SECTION 4.3. ANTIFERROMAGNETISM 27
The temperature dependence of each of the two sublattice moments can be obtained
by means of Eq. (3.1.9):
with
A similar expression holds for
In analogy with Eq. (4.2.3), it is relatively easy to derive expressions for the sublattice
moments in the high-temperature limit:
where
and
for H =
vanishes:
The two coupled equations for will lead to spontaneous sublattice moments
0) if the determinant of the coefficients of and
The temperature at which the spontaneous sublattice moment develops is called the Néel
temperature Solving of Eq. (4.3.9) leads to the expression where
is the correct solution. We know that and The solution
is not acceptable since, if this leads to a negative value of the magnetic-ordering
temperature which is unphysical.
For temperatures above
we may write
Since we find
where the paramagnetic Curie temperature is now given by