MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

Critical Transport and Magnetization of La 0.67 Ca 0.33 MnO 3
exponent for σ 0 and σ H to be 0.6 and -0.6 respectively. Experimentally,
however σ 0 ∝ (1 - T/T C ) 1.8 and σ H ∝ (1 - T/T C ) 0.7 .
An M 2 dependence of the magnetoresistance (as opposed to the
magnetoconductance) where ρ ≈ ρ0 - ρMM 2 2
≈ (ρ0 - ρMM0 ) - 2ρMχM 0H below TC ,
2
is also inconsistent. For low fields ρ = (ρ∞ + 1/σ0 ) - (σH /σ0 )|H| is found
2
experimentally, which has a field dependent term (σH /σ0 ), which varies as
(1 - T/T C ) -2.9 . This is quite different from 2ρ M χM 0 which has a critical exponent
of β - γ ≈ -0.6.
Below T C , in agreement with previous work [23, 107], the conductivity is
exponentially dependent upon M. Removing the slowly varying
contribution due to ρ ∞ , this model predicts σ(H,T) = σ E exp[M(H,T)/M E ] ≈
σ 0 + σ H H. For H = 0 this reduces to σ 0 = σ E exp[M 0 (T)/M E ]. The experimental
relationship M 0 (T) ∝ (1 - T/T C ) β with β = 0.3 can be used to fit the magneto-
resistance data. The higher quality of this fit compared to the M 2 fit is shown
in Figure 7-10, with M E ≈ 0.4 µ B (M E = 1.0 µ B in [107]) and σ E ≈ 4 × 10 -3 mΩcm -1 .
An exponential dependence of the conductivity may suggest a tunneling
mechanism is responsible. Tunneling conductivity depends exponentially on
the length of the tunneling barrier. If, in some way, this barrier is decreased
by an increase in the magnetization, then the conductivity will depend
exponentially on M as observed for large M. Spin dependent tunneling is
reported to be the mechanism of the large domain boundary
magnetoresistance observed in these materials [140].
Furthermore, the temperature dependence of σ H can also be explained
with the exponential model. According to this model, the field dependent
conductivity
d d M M
σH σ σE
dH dH
σσ E σE σχ
e
/ E
= = 0 dM
= = 0
M dH M
(where
E
E
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