This was a fun one to do! How far did you get? #physics #magnet #5levels #explained

I'm going to explain magnets at five levels. Can you keep up? Level one. A magnet is a special kind of rock, metal, or other material that can pull things towards it without touching. But they don't work on everything. Metals like iron or nickel are more magnetic than others. Put two magnets together, and sometimes they'll pull together. Other times they'll push apart. That's because magnets have north and south poles. Ops, it pulls attract while the same poles repel. Now, you might think that magnets rely on electricity inside of them that will eventually run out, but a permanent magnet can stay magnetic for an extremely long time unless it gets too hot or something disrupts its magnetism. Level two. Inside a permanent magnet are a bunch of tinier magnets. Atoms have a nucleus surrounded by electrons, and those electrons behave like tiny magnets. Usually, though, their magnetic effects cancel out. But in substances like iron, cobalt, or nickel, large groups of those electrons can prefer to align. If you encourage that alignment, say with a strong magnetic field, more groups point in the same direction. And in a permanent magnet, the material's structure makes that alignment difficult to turn around, almost like it has frozen into place. And that's why cutting a magnet in half just makes two smaller magnets, each with its own north and south pole. The alignment can still be broken, though, by a strong opposing field or enough heat to disrupt the order. Level three. Fundamentally, a magnet is a quantum mechanical object. Electrons aren't tiny spinning balls of charge, but they have an intrinsic property called spin, which gives them a tiny magnetic field. And electrons are also fermions, meaning they obey the poly exclusion principle. Two electrons can't occupy the same quantum state. Electrons with the same spin, therefore, occupy different spatial states, making them less likely to be found close together. And that matters because electrons are pale one another, so material can lower its energy by having more electrons with one spin direction than the other. But there's a cost. They can't all fit into the lowest energy states, so some must occupy higher ones. Whether the material becomes magnetic depends on which effect wins. The energy saved by reducing electron repulsion or the energy spent filling higher states. If the saving wins, the electrons favor one spin direction. To make that magnetism permanent requires the material to resist having its alignment reversed. Level four. For a crystal, the poly exclusion principle means the many electron wave function must be anti-smetric under exchange. Put another way, swapping two electrons changes the wave function by a minus sign. So if two electrons have the same spin, the spatial part of their combined wave function must be anti-smetric. This suppresses the chance of finding them close together lowering their coolant energy. But spin polarizing more electrons also forces some into higher energy states. A spin imbalance is stable only if that reduction beats the band energy cost. But that becomes easier when many electron states are packed into a narrow energy range near the highest occupied energy. For a fixed interaction strength, there's a threshold density of states above which the unpolarized state becomes unstable. This is hilariously called the stoner criterion. Of note, is that a uniformly magnetized object also produces an external field which stores energy. So a large magnet may split into regions whose magnetizations point in different directions. But not enough to cancel out. These are domains, and they reduce the energy stored outside the material. Level five. Ferromagnetism, broadly speaking, is a many-body instability of an interacting electron system. The electrons occupy block states extending throughout the crystal, while fermionic anti-symmetry generates a same spin exchange hole that reduces coolant energy. Spin polarization lowers the interaction energy, but redistributes occupation between spin-resolved bands raising the band energy. The stoner model is the mean-fueled version of that competition. In iron cobalt and nickel, though, the relevant D electrons are neither fully localized nor weakly interacting. Rather, their behavior depends on bandwidth, intraatomic hummed coupling, crystal field splitting, orbital hybridization, and dynamical electronic correlations. Atomic scale moments can therefore coexist with itinerant block electrons, so a rigid stoner splitting is only an approximation. Once magnetized, the system selects a direction in spin space. Spin orbit coupling ties that direction to the lattice, exchange stiffness penalizes spatial variation, and the non-local demagnetizing field favors flux closure. Their competition produces single domain states, multi-domain textures, and find it with domain walls, and you have a magnet. So how far did you get?