MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

150 Chapter 7
σ = σ E exp[M(H,T)/M E ], which gives at low T and H,
∆ρ/H = -χexp[-M 0 /M E ]/M E σ E ; requiring χ = 32.9 × 10 -5 emu/Oe cm 3 . A mag-
2 2 2
netoresistive model ρ = (ρ∞ + 1/σ0 ) - (σM 2/σ0 )M giving ∆ρ = -2χσM2M0H /σ0 is
2
significantly worse since it would predict χ = -∆ρσ0 /(2σM2M0H ) = 2 × 10 -7
emu/Oe cm 3 .
In a similar manner, the correlation between the magnetization and the
resistivity should contribute to the T 2 contribution (section 4.2.1.2) to the low
temperature resistivity ρ = R 0 + R 2 T 2 + … . This is because the magnetization
can be approximated with M = M 0 (1 - (T/Θ) 2 ) for these temperatures (where
Θ ≈ 500 K, section 4.1.1), giving ρ(T) ∝ -M(T) ∝ T 2 . For the σ = σ 0 + σ M 2M 2
model ρ(T) - ρ(0) = -ρ 2 (σ(T) - σ(0)) = 2σM 2ρ 2 2 2 -7 -2 2
M0 (T/Θ) ≈ 1.26 × 10 mΩcm K T .
For the ρ = exp[-M(H,T)/M E ]/σ E model ρ(T) - ρ(0) = exp[-M 0 /M E ]/σ E ×
(T/Θ) 2 M 0 /M E ≈ 1.14 × 10 -6 mΩcm K -2 T 2 . Both of these proposed contributions
are less than the observed value (section 4.2.1.2) R 2 ≈ 1.96 × 10 -5 mΩcm K -2 ,
suggesting that scattering mechanisms such as electron-electron, or electron-
magnon scattering dominates the R 2 T 2 term.
7.3 Conclusion
A scaling relation has been found that satisfactorily characterizes the
magnetic and magnetoresistive properties of La 0.67 Ca 0.33 MnO 3 near T C .
However the scaling exponents, particularly γ < 1, show that critical scaling
has not been reached even though the measurements reach 0.01 T/T C where
simple ferromagnets are expected to exhibit critical scaling.
An unusual positive nonlinear magnetic susceptibility, which does not
disrupt the scaling, is also observed. The positive non-linear susceptibility
and susceptibility exponent γ < 1 may result from the coupling of the