Paramagnetism

Magnetic fieald in a medium. The field gets stronger, due to the present magnetic moment. Magnetic moments would be fully aligned, but thermic effects. Boltzmann factor. This is paramagnetic response. Diamagnetism: the medium increased energy, the field must decrease. Relation between angular and magnetic moment. Spin and normal magnetic moment different proportionality - Lande factor.

Bohr Magneton. Units. g is the proportionality (dimensionless) factor. Estimating the effect uses density. The density represented via rs. a0 is Bohr radius, appr. size of atoms.
Energy of a given state (magnetic substate) prop. to Jz

Evaluation of the average Jz will give the average contribution to the magnetization. The sums are like sum of power series. The average value can be obtained by differentiating the sum of the power series. For J=1/2 very simple result. x is the variable containing the exponent of the Boltzmann expression.

The magnetization characterized by chi. To obtain a reasonable expression, The Brillouin function BJ(x) must be Taylor-expanded

Evaluation of chi in detail, lower part. Above: from before

The estimate of chi.
Starting Ferromagnetism.

.....Starting Ferromagnetism. This is the origin of the exchange interaction - details next time.