48
2 Basic Elements of Spintronics
Fig. 2.12 Illustration of spin
relaxation. The magnitude of
spin polarization of the
electron ensemble decreases
exponentially with time and
distance
spin ensemble decreases both with time (t) and distance (x), as estimated from the
point of spin injection into the paramagnetic semiconductor (Fig. 2.12). Such gradual
loss in the magnitude of the spin polarization of the injected electron ensemble in
the paramagnetic medium is termed as spin relaxation phenomenon. The variation
in the injected spin polarization with respect to distance/time in the paramagnetic
semiconductor has been found to follow an exponential decay, as demonstrated in
Fig. 2.12.
As is shown in Fig. 2.12, spin relaxation or diffusion length/time, i.e., L S /τ S is
defined as the distance/duration over which the spin polarization reduces to 1/e times
of its initial value. When x L S (or t τ S ), then spin polarization of the ensemble
tends to zero, i.e., P → 0, implying complete loss of spin polarization. Thus, spin
relaxation phenomenon in a paramagnet tends to bring the non-equilibrium population of spin back to the equilibrium unpolarized condition. Here lies the paramount
importance of spin relaxation in spintronics since everyone is concerned with using
spin polarization of either a single-charge carrier or the net spin polarization of
ensemble of charge carriers to encode and decode information. If the given spins
were to host the information reliably for considerable time, it must be protected
against random or spontaneous depolarization caused by a various relaxation mechanism. Thus, with the objective to attain ‘non-zero spin polarization’, the continuous
effort is to suppress spin relaxation process; in other words to improve spin relaxation
length and time into the paramagnetic semiconductor.
Several mechanisms are there in solids and those are responsible for spin relaxation of electrons in the conduction band of a semiconductor. Among them, the
four main spin relaxation processes are: (a) Elliott–Yafet mode of spin relaxation,
(b) D’yakonov-Perel’ mode of spin relaxation, (c) Bir-Aronov-Pikus mode of spin
relaxation and (d) hyperfine interaction of electron spins with nuclear spins.. Spin–
orbit interaction is the primary cause of the first two mechanisms, whereas the third
one arises due to the exchange coupling between electron and hole spins. The last
2 Basic Elements of Spintronics
Fig. 2.12 Illustration of spin
relaxation. The magnitude of
spin polarization of the
electron ensemble decreases
exponentially with time and
distance
spin ensemble decreases both with time (t) and distance (x), as estimated from the
point of spin injection into the paramagnetic semiconductor (Fig. 2.12). Such gradual
loss in the magnitude of the spin polarization of the injected electron ensemble in
the paramagnetic medium is termed as spin relaxation phenomenon. The variation
in the injected spin polarization with respect to distance/time in the paramagnetic
semiconductor has been found to follow an exponential decay, as demonstrated in
Fig. 2.12.
As is shown in Fig. 2.12, spin relaxation or diffusion length/time, i.e., L S /τ S is
defined as the distance/duration over which the spin polarization reduces to 1/e times
of its initial value. When x L S (or t τ S ), then spin polarization of the ensemble
tends to zero, i.e., P → 0, implying complete loss of spin polarization. Thus, spin
relaxation phenomenon in a paramagnet tends to bring the non-equilibrium population of spin back to the equilibrium unpolarized condition. Here lies the paramount
importance of spin relaxation in spintronics since everyone is concerned with using
spin polarization of either a single-charge carrier or the net spin polarization of
ensemble of charge carriers to encode and decode information. If the given spins
were to host the information reliably for considerable time, it must be protected
against random or spontaneous depolarization caused by a various relaxation mechanism. Thus, with the objective to attain ‘non-zero spin polarization’, the continuous
effort is to suppress spin relaxation process; in other words to improve spin relaxation
length and time into the paramagnetic semiconductor.
Several mechanisms are there in solids and those are responsible for spin relaxation of electrons in the conduction band of a semiconductor. Among them, the
four main spin relaxation processes are: (a) Elliott–Yafet mode of spin relaxation,
(b) D’yakonov-Perel’ mode of spin relaxation, (c) Bir-Aronov-Pikus mode of spin
relaxation and (d) hyperfine interaction of electron spins with nuclear spins.. Spin–
orbit interaction is the primary cause of the first two mechanisms, whereas the third
one arises due to the exchange coupling between electron and hole spins. The last