Chemistry Reference
In-Depth Information
30
20
10
0
100
200
T
(K)
Figure 7.7
The experimentally measured variation of the susceptibility
χ
of a single
domain sample of the antiferromagnetic crystal, MnF
2
. The susceptibility,
χ
, drops to zero when the applied field is parallel to the magnetisation
direction, but remains approximately constant below the Néel temperature
when
H
⊥
M
. (Experimental data after Trapp and Stout, © 1963 by the
American Physical Society.)
a magnetic moment, so a spin-polarised neutron beam can detect the
additional order in a spontaneously magnetised crystal, with two dis-
tinct magnetic sublattices, compared to a disordered crystal where the two
sublattices are equivalent.
Because
M
0 in an antiferromagnet for zero applied field, it is still pos-
sible to define the susceptibility,
=
, below the Néel temperature,
T
N
.The
susceptibility is found to depend on the direction of the applied field
H
0
relative to the magnetisation direction, as illustrated in fig. 7.7. When the
applied field is perpendicular to the magnetisation direction, a net mag-
netisation can be achieved by effectively tilting the magnetic moments
slightly along the field direction. Tilting each spin through a small angle,
θ
χ
, gives a net magnetisation proportional to sin
θ
, that is, the magnetic
energy gained through interaction with the field
. By contrast, when
the field is applied parallel to the magnetisation direction, tilting each spin
through an angle
∼
θ
would cost the same amount of energy in terms of dis-
rupting the two sublattices, but now only gains an energy proportional to
(
θ
1
−
cos
θ)
through interaction with the applied field, that is, the energy
2
. This becomes progressively less advantageous as the tem-
perature decreases, so that
gained
∼
θ
χ
→
→
0as
T
0, while it can be shown
that
is approximately constant below
T
N
. In practice, the anisotropy
in susceptibility is only observed in single domain samples, where all
spins on a given sublattice point along the same direction. Most macro-
scopic samples consist of many domains, each with its own magnetisation
direction. The low temperature suscepibility is then isotropic, and equal to
χ
⊥
