through the ferromagnet
under proper biasing condition. In this layer, spin magnetic moment of electron
experiences strong exchange interaction with the magnetization of the ferromagnet.
As already discussed, spin of the incident electron is assumed not to be parallel
with the magnetization of the FM. Hence, electron spin is supposed to execute
precession about the direction of the exchange field. Considering conservation of
angular momentum, the magnetization associated with the FM must also experience
precession about the direction of electron spin. This precession has been found to be
extremely rapid. As a result, electron traverses only a few lattice spacings per precession period. Thus, even for a 3 or 4 nm thin film, electron may undergo precession
several times before leaving the rear side of the FM layer. Finally, whether electron
would exit the ferromagnet with either positive or negative spin components in the x
and y directions is decided by exactly how many fractions of a turn the electron
has precessed before leaving the ferromagnet. Quite expectedly, the z component
of the spin should not change during the precessional motion of the electron as the
precession occurs around z-axis.
Transit of many electrons: The above discussion is oversimplified since only
single electron has been considered. But, in case of a real device, a large number
of electrons are travelling simultaneously through the FM layer. Those electrons are
propagating with different energies and incident angles in real space. Let us suppose,
every electron began with exactly the identical initial angle for its spin polarization.
Nevertheless, each electron would undergo a different degree of precession within the
FM layer, since each of them is supposed to take a different amount of time to traverse
the FM layer. Therefore, even for the fractions of electrons having same initial angle,
based on exactly how much fractions of a turn each electron has precessed, it could
leave the FM layer with either positive or negative spin components in the x and
y directions. Quite expectedly, in this scenario spin component along z direction
would not change during the transit of electrons through the ferromagnetic layer.
Thus, summing over total spin angular momentum of all the electrons, exiting the
FM layer, yields the only non-negligible spin component pointing along z direction,
i.e., parallel to the magnetization direction of the FM layer. It can be understood
that the spin components along x and y directions should average out to be zero. In
this way, by virtue of spin-transfer torque process, spin magnetic moments of the
incoming electrons become parallel to the magnetization direction of the FM layer.
129
have larger transmission amplitude through the interface compared to spin-down
electrons. As a result, spin polarization of the transmitted electron across the interface
between the NM metal and the FM layer is supposed to be oriented at a smaller
angle θ with respect to z-axis than its initial incident angle.
Region 2: Ferromagnetic (FM) layer
After entering the FM layer, electron continues to travel through the ferromagnet
under proper biasing condition. In this layer, spin magnetic moment of electron
experiences strong exchange interaction with the magnetization of the ferromagnet.
As already discussed, spin of the incident electron is assumed not to be parallel
with the magnetization of the FM. Hence, electron spin is supposed to execute
precession about the direction of the exchange field. Considering conservation of
angular momentum, the magnetization associated with the FM must also experience
precession about the direction of electron spin. This precession has been found to be
extremely rapid. As a result, electron traverses only a few lattice spacings per precession period. Thus, even for a 3 or 4 nm thin film, electron may undergo precession
several times before leaving the rear side of the FM layer. Finally, whether electron
would exit the ferromagnet with either positive or negative spin components in the x
and y directions is decided by exactly how many fractions of a turn the electron
has precessed before leaving the ferromagnet. Quite expectedly, the z component
of the spin should not change during the precessional motion of the electron as the
precession occurs around z-axis.
Transit of many electrons: The above discussion is oversimplified since only
single electron has been considered. But, in case of a real device, a large number
of electrons are travelling simultaneously through the FM layer. Those electrons are
propagating with different energies and incident angles in real space. Let us suppose,
every electron began with exactly the identical initial angle for its spin polarization.
Nevertheless, each electron would undergo a different degree of precession within the
FM layer, since each of them is supposed to take a different amount of time to traverse
the FM layer. Therefore, even for the fractions of electrons having same initial angle,
based on exactly how much fractions of a turn each electron has precessed, it could
leave the FM layer with either positive or negative spin components in the x and
y directions. Quite expectedly, in this scenario spin component along z direction
would not change during the transit of electrons through the ferromagnetic layer.
Thus, summing over total spin angular momentum of all the electrons, exiting the
FM layer, yields the only non-negligible spin component pointing along z direction,
i.e., parallel to the magnetization direction of the FM layer. It can be understood
that the spin components along x and y directions should average out to be zero. In
this way, by virtue of spin-transfer torque process, spin magnetic moments of the
incoming electrons become parallel to the magnetization direction of the FM layer.