MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

Electronic and Magnetic Measurements 61
exponent γ = 1. Along the critical isotherm T = T C , H = 4bM 3 so the critical
exponent δ = 3.
3.2.2.2.6 Arrott Plot
According to the Landau equation of state H/M = 2a(T - T C ) + 4bM 2 , a plot
of M 2 vs. H/M at a constant temperature gives a straight line. At T C , this line
intersects the origin. The M 2 = 0 intercept gives the inverse susceptibility
1/χ 0 (H = 0) while the H/M intercept gives the spontaneous magnetization
2
M0 (H = 0).
In real systems near the critical point, non mean field critical exponents
are observed. Thus the plot of M 2 vs. H/M (Arrott plot) will not necessarily
be straight lines, but allows a visual analysis of the data [94]. The T C
determined from the Arrott plot is the isotherm that extrapolates to the
origin. Likewise, the extrapolation to the axis intercepts give the H = 0
spontaneous magnetization M 0 (T < T C ) and inverse susceptibility
1/χ 0 (T > T C ) and allows a visual exstimation of the error. From these M 0 (T)
and χ 0 (T) the critical exponents β and γ can be estimated by fitting
M 0 (T) ∝ (1 - T/T C ) β and χ 0 (T) ∝ (T/T C - 1) -γ .
If the assumption of scaling is incorrect, such as a crossover from one
scaling region to another as the temperature changes, then the entire data will
not scale with the same exponents. In this case, the method described above
is better for characterizing the separate regions. Such a crossover is observed
in SrRuO 3 where β appears to change from 0.32 to 0.38 (Appendix A) so that
the entire data does not scale very well with a single average value for β.
3.2.2.2.7 The Curie temperature
Because the Curie temperature affects many of the properties, there are
several ways of measuring it. One of the simplest is finding the paramagnetic