Physics of Magnetism

SECTION 4.3. ANTIFERROMAGNETISM 29

where

Since the field is applied parallel to the A sublattice and antiparallel to the B sublattice,

the A-sublattice magnetization will be slightly larger then the B-sublattice magnetization.

The induced magnetization can then be obtained from

For small applied fields, one may find and by expanding the corresponding

Brillouin functions as a Taylor series in H and retaining only the first-order terms. After

some tedious algebra, one eventually finds

where is the derivative of the Brillouin function with respect to its argument. For
more details, the reader is referred to the textbooks of Morrish (1965) and of Chikazumi
and Charap (1966).
It can be inferred from Eq. (4.3.19) that at zero kelvin and that increases

sublattices, the magnetically ordered state below

with increasing temperature. The physical reason behind this is a very simple one. For both

is due to the molecular field which

leads to a strong splitting of the 2J + 1 ground-state manifold (like in Fig. 3.1.1), so that in

each of the two sublattices the statistical average value of is nonzero when H = 0. The

absolute values of are the same for both sublattices, only the quantization directions of

are different because the molecular fields causing the splitting have opposite directions.

If we now apply a magnetic field parallel to the easy direction, the total field will be slightly

increased for one of the two sublattices, for the other sublattice it will be slightly decreased.

This means that the total splitting of the former sublattice is slightly larger than in the latter

sublattice. When calculating the thermal average of both sublattices (Eq. 3.1.9), one

finds that there is no difference at zero kelvin since for both sublattices only the lowest level

is occupied and one has

and consequently

However, as soon as the temperature is raised there will be thermal population of the

2 J + 1 levels. Because the total splitting for the two sublattices is different, one obtains

different level occupations for both sublattices. The corresponding difference in the thermal

averages becomes stronger, the lower the population of the two lowest levels. In other

words, although in both sublattices the statistical average decreases with increasing

temperature, the difference between for the two sublattices increases and causes the

susceptibility to increase with temperature (see Fig. 4.3.2).