MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

Electronic and Magnetic Measurements 65
Figure 3-10, depends on the temperature T, thus altering the temperature
dependence of the magnetization to have an effective power higher than 3/2
[97]. The Bose-Einstein integral function [95] F P (x) is given by F P (x) =
and ζ(P) =
−
e
n
∞ n x
∑ P
n=
/
1
∞
1
∑ (e.g. ζ(3/2) = 2.612 and ζ(1/2) = -1.460). The correction C(t) to
1 n P
n=
the T 3/2 contribution to the heat capacity is similar: C(t) = [F 5/2 (t) + 4F 3/2 (t)/5t +
4F 1/2 (t)/15t 2 )]/ζ(5/2), where t = k B T/gµ B H. The correction factor C(t) is shown
in Figure 3-11. Due to the Maxwell relation the increase in the effective
power in M(T) also increases the effective power of dc/dH (T).
Correction Factor C(t)
1.0
0.8
0.6
0.4
0.2
1.0
0.8
0.6
0.4
0.2
0.0
0.0 0.5 1.0 1.5 2.0
0.0
0 2 4 6 8 10
k B T/gµ B H
Figure 3-11 Correction factor to the T 3/2 contribution of the
heat capacity in the spin wave theory due to a magnetic field
H.