3.7 Magnetoresistance Theory
97
Thus for four-component superlattice, Eq. (3.15) turns out to be
1
R
↑↑
= 2(M + N)
1
Mρ
L
F M + Nρ N M
+
1
Mρ
H
F M + Nρ N M
(3.16)
3.7.3 Calculation for Antiferromagnetic Configuration
Adopting similar procedure as that followed in case of ferromagnetic configuration, the calculation of four-component superlattice resistance for antiferromagnetic
configuration using Eq. (3.12) results in
1
R
↑↓
=
8(M + N)
Mρ
L
F M + Mρ
H
F M + Nρ N M
(3.17)
Recalling GMR (%) =
R
R
=
R ↓↑ −R ↑↑
R ↑↑
, substituting Eqs. (3.16) and (3.17), we get
R
R
=
M
2
(ρ
L
F M − ρ
H
F M )
2
4(Mρ
L
F M + Nρ N M )
Mρ
H
F M + Nρ N M
(3.18)
An attempt to simplify the expression in R.H.S. of Eq. 3.18 results in
R
R
=
⎡
⎢
⎣
1 −
ρ
H
F M
ρ
L
F M
2
4
1 +
N
M
ρ N M
ρ
L
F M
ρ
H
F M
ρ
L
F M
+
N
M
ρ N M
ρ
L
F M
⎤
⎥
⎦
or,
R
R
=
⎡
⎣
(1 − β)
2
4
1 +
N
Mμ
β +
N
Mμ
⎤
⎦
(3.19)
where β =
ρ
H
F M
ρ
L
F M
and μ =
ρ
L
F M
ρ N M
.
From the above equation, it is now straightforward to identify the prime factors
that decide GMR. Equation (3.19) evidently suggests the following:
1. Two variables, β and (Mμ/N), govern GMR (R/R).
2. Spin asymmetry ratio, β should be pretty large in order to yield large GMR.
3. For a given value of β, GMR is supposed to increase with increasing (Mμ/N)
values and saturates eventually.