Spin, like mass or charge, is an intrinsic property of atoms: the particles rotate around an axis in either a clockwise manner (often described as "down") or anticlockwise ("up"). Based on their spin, atoms can react to magnetic fields in different ways, for example by aligning themselves with other atoms in a specific pattern.
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The spin of many atoms together in a magnetic material that is exposed to a magnetic field can reach an equilibrium state, where all the atom spins are aligned; or the atoms can adopt dynamic behavior, where the spins across many atoms create a wave-like pattern.