Hard ferrites have wide coercive forces, in another terms more field is required for demagnetizing. They are widely used in permanent magnets, and have a few kOe of Hc .
Soft ferrites have small coercive fields in the range of ~100 Oe. They are mainly used as electronic sensors, ferrite cores with low losses and stability. Computer technology have a usage in mainboards with soft ferrite core capacitor.
Pls. find attached a file which gives the required points of difference between the hard and soft cores in a tabular form.
Area under MH plot for soft ferrite is negligible, on the other hand for hard ferrite is very large. Example of hard ferrites are Co-Zn ferrites and soft ferrites are Ni-Zn ferrites.
The difference between soft and hard ferrites lies in essence in the nature and strength of the magnetic anisotropy, that is, the crystalline structure of the material. Hard ferrites have hexagonal atomic structure and uniaxial anisotropy. Soft ferrites have cubic symmetry and, consequently, three easy axis. Uniaxial anisotropy is pre-requisite for hard magnetic behavior. With cubic anisotropy it is not generally possible to achieve very high values of the coercive field. It is instead possible in cubic ferrites to modulate the anisotropies brought about by the Fe ions, so as to minimize the resulting anisotropy, thereby maximizing the material permeability and minimizing the coercivity.
It is really very easy to find data about hard and soft ferrites in literature. The most general is in http://en.wikipedia.org/wiki/Ferrite_%28magnet%29
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