MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

180 Appendix B
corrections are included. Using these corrections, the predicted
magnetization fit to T n will necessarily have n ≈ 2 to fit the data.
At low temperatures and finite fields, a gap is expected in the spin wave
dispersion [95], predicting an exponential temperature dependence of the
magnetization at the lowest temperatures. Combined with the spin wave n =
3/2, H = 0 form, this effectively increases n [97]. The inclusion of this gap
affects the predicted ∆cPH
, T
T∆H ( ) primarily at low temperatures, as is shown in
(Figure 3-11).
The linear term in the specific heat γ is usually interpreted in terms of the
(nonmagnetic) electronic contribution to the specific heat. Spin fluctuations
are predicted to enhance γ in ferromagnetic and nearly ferromagnetic metals
[84]. For γ = γ ele (1 + λ e-p + λ mag ) where γ ele is γ expected from band calculations
and λ e-p ≈ 0.5 is the electron-phonon mass enhancement [176]. From these
values λ mag ≈ 3.1, the electron-spin fluctuation mass enhancement, is
estimated. Theoretically, in the presence of a magnetic field, spin fluctuations
are suppressed and therefore γ will decrease [203, 204]. From equation 1, these
spin fluctuations which cause the field dependence of γ are required to give a
T 2 dependence of the magnetization, thereby unifying the two interpretations
for the field dependence of γ. A decrease in the coefficient of the linear-T
term, γ, has also been observed in the weak itinerant ferromagnets ZrZn 2 and
Sc 3 In [199, 205] (which also show a T 2 dependence of the magnetization).
In conclusion, the magnetic field dependence of the heat capacity provides
a useful method for studying the low-lying excitations, and for determining
the temperature dependence of the magnetization via thermodynamic
relations. For a ferromagnetic substance the magnetic field dependence of the
low-temperature heat capacity can be a more sensitive probe of the low-