116
4 Tunnelling Magnetoresistance (TMR)
Fig. 4.7 Schematic description of the TMR as explained by Jullière model
ferromagnetic electrode and vice versa. This model is clearly depicted in Fig. 4.7. In
order to simplify the calculation, let us suppose negligible direct magnetic coupling
between the ferromagnetic electrodes and that the bulk effects are determining the
alignment of magnetization in each ferromagnetic electrode.
Furthermore, it is understandable that
D ↓ (E F ) ∝ N ↓
D ↑ (E F ) ∝ N ↑ .
(4.25)
where N ↓ and N ↑ are the number of electrons with down- and up-spin, respectively.
Second, conductance (G) of the electron for a particular spin orientation tunnelling
from one ferromagnetic electrode to another is proportional to the product of the
effective density of states at Fermi level (E F ) of the two ferromagnetic electrodes.
Thus, considering Eq. (4.25) one may expect that
G
↑
P ∞N
↑
L N
↑
R ,
G
↓
P ∞N
↓
L N
↓
R ,
G
↑
AP ∞N
↑
L N
↓
R ,
4 Tunnelling Magnetoresistance (TMR)
Fig. 4.7 Schematic description of the TMR as explained by Jullière model
ferromagnetic electrode and vice versa. This model is clearly depicted in Fig. 4.7. In
order to simplify the calculation, let us suppose negligible direct magnetic coupling
between the ferromagnetic electrodes and that the bulk effects are determining the
alignment of magnetization in each ferromagnetic electrode.
Furthermore, it is understandable that
D ↓ (E F ) ∝ N ↓
D ↑ (E F ) ∝ N ↑ .
(4.25)
where N ↓ and N ↑ are the number of electrons with down- and up-spin, respectively.
Second, conductance (G) of the electron for a particular spin orientation tunnelling
from one ferromagnetic electrode to another is proportional to the product of the
effective density of states at Fermi level (E F ) of the two ferromagnetic electrodes.
Thus, considering Eq. (4.25) one may expect that
G
↑
P ∞N
↑
L N
↑
R ,
G
↓
P ∞N
↓
L N
↓
R ,
G
↑
AP ∞N
↑
L N
↓
R ,