MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

132 Chapter 7
for T > T C . The regions of negative slope on the M 2 vs. H/M plot (χ 3 > 0)
make the scaled T > T C curve also approach M 2 = 0 with a negative slope. For
T - T C < 0.01 T C , the scaled data break away from this region of negative slope
to giving a nearly straight curve typical of a ferromagnet. This crossover in
scaling suggests that the true critical regime only begins with |T - T C | < 0.01
T C , and that the exponents reported here, which will be quite useful in
modeling the magnetization, are effective rather than true critical exponents.
The true critical regime is reached when the magnetic critical fluctuations
become as large as the net magnetization itself.
The experimental value of the critical exponent δ, H = M δ when T = T C ,
depends strongly on the demagnetization correction, and therefore not
analyzed here. The scaling relation δ = 1 + γ/β can be used to estimate δ. The
other critical exponents γ and β do not vary significantly when a different
demagnetization correction is used.
7. 1. 1 Spontaneous magnetization exponent
The square of the magnetization M 2 , plotted vs. H/M (Figure 7-1)
facilitates understanding the critical behavior of La 0.67 Ca 0.33 MnO 3 . The
isotherm which extrapolates to M 2 = 0, H/M = 0 is the critical isotherm T = T C .
In this way T C = 262.2 K ± 0.5 K is estimated. The uncertainty in T C is due to
the uncertainty of the demagnetization correction. The isotherms below T C
should be approximately linear and intersect H/M = 0 at M 0 . From these
M 0 (T) the (magnetic order parameter) critical exponent β ≈ 0.30 and
T C = 262.2 K can be estimated by fitting M 0 (T) ∝ (1 - T/T C ) β (Figure 7-3).
The fit is not as good as this method, in the same apparatus, allows
(Appendix A), perhaps due to the contributions in low fields from the
magnetocrystalline anisotropy, which have been ignored. Therefore, the