Chapter 2
Basic Elements of Spintronics
In this chapter, we will discuss several basic phenomena that give rise to spintronics
properties (Bandyopadhyay and Cahay 2008; Zutic et al. 2004).
2.1 Spin Polarization
An ensemble of electrons is said to be polarized if the electron spins have a preferential
orientation. If in an ensemble of N electrons, N 1 electrons have up-spin and N 2
electrons have down-spin orientations, then spin polarization could be defined as
P =
N 1 − N 2
N 1 + N 2
%, where N 1 + N 2 = N
(2.1)
(a) Unpolarized electron beam—If the number of electrons having spin-up orientations and that having spin-down orientations are the same, i.e., N 1 = N 2 ,
then P = 0, thus the ensemble becomes unpolarized. This kind of ensembles
is said to be unpolarized electron beam.
(b) Polarized electron beam—If the number of electrons having spin-up orientations and that having spin-down orientations are not the same, i.e., N 1 = N 2 ,
P should have some finite value, thus the ensemble should have some spin
polarization. This kind of ensembles is said to be polarized.
(i) Fully Polarized Electron: In this case, all the electron spins have same
orientations (either spin-up or spin-down) and all electron spins can be
described by a single spin function. This kind of ensemble of electrons
is said to be fully spin polarized. In this case, if N be the total number of
electrons in the ensemble, then either N 1 = N and N 2 = 0 or N 2 = N and
N 1 = 0, thus P = 100%, hence fully spin-polarized electron beam.
© Springer Nature Singapore Pte Ltd. 2021
P. Dey and J. N. Roy, Spintronics,
https://doi.org/10.1007/978-981-16-0069-2_2
23
Basic Elements of Spintronics
In this chapter, we will discuss several basic phenomena that give rise to spintronics
properties (Bandyopadhyay and Cahay 2008; Zutic et al. 2004).
2.1 Spin Polarization
An ensemble of electrons is said to be polarized if the electron spins have a preferential
orientation. If in an ensemble of N electrons, N 1 electrons have up-spin and N 2
electrons have down-spin orientations, then spin polarization could be defined as
P =
N 1 − N 2
N 1 + N 2
%, where N 1 + N 2 = N
(2.1)
(a) Unpolarized electron beam—If the number of electrons having spin-up orientations and that having spin-down orientations are the same, i.e., N 1 = N 2 ,
then P = 0, thus the ensemble becomes unpolarized. This kind of ensembles
is said to be unpolarized electron beam.
(b) Polarized electron beam—If the number of electrons having spin-up orientations and that having spin-down orientations are not the same, i.e., N 1 = N 2 ,
P should have some finite value, thus the ensemble should have some spin
polarization. This kind of ensembles is said to be polarized.
(i) Fully Polarized Electron: In this case, all the electron spins have same
orientations (either spin-up or spin-down) and all electron spins can be
described by a single spin function. This kind of ensemble of electrons
is said to be fully spin polarized. In this case, if N be the total number of
electrons in the ensemble, then either N 1 = N and N 2 = 0 or N 2 = N and
N 1 = 0, thus P = 100%, hence fully spin-polarized electron beam.
© Springer Nature Singapore Pte Ltd. 2021
P. Dey and J. N. Roy, Spintronics,
https://doi.org/10.1007/978-981-16-0069-2_2
23