Magnet
Many materials have unpaired electron spins, and the majority of these materials are paramagnetic. When the spins interact with each other in such a way that the spins align spontaneously, the materials are called ferromagnetic (what is often loosely termed as magnetic). Because of the way their regular crystalline atomic structure causes their spins to interact, some metals are ferromagnetic when found in their natural states, as ores. These include iron ore (magnetite or lodestone), cobalt and nickel, as well as the rare earth metals gadolinium and dysprosium (when at a very low temperature). Such naturally occurring ferromagnets were used in the first experiments with magnetism. Technology has since expanded the availability of magnetic materials to include various man-made products, all based, however, on naturally magnetic elements.
Abrasive
Typically, materials used as abrasives are either hard minerals (rated at 7 or above on Mohs scale of mineral hardness) or are synthetic stones, some of which may be chemically and physically identical to naturally occurring minerals but which cannot be called minerals as they did not arise naturally. (While useful for comparative purposes, the Mohs scale is of limited value to materials engineers as it is an arbitrary, ordinal, irregular scale.) Diamond, a common abrasive, for instance occurs both naturally and is industrially produced, as is corundum which occurs naturally but which is nowadays more commonly manufactured from bauxite. However, even softer minerals like calcium carbonate are used as abrasives, such as "polishing agents" in toothpaste.