MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

178 Appendix B
are vectors. Thus for an ideal, simple experiment, the sample would be very
soft magnetically (no magnetic hysteresis) and the magnetic field would be
aligned in the magnetic easy direction to keep M and H parallel. If possible,
the magnetic and heat capacity experiments should be done on the same
sample in the same direction; although, in principle different samples should
give the same result since both M and C P in a reversible sample should not
depend on the microstructure. In order to use equation 1 to relate the
reversible magnetization from the measured specific heat, it is assumed that
effects due to the field dependence of the magnetocrystalline anisotropy are
insignificant.
The simplest spin wave model (section 3.2.2.2.8) predicts a T 3/2 dependence
of the magnetization at low temperatures:
MHT ( , ) T
≈1− MH ( , 0)
3 ( H)
⎛ ⎞
⎜ ⎟
⎝ Θ ⎠
with Θ 3/2 ≈ 2.42T C = 400K [95, 186] for SrRuO 3 . Corrections due to H ≠ 0 and
T > 0 can also be calculated [95]. The Stoner/Wohlfarth theory of magnetism
(section 3.2.2.2.2) [81] predicts a somewhat different temperature dependence:
MHT ( , ) T
≈1− MH ( , 0)
( H)
⎛ ⎞
⎜ ⎟
⎝ Θ ⎠
(Θ 2 ≈ √2T C = 231K for SrRuO 3 ) due to single (k-space) particle excitations.
The Maxwell relation together with the observed magnetic field
dependence of the specific heat above 4 K, γ ´HT, implies that the second
2
⎛ ∂ M⎞
derivative of the magnetization with respect to temperature, ⎜ 2 ⎟ , is a
⎝ ∂T
⎠ H
constant. This result is consistent with the dominant T 2 temperature
dependence of the reversible discussed above.
In order to make quantitative comparisons between the specific heat data
and the magnetization data, equation 1 can be integrated with respect to H
2
2
3 2
2
(2)
(3)