Pauli paramagnetism
/ POW-lee PAIR-uh-mag-net-ism /
Every electron is a tiny magnet, with a north and south pole pointing one of two ways — call them "up" and "down." Put a metal in a magnetic field and you'd expect all these little magnets to swing into line, giving a strong response. They mostly don't, and Pauli paramagnetism is the story of why the metal's electron gas responds only feebly.
The reason is the no-sharing rule. In the absence of a field, equal numbers of electrons point up and down, and they're stacked all the way to the Fermi energy. A field makes one direction slightly cheaper in energy, but to flip, an electron must find an empty state of the other kind — and almost all of them are taken. Only the thin sliver near the Fermi energy can flip, so the metal gains just a small, steady magnetization.
It matters because it explains a long-standing puzzle: why ordinary metals like sodium are so weakly magnetic, far weaker than a naive count of their electron magnets would suggest. The honest caveat: this is only the spins' contribution. The electrons' orbital motion adds a small opposing effect, and in magnetic metals like iron entirely different, far stronger physics takes over.
Sodium metal is paramagnetic, but only just — a magnet barely tugs at it. If every one of its free electrons could line up its little magnet, the pull would be far stronger; the no-sharing rule lets only a handful near the Fermi energy respond, and the rest stay locked in opposing pairs.
Sodium responds only weakly to a magnet — most of its electron magnets are locked in opposing pairs.
"Paramagnetism" just means a material is weakly pulled toward a magnet (the opposite of being pushed away). Pauli paramagnetism is the specific, temperature-insensitive version that comes from a free-electron gas, quite distinct from the temperature-dependent paramagnetism of isolated atomic magnets.