Physics of Magnetism

30 CHAPTER 4. THE MAGNETICALLY ORDERED STATE

We will now consider the susceptibility of an antiferromagnetic single crystal with

the magnetic field applied perpendicular to the easy direction. The applied field will then

produce a torque that will bend the two sublattice moments away from the easy direction, as

is schematically shown in the inset of Fig. 4.3.2. This process is opposed by the molecular

field that tries to keep the two sublattice moments antiparallel. The total torque on each

sublattice moment must be zero when an equilibrium position is reached after application

of the magnetic field. For the A-sublattice moment, this is expressed as follows:

with

with

A similar expression applies to the torque experienced by the B-sublattice moment but

in a direction opposite to Eq. (4.3.22) can be written as

The components of the two sublattice moments in the direction of the field lead to a net

magnetization equal to

After combining Eqs. (4.3.24) and (4.3.25), one obtains

Since is negative, we may write

This result shows that the susceptibility of an antiferromagnet measured perpendicular to the

easy direction is temperature independent and that its magnitude can be used to determine

the absolute value of the intersublattice-molecular-field constant.

If the applied field makes an arbitrary angle with the easy direction, the susceptibility



in the direction of the field,



and perpendicular components:

can be calculated by decomposing the field into its parallel

The magnetization in the direction of the field is then given by