MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

148 Chapter 7
σ E exp[M 0 (T)/M E ] ≈ σ 0 is used) should have the same temperature dependence
as σ 0 χ. Experimentally, σ 0 χ has an approximate temperature dependence of
(1 - T/T C ) 1.8-0.9 , assuming γ ′ (susceptibility exponent for T < T C ) = γ. This is
within experimental error of the critical exponent found (Figure 7-11) for σ H
(about 0.7).
7. 2. 3 Magnetoresistance scaling at T C
At or very near T C , the magnetic properties should be described by the
critical exponent δ, where M ∝ H 1/δ when T = T C . The magnetoresistance data
for T = 262 K ≈ T C is shown in Figure 7-12, and can be fit to ρ = ρ ∞ +
1/(σ 0 + σ H nH n ), where n is an additional free parameter. The data fit well with
n = 1.2 ± 0.1, where the variation of n arises from different ranges and
weighting of the fit. Thus, if at T C , the conductivity σ ∝ M 2 then σ ∝ H 2/δ , or
δ = 2/n. This is clearly not the case since 2/n ≈ 1.6 while typically δ ≈ 4.8, or
from the data presented above and the scaling relation δ = 1 + γ/β the value
δ ≈ 4.3 is found.
The T = 262 K data fit well to the composite relation proposed by Sun et al.
[23] σ ∝ M 2 exp[M/M E ] combined with H = M δ . Above T C this relation reduces
to σ ∝ M 2 , which, as was shown above, is quite accurate. Below T C , the
exponential term dominates invalidating the simple σ ∝ M 2 relationship.