Materials respond differently to an applied magnetic field because their microscopic magnetic moments and electronic structure respond differently.

Magnetization

The collective magnetic response of a material is described by its magnetization $\mathbf M$, the magnetic dipole moment per unit volume.

In a simple linear material,

$$\mathbf M=\chi_m\mathbf H,$$

where $\chi_m$ is the magnetic susceptibility.

Diamagnetic materials

Diamagnetic materials develop a weak magnetization opposing the applied field. Their susceptibility is negative and the effect usually disappears when the applied field is removed.

Paramagnetic materials

Paramagnetic materials have microscopic moments that tend to align weakly with an applied field, giving a small positive susceptibility.

Ferromagnetic materials

Ferromagnetic materials can produce a much stronger response because neighboring moments form domains that can align collectively. Their behavior is nonlinear and can retain magnetization after the external field is removed.

The simple relation between magnetic field and material response therefore depends strongly on the material. Ferromagnetic nonlinearity leads directly to saturation and hysteresis phenomena.