Ferromagnetism and anti-ferromagnetism.

    The relationship between ferromagnetism and what is called "anti-ferromagmetism" is not simple.   Ferromagnetism occurs in metals and is driven by the tendency of electrons to, in some circumstances, use spin alignment in order to avoid each other. In this way the overall coulomb energy associated with electron-electron repulsion can be diminished.
     Antiferromagnetism, on the other hand, usually involves electrons that are confined (that is, electrons in non-metallic systems). Confinement has increased the kinetic energy of these electrons. The electrons seek a way to lower their confinement-related kinetic energy.   Communicating through their spins, the electrons find a way to lower their KE through an inherently collective, cooperative behavior involving spin alignment. In an antiferromagnet, each spin tends to point in the opposite way of its nearest neighbors. Antiferromagnetism is not just the alternating of classical spins.  It is a sophisticated many-electron quantum collective state.
    The names, FM and AFM,  tend to be rather misleading. The magnetism part makes sense, however, ferro is just from an ancient greek name for a material in which magnetism was observed long ago. It tells us nothing about the underlying origin. One might instead call it magnetism from spontaneous spin alignment, or just "spontaneous magnetism".
     More importantly, anti-ferromagnetism is not really the opposite of ferromagnetism. It is its own collective phenomenon with its own origins. These are very different and probably even more intriguing and subtle than those of ferromagnetism. Anti-ferromagetism involves a collective state with broken symmetry which arises to enable electrons to lower their quantum kinetic energy.