Ferromagnetic materials like iron have extremely high relative permeability ($\mu_r \approx 1000 - 5000$).

Diamagnetic (e.g., Copper, Silver) and paramagnetic (e.g., Aluminum) materials have $\mu_r \approx 1$, providing negligible change to magnetic field strength.

Soft iron is preferred over hard iron because it easily magnetizes and demagnetizes, minimizing hysteresis loss.

Dramatically increases magnetic flux density with the same electric current input.

Reduces energy consumption required to create strong electromagnetic fields.

Introduces core losses (hysteresis loss and eddy current loss) in AC applications.

Causes magnetic saturation beyond a certain current threshold.

Electromagnets and relay coils.

Transformers, electric motors, and generators.

Solenoid valves and magnetic actuators.

Copper and Silver are diamagnetic materials with $\mu_r < 1$, slightly weakening or having no noticeable effect on the field.

Aluminum is paramagnetic with $\mu_r \approx 1.000022$, producing virtually no amplification of the magnetic field.

Iron is ferromagnetic with $\mu_r \gg 1$, multiplying the magnetic field strength immensely.