You can observe ferrimagnetism in a naturally occurring oxide of iron called magnetite, with chemical formula Fe3O4. It remains magnetic as long as it is kept below a certain temperature called the "Curie" temperature. The magnetism is a result of the alignment of very tiny regions in the material called "magnetic domains" or "magnetic moments" in the material. For ferrimagnetism, these magnetic moments are in opposite directions.
Ferromagnetism occurs spontaneously in some elements such as iron, nickel and cobalt. In these elements, the magnetic moments align in the same direction and parallel to each other to produce strong magnets. Temperature affects the alignment of the magnetic moments. The maximum temperature at which ferromagnetism still exists in a material is the Curie temperature. For some ferromagnets, it can be as high as 1,200 degrees Celsius.
The highest Curie temperatures are obtained with ferromagnetic materials, which are usually metals or alloys of metals, rather than with ferrimagnetic materials. Cobalt, a ferromagnet, for example has a Curie temperature of 1,131 degrees Celsius versus 580 degrees Celsius for magnetite, which is a ferrimagnet.
Usually magnetism and superconductivity are antagonistic with magnetism tending to destroy the presence of superconductivity. Recently, however, physicists have found that ferromagnetism and superconductivity can coexist in some materials at low temperatures. Understanding how this happens is one of the challenges in materials science and physics.
Some magnetic moments in ferrimagnetism point in the same direction and some in the opposite direction. However, in ferromagnetism they all point in the same direction. The implication is that stronger magnetic fields can be generated with a ferromagnet than with a ferrimagnet. Ferromagnets are often described as "permanent" magnets and are of the type such as those used to hold paper on refrigerator doors.