96
3 Giant Magnetoresistance (GMR)
Fig. 3.13 Schematic
illustration of distribution of
local resistivities in a
magnetic unit cell.
a Ferromagnetic (FM) and
b antiferromagnetic (AFM)
configurations
More precisely,
• for the ferromagnetic configuration, the process could be reduced to the estimation
of the resistance only for a two-component superlattice.
• for the antiferromagnetic configuration, one has to consider the whole fourcomponent superlattice.
3.7.2 Calculation for Ferromagnetic Configuration
For simplicity, let us suppose that in a two-component superlattice structure, a and b
are the thicknesses of the alternating regions having high (ρ
a
) and low (ρ
b
) resistivity,
respectively. Thus, in a two-component superlattice structure, average resistivity
experienced by conduction electrons is given by
ρ =
aρ
a
+ bρ
b
a + b
(3.13)
Now, using the above generalization, we can go for evaluating the MR:
(R ↑ ) ↑↑ =
Mρ
L
F M + Nρ N M
M + N
, (R ↓ ) ↑↑ =
Mρ
H
F M + Nρ N M
M + N
(3.14)
where M and N are the number of atomic planes of each ferromagnetic and
non-magnetic layers, respectively. Adding both parts in Eq. (3.14) results the
two-component superlattice resistance for ferromagnetic configuration given by
1
R
↑↑
= (M + N)
1
Mρ
L
F M + Nρ N M
+
1
Mρ
H
F M + Nρ N M
(3.15)