Physics of Magnetism

SECTION 7.2. SUSCEPTIBILITY ENHANCEMENT 65

Since

one may write

If the state of lowest energy corresponds to p = 0 and the system

is non-magnetic. However, if the 3d band is exchange split (p >

0), which corresponds to ferromagnetism. The latter condition is the Stoner criterion for

ferromagnetism, which is frequently stated in the more familiar form (Stoner, 1946)

By means of this model, it can be understood that 3d magnetism leads to non-integral
moment values if expressed in Bohr magnetons per 3d atom,
The conditions favoring 3d moments in metallic systems are obviously: a large value
for but also a large value for The density of states of the s- and p-electron
bands is considerably smaller than that of the d band, which explains why band magnetism is
restricted to elements that have a partially empty d band. However, not all of the d-transition
elements give rise to d-band moments. For instance, in the 4d metal Pd, the Stoner criterion
is not met, although it comes very close to it.

7.2. SUSCEPTIBILITY ENHANCEMENT

The same formalism as used above can also be employed for calculating the magnetic

susceptibility at zero temperature in a field H when the magnetic state is not stable with

respect to the state without magnetic moment. The field will favor electron states with spin

direction parallel to the field direction. If the latter is in the spin-up direction, the field will

lead to a repopulation of the band states by transfer of electrons from the spin-down to the

spin-up band. If p is the fraction of electrons transferred, we can use again Eq. (7.1.3) to

calculate the energies involved in the electron transfer. Because a magnetic field is present,

we have to add a Zeeman term to the magnetic energy. This leads to

The equilibrium condition is

After differentiation of the expression for the energy, we find

where is the magnetic susceptibility per atom, and where represents the “bare”

unenhanced magnetic susceptibility which is given by