52
2 Basic Elements of Spintronics
kind of inversion asymmetry is called structural inversion asymmetry, which
gives rise to Rashba spin–orbit interaction (Bychkov and Rashba 1984). Now,
the presence of structural inversion asymmetry in case of disordered organic
semiconductors is typically due to the microscopic electric fields arising owing
to the presence of charged impurities and surface states, i.e., dangling molecular
bonds.
It comes out that both Dresselhaus and Rashba spin–orbit interactions lift off the
degeneracy between the two spin states corresponding to any arbitrary wavevector.
Therefore, those non-degenerate up- and down-spin states possess different energies
corresponding to the same wavevector state. In effect, these spin–orbit interactions
resemble effective magnetic fields in a sense that magnetic fields also transform the
degenerate up- and down-spin states to non-degenerate one, for any given wavevector
due to Zeeman interaction.
2.7.2 D’yakonov-Perel’ Mode of Spin Scattering Mechanism
Thus, it comes out that both bulk and structural inversion asymmetries, i.e., Rashba
and Dresselhaus interactions, give rise to effective electrostatic potential gradient.
This in turn generates electric field experienced by charge carriers. Hence, electrons in this kind of solid, having inversion asymmetry, will experience strong spin–
orbit interaction. Now, considering the rest frame of reference of a mobile charge
carrier, such electric field may be considered to be Lorentz transformed to an effective magnetic field
B
v
, which in turn is a function of the carrier’s velocity
v.
Consequently, spin of charge carriers, i.e., electrons in an inversion asymmetric
solid is supposed to perform continuous Larmor precession about that
B
v
with
the precession axis being collinear with the magnetic field.
Now, let us suppose a simplified picture of an ensemble of electrons drifting and
diffusing in such an inversion asymmetric solid. Let us first consider the velocity
v of
all the electrons in the ensemble be the same and does not change with time. Then the
magnetic field,
B
v
, experienced by all the electrons will also be the same. Consequently, spin magnetic moment of every electron in the ensemble should perform
precession about this constant magnetic field with a fixed frequency. Interestingly,
this does not cause any spin relaxation at all! In order to understand this, let us
consider that all the electrons in the ensemble are in the same spin polarization states
just after spin injection into the solid, i.e., at the onset of their journey through the
solid under the applied bias. Then after any arbitrary time interval, all of them must
have undergone same degree of precession by exactly the same angle. Hence, the
ensemble of electrons again has the same spin polarization. Although the direction
of this spin polarization might be different from the initial one, but that does not
matter. More significant point is that the magnitude of this ensemble averaged spin
2 Basic Elements of Spintronics
kind of inversion asymmetry is called structural inversion asymmetry, which
gives rise to Rashba spin–orbit interaction (Bychkov and Rashba 1984). Now,
the presence of structural inversion asymmetry in case of disordered organic
semiconductors is typically due to the microscopic electric fields arising owing
to the presence of charged impurities and surface states, i.e., dangling molecular
bonds.
It comes out that both Dresselhaus and Rashba spin–orbit interactions lift off the
degeneracy between the two spin states corresponding to any arbitrary wavevector.
Therefore, those non-degenerate up- and down-spin states possess different energies
corresponding to the same wavevector state. In effect, these spin–orbit interactions
resemble effective magnetic fields in a sense that magnetic fields also transform the
degenerate up- and down-spin states to non-degenerate one, for any given wavevector
due to Zeeman interaction.
2.7.2 D’yakonov-Perel’ Mode of Spin Scattering Mechanism
Thus, it comes out that both bulk and structural inversion asymmetries, i.e., Rashba
and Dresselhaus interactions, give rise to effective electrostatic potential gradient.
This in turn generates electric field experienced by charge carriers. Hence, electrons in this kind of solid, having inversion asymmetry, will experience strong spin–
orbit interaction. Now, considering the rest frame of reference of a mobile charge
carrier, such electric field may be considered to be Lorentz transformed to an effective magnetic field
B
v
, which in turn is a function of the carrier’s velocity
v.
Consequently, spin of charge carriers, i.e., electrons in an inversion asymmetric
solid is supposed to perform continuous Larmor precession about that
B
v
with
the precession axis being collinear with the magnetic field.
Now, let us suppose a simplified picture of an ensemble of electrons drifting and
diffusing in such an inversion asymmetric solid. Let us first consider the velocity
v of
all the electrons in the ensemble be the same and does not change with time. Then the
magnetic field,
B
v
, experienced by all the electrons will also be the same. Consequently, spin magnetic moment of every electron in the ensemble should perform
precession about this constant magnetic field with a fixed frequency. Interestingly,
this does not cause any spin relaxation at all! In order to understand this, let us
consider that all the electrons in the ensemble are in the same spin polarization states
just after spin injection into the solid, i.e., at the onset of their journey through the
solid under the applied bias. Then after any arbitrary time interval, all of them must
have undergone same degree of precession by exactly the same angle. Hence, the
ensemble of electrons again has the same spin polarization. Although the direction
of this spin polarization might be different from the initial one, but that does not
matter. More significant point is that the magnitude of this ensemble averaged spin