The Stoner criterion is a condition to be fulfilled for the ferromagnetic order to arise in a simplified model of a solid. It is named after Edmund Clifton Stoner.

Stoner model of ferromagnetism

Ferromagnetism ultimately stems from Pauli exclusion. The simplified model of a solid which is nowadays usually called the Stoner model, can be formulated in terms of dispersion relations for spin up and spin down electrons,

where the second term accounts for the exchange energy) is the dimensionless density is the dispersion relation, the system prefers to remain paramagnetic, polarized ground states occur. It can be shown that for

density of states at the Fermi energy.

even before the Stoner criterion is fulfilled.

Relationship to the Hubbard model

The Stoner model can be obtained from the Hubbard model by applying the mean-field approximation and the product of spin-up and spin-down fluctuations is neglected. We obtain

With the third term included, which was omitted in the definition above, we arrive at the better-known form of the Stoner criterion

Notes

References

• Stephen Blundell, Magnetism in Condensed Matter (Oxford Master Series in Physics).