Susceptibility Below the
Neel Temperature
There are two situations: with the applied
magnetic field perpendicular to the axis of
the spins; and with the field parallel to the
axis of the spins.
At and above the Neel temperature the
susceptibility is nearly independent of the
direction of the field relative to the spin axis.
For Ba perpendicular to the axis of the spins
we can calculate the susceptibility by
elementary considerations.
The energy density in the presence of the
fields is, with
M=
|
MA
|
=
|
MB
|
.
U=μ M A. M B−Ba.
(
MA+MB
)
≅−μ M 2
[
1−1
2
(
2φ
)
2
]
−2BaMφ(1)
Where,
2φ
is the angle the spins make with
each other.
The energy is minimum when
dU
dφ =0=4μ M2φ−2BaM ; φ=Ba
2μM ,(2)
So that
χ⊥=2Mφ
Ba
=1
μ(3)
In the parallel orientation the magnetic
energy is not changed if the spin systems A
and B make equal angles with the field.
Thus, the susceptibility at T-0 K is zero:
χ∥
⟨
0
⟩
=0(4)
