24
2 Basic Elements of Spintronics
Spin polarization P is less than one for metallic ferromagnetic elements. For
instance, in case of Fe, Co and Ni elemental ferromagnet P is 0.44, 0.34 and 0.11,
respectively. However, in some materials spin polarization has been found to be unity.
Examples are CrO 2 , Fe 3 O 4 and some of the manganites. This feature originates from
the fact that in these materials one spin-split band is totally empty, which results in
the metallicity of the electrons of one spin band and insulating of those of another
spin band. Hence, these materials are named as half -metallic or half -insulating
ferromagnets.
2.2 Spin Filter Effect
Spin-dependent scattering, suffered by electrons in a ferromagnet because of its spindependent band structure (discussed above), leads to spin filtering effect (Ohno et al.
1999; Jedema et al. 2001; Appelbaum et al. 2007; Saikin 2004; Yu et al. 2012; Suzuki
et al. 2009; Tang et al. 2002; Schmidt et al. 2000; Wu et al. 2010). Spin-dependent
scattering mechanism will be discussed in detail in Chap. 3. Let us consider a passage
of electronic current through a ferromagnet, which is magnetized to saturation. Now,
magnetization is defined as: M ≈ n ↑ −n ↓ , where n ↑ and n ↓ are the total number of
up-spin and down-spin electrons, respectively. It can be clearly seen from the filled
states of the band structure, shown by striped portion, that the number of up-spin
and down-spin electrons are different in case of ferromagnet (Fig. 2.1a), whereas
they are equal in case of paramagnet (Fig. 2.1b). Therefore, it is quite natural that
such imbalance in the number of up-spin and down-spin electrons in ferromagnets
could possibly give rise to a net magnetization, whereas paramagnet could not have
such net magnetization. Furthermore, direction of that magnetization in ferromagnets
follows the spin direction, i.e., up-spin or down-spin directions of the electrons that
Fig. 2.1 Spin-resolved energy band structure for a paramagnet and b ferromagnet
2 Basic Elements of Spintronics
Spin polarization P is less than one for metallic ferromagnetic elements. For
instance, in case of Fe, Co and Ni elemental ferromagnet P is 0.44, 0.34 and 0.11,
respectively. However, in some materials spin polarization has been found to be unity.
Examples are CrO 2 , Fe 3 O 4 and some of the manganites. This feature originates from
the fact that in these materials one spin-split band is totally empty, which results in
the metallicity of the electrons of one spin band and insulating of those of another
spin band. Hence, these materials are named as half -metallic or half -insulating
ferromagnets.
2.2 Spin Filter Effect
Spin-dependent scattering, suffered by electrons in a ferromagnet because of its spindependent band structure (discussed above), leads to spin filtering effect (Ohno et al.
1999; Jedema et al. 2001; Appelbaum et al. 2007; Saikin 2004; Yu et al. 2012; Suzuki
et al. 2009; Tang et al. 2002; Schmidt et al. 2000; Wu et al. 2010). Spin-dependent
scattering mechanism will be discussed in detail in Chap. 3. Let us consider a passage
of electronic current through a ferromagnet, which is magnetized to saturation. Now,
magnetization is defined as: M ≈ n ↑ −n ↓ , where n ↑ and n ↓ are the total number of
up-spin and down-spin electrons, respectively. It can be clearly seen from the filled
states of the band structure, shown by striped portion, that the number of up-spin
and down-spin electrons are different in case of ferromagnet (Fig. 2.1a), whereas
they are equal in case of paramagnet (Fig. 2.1b). Therefore, it is quite natural that
such imbalance in the number of up-spin and down-spin electrons in ferromagnets
could possibly give rise to a net magnetization, whereas paramagnet could not have
such net magnetization. Furthermore, direction of that magnetization in ferromagnets
follows the spin direction, i.e., up-spin or down-spin directions of the electrons that
Fig. 2.1 Spin-resolved energy band structure for a paramagnet and b ferromagnet