58
S. J. Blundell
(a)
(b)
p x
p y
p z
x
x
x
z
y
z
z
y
y
d xy
d zx
d yz
d z 2
d x 2 −y 2
z
x
y
x
y
z
z
x
y
z
x
y
z
x
y
Fig. 2.10 Angular representation of a p-orbitals and b d-orbitals
| p x =
|1 + | − 1
√
2
| p y =
|1 − | − 1
√
2i
| p z = |0 .
(2.52)
What we see here is the phenomenon of quenching of angular momentum and it is
interesting that it shows up even in the unfamiliar setting of the ‘balloon animals’
of p-orbitals. Of course in magnetism we are usually more interested in considering
d-orbitals or f -orbitals but the same principles hold. For example, the equivalent
equations for the d-orbitals [see Fig. 2.10b] are
|d xy =
|2 − | − 2
√
2i
|d x 2 −y 2 =
|2 + | − 2
√
2
|d yz =
−|1 − | − 1
√
2i
|d zx =
−|1 + | − 1
√
2
|d z 2 = |0 .
(2.53)
2.4.3 Jahn–Teller Effect
It can sometimes be energetically favourable for, say, an octahedron to spontaneously
distort as shown in Fig. 2.11 because the energy cost of increased elastic energy is
balanced by a resultant electronic energy saving due to the distortion. This phe-