Antiferromagnetism

Below $T_{N}$ the two sublattices of an antiferromagnet spontaneously magnetise in the same way as a ferromagnet but the net magnetisation is zero due to the opposing orientation of the sublattice's magnetisation. If an external field, $H$, is applied a small net magnetisation can be detected. The resultant magnetisation depends upon the orientation of the field with respect to the magnetisation or spin axis.

If the field is applied parallel to the spin axis the zero-field value of magnetisation of one sublattice, A, is increased by $\Delta M_{A}$ whilst the other, B, is decreased by $\Delta M_{B}$. The net magnetisation in the direction of the field is then

$$M = \vert \Delta M_{A} \vert + \vert \Delta M_{B} \vert$$ (3.5)

If the field is applied perpendicular to the spin axis each sublattice magnetisation is turned from the spin axis by a small angle, $\alpha$, as shown in Figure 3.6. The spins reorient by angle $\alpha$ given by

$$2\left(H_{mA}\sin\alpha\right) = H$$ (3.6)

where $H_{mA}$ is the molecular field given by $H_{mA} = 2AM$ where $A$ is the exchange energy and the resultant magnetisation is then equal to

$$M = 2M_{A}\sin\alpha$$ (3.7)

This magnetisation is linear with applied field with no hysteresis.

Figure 3.6: Rotation of sublattice magnetisation under an applied field, $H$, perpendicular to the spin axis.