Spin
Have you ever wondered how magnets work? How is it possible that some materials, like iron, show magnetic properties, while other materials, like wood, seem to ignore magnetism entirely? It turned out that the answer to these questions lies in a strange property of all particles called spin.
One could say that there are two types of momentum in the macroworld – “classical” momentum, which objects acquire by moving in a certain direction, and angular momentum, better known as rotation. However, objects from the microworld have an additional type of momentum – intrinsic angular momentum or spin. Spin is often compared to classical rotation (hence the name “spin”). However, this comparison is not accurate, since objects with spin do not actually rotate, the rotation is purely “intrinsic”.
Spin is typical for elementary particles, composite particles and atomic nuclei. The unit of spin is the reduced Planck constant (ħ). Particles with half-integer spin (1/2 ħ, 3/2 ħ, 5/2 ħ, etc.) are called fermions. Particles with integer spin (1 ħ, 2 ħ, 3 ħ, etc.) are called bosons. We are going to learn more about these particles in the following chapters.
But what is the connection between spin and magnetism? It turns out that particles with spin behave like peculiar tiny magnets by generating weak magnetic fields. That is why objects from the macroworld, which are composed of many of such “small magnets”, are magnetic. But that does not explain why only a handful of materials are magnetic, when all macroscopic materials are made up of these tiny magnets. How is that possible?
The reason is that magnetic fields generated by individual particles (mostly electrons, whose magnetic fields are much stronger than those of protons or neutrons) often cancel out, which in turn makes most materials non-magnetic.
For instance, if an atomic orbital is completely filled, electrons in this orbital have opposite spins, which causes their magnetic fields to cancel out. This means that no atom with filled or almost filled orbitals can be magnetic. For an atom to be magnetic, it must have half-filled orbitals so that the magnetic fields of individual electrons reinforce one another.
However, not all materials made up of magnetic atoms exhibit magnetic properties. This is due to the configuration of individual atoms. Many materials have their atoms arranged so that their magnetic fields cancel out. Only a fraction of materials has the atoms arranged so that their magnetic fields mutually reinforce. This is why magnetic materials are so rare.
In the previous paragraphs, particles were compared to tiny magnets. However, this comparison is not completely accurate, because magnetic fields created by particles behave rather oddly. We can demonstrate this on a simple experiment. Say we have two axes: x and y, which are perpendicular to each other. Now let us take a particle which has a spin of 1 pointing in the direction of the x-axis (i.e., if we were to measure its spin in the direction of the x-axis, we would get 1). But what happens if we try to measure its spin (magnetic field) in the y-axis? If we took a classical magnet, pointed it in the direction x and conducted the same experiment, we would measure no magnetic field pointing in the y direction, of course (since the x-axis is perpendicular to the y-axis). However, particles behave in a completely different way. If we measure the spin of a particle in the y direction, half the time we get spin 1, the other half of the time we get spin -1. Even if we try to measure the spin in different directions, we always get either 1 or −1. However, the average of the values we get is always equal to the value we would expect to get with classical magnets. We can demonstrate this rule on our particle. The average of the values we got (half the time 1, half the time -1) is equal to zero, which is the value we would get with a normal magnet.
