5.2 Spin-Transfer Torque in Ferromagnetic Layer Structures
131
Case I: Flow of electrons from thicker to thinner layer—In this case, injection
of electrons take place from the left side in the multilayer structure, as shown in
Fig. 5.2a. This is referred to as negative current. As already mentioned, if unpolarized
electrons are injected into the thick fixed layer, then spin-filtering phenomenon would
take place. As a result, the spin filtered electrons from the thick fixed layer emerges
into the non-magnetic metallic spacer layer having the direction of their average
spin magnetic moment parallel to the magnetization direction of the fixed layer.
Subsequently, these polarized electrons enter the thin free ferromagnetic layer and
interact with the magnetization of this free layer. Consequently, the magnetization of
this free layer experiences a torque. This torque in turn tends to orient the associated
magnetic moment of the free layer towards the direction of the spin magnetic moment
of the incoming polarized electrons from the thick fixed layer. In effect, this torque on
the free layer magnetic moment will turn its associated magnetization in the direction
of the fixed layer’s magnetization. Thus, a parallel orientation between the magnetic
moments or magnetizations of these two FM layers can be achieved.
Case II: Flow of electrons from thinner to thicker layer—In this case, injection
of electrons take place from the right side in the multilayer structure, as shown in
Fig. 5.2b. This is referred to as positive current. This indicates that the net flow
of electrons takes place from the free layer to the fixed layer. Similar to Case I,
unpolarized electrons entering the free FM layer will first experience spin filtering
effect and become spin polarized, having average spin magnetic moment parallel to
the magnetization of the free FM layer. It is evident that at this step, no net torque is
applied to the magnetic moment of the free FM layer by the unpolarized electrons.
Subsequently, spin-polarized electrons, produced at free FM layer, will flow into the
central NM-metallic spacer layer. These spin-polarized electrons will then enter the
fixed FM layer. Here, one may expect that spin magnetic moment associated with
these spin-polarized electrons would transfer angular momentum and hence apply
a torque to the magnetic moment of the fixed FM layer. However, in reality this is
not the case. Actually, the magnetic moment of the fixed layer is so rigidly held in
place that we cannot expect any torque acting on it. Since the fixed FM layer is made
of high magnetic moment material, Fermi level is expected to pass through very
little portion of (or may be not at all through) minority spin band. Consequently, the
fraction of electrons, having polarization parallel to the magnetization of the fixed
FM layer, will be readily transmitted through this layer, whereas the fraction having
polarization antiparallel to the fixed layer moment will be reflected back towards
the free FM layer from the NM/fixed FM layer interface. Those reflected electrons,
having spin magnetic moment antiparallel to the magnetization of the fixed FM layer,
now approach to the free FM layer and exert a torque on the magnetic moment of
the free FM layer. This, in turn, tends to orient the associated magnetic moment of
the free FM layer towards the orientation of the reflected spin moment, i.e., in effect,
away from the direction of the fixed-layer moment. This implies that a large-enough
positive current might destabilize the parallel orientation of the magnetization of
those two FM layers and might establish an antiparallel alignment among them.
131
Case I: Flow of electrons from thicker to thinner layer—In this case, injection
of electrons take place from the left side in the multilayer structure, as shown in
Fig. 5.2a. This is referred to as negative current. As already mentioned, if unpolarized
electrons are injected into the thick fixed layer, then spin-filtering phenomenon would
take place. As a result, the spin filtered electrons from the thick fixed layer emerges
into the non-magnetic metallic spacer layer having the direction of their average
spin magnetic moment parallel to the magnetization direction of the fixed layer.
Subsequently, these polarized electrons enter the thin free ferromagnetic layer and
interact with the magnetization of this free layer. Consequently, the magnetization of
this free layer experiences a torque. This torque in turn tends to orient the associated
magnetic moment of the free layer towards the direction of the spin magnetic moment
of the incoming polarized electrons from the thick fixed layer. In effect, this torque on
the free layer magnetic moment will turn its associated magnetization in the direction
of the fixed layer’s magnetization. Thus, a parallel orientation between the magnetic
moments or magnetizations of these two FM layers can be achieved.
Case II: Flow of electrons from thinner to thicker layer—In this case, injection
of electrons take place from the right side in the multilayer structure, as shown in
Fig. 5.2b. This is referred to as positive current. This indicates that the net flow
of electrons takes place from the free layer to the fixed layer. Similar to Case I,
unpolarized electrons entering the free FM layer will first experience spin filtering
effect and become spin polarized, having average spin magnetic moment parallel to
the magnetization of the free FM layer. It is evident that at this step, no net torque is
applied to the magnetic moment of the free FM layer by the unpolarized electrons.
Subsequently, spin-polarized electrons, produced at free FM layer, will flow into the
central NM-metallic spacer layer. These spin-polarized electrons will then enter the
fixed FM layer. Here, one may expect that spin magnetic moment associated with
these spin-polarized electrons would transfer angular momentum and hence apply
a torque to the magnetic moment of the fixed FM layer. However, in reality this is
not the case. Actually, the magnetic moment of the fixed layer is so rigidly held in
place that we cannot expect any torque acting on it. Since the fixed FM layer is made
of high magnetic moment material, Fermi level is expected to pass through very
little portion of (or may be not at all through) minority spin band. Consequently, the
fraction of electrons, having polarization parallel to the magnetization of the fixed
FM layer, will be readily transmitted through this layer, whereas the fraction having
polarization antiparallel to the fixed layer moment will be reflected back towards
the free FM layer from the NM/fixed FM layer interface. Those reflected electrons,
having spin magnetic moment antiparallel to the magnetization of the fixed FM layer,
now approach to the free FM layer and exert a torque on the magnetic moment of
the free FM layer. This, in turn, tends to orient the associated magnetic moment of
the free FM layer towards the orientation of the reflected spin moment, i.e., in effect,
away from the direction of the fixed-layer moment. This implies that a large-enough
positive current might destabilize the parallel orientation of the magnetization of
those two FM layers and might establish an antiparallel alignment among them.