2.7 D’yakonov-Perel’ Mechanism
53
polarization does not change with time. Therefore, this scenario does not lead to any
spin relaxation.
Now, let us consider a different scenario where the ensemble of electrons undergoes momentum-relaxing scattering events. This in turn results in the random change
of their corresponding
v with time. Accordingly, the magnitude of
B
v
would also
get changed since
B
v
is proportional to the velocity
v of the charge carrier. Thus,
in this case
B
v
is expected to have a large distribution of values. Consequently,
every electron in the ensemble should perform precession about the magnetic field,
experienced by it, with different precession frequencies. In this scenario, after a
certain interval of time after spin injection into the solid, different electrons would
have precessed by different angles since their scattering histories are different. Even
if considering an over-simplified picture of all the electrons in the ensemble were
injected with the same spin polarization, after a given time from the spin injection into
solid the orientation of the precessing spins would be different for various electrons
in the ensemble. Consequently, spin polarization of the ensemble of electrons gradually becomes out of phase with respect to each other during the passage of carriers
through the solid, and the ensemble averaged spin polarization decays with time.
Finally, after a sufficiently long time, the average spin polarization of the ensemble
will decay to zero. This is the conceptual representation of the D’yakonov-Perel’
mode of spin relaxation (Fig. 2.15).
S(0)
S(t)
Fig. 2.15 Schematic description of D’yakonov-Perel’ spin relaxation mechanisms
53
polarization does not change with time. Therefore, this scenario does not lead to any
spin relaxation.
Now, let us consider a different scenario where the ensemble of electrons undergoes momentum-relaxing scattering events. This in turn results in the random change
of their corresponding
v with time. Accordingly, the magnitude of
B
v
would also
get changed since
B
v
is proportional to the velocity
v of the charge carrier. Thus,
in this case
B
v
is expected to have a large distribution of values. Consequently,
every electron in the ensemble should perform precession about the magnetic field,
experienced by it, with different precession frequencies. In this scenario, after a
certain interval of time after spin injection into the solid, different electrons would
have precessed by different angles since their scattering histories are different. Even
if considering an over-simplified picture of all the electrons in the ensemble were
injected with the same spin polarization, after a given time from the spin injection into
solid the orientation of the precessing spins would be different for various electrons
in the ensemble. Consequently, spin polarization of the ensemble of electrons gradually becomes out of phase with respect to each other during the passage of carriers
through the solid, and the ensemble averaged spin polarization decays with time.
Finally, after a sufficiently long time, the average spin polarization of the ensemble
will decay to zero. This is the conceptual representation of the D’yakonov-Perel’
mode of spin relaxation (Fig. 2.15).
S(0)
S(t)
Fig. 2.15 Schematic description of D’yakonov-Perel’ spin relaxation mechanisms