Steel, contain silicon, which is used for low frequency transformers cannot be used in high frequency transformers as the core loss due to hysteresis and eddy current loss will be phenomenal.
Ferrite has a high permeability which makes it suitable for use as a core. It also has very high resistivity. This ensures that eddy currents and hysteresis losses are kept to a minimum.
The combination of high permeability and high resistivity makes Ferrite ideal for high frequency transformer core design. The only disadvantage is that being a ceramic it is brittle and is vulnerable to cracks.
It is also used for high frequency filters such as harmonic filters.
Ferrites are classified into hard and soft ferrites. While soft ferrites are used to make transformer cores, hard ferrites are used to make permanent magnets.