Spin liquids are an exotic state of matter that can only exist in the world of quantum mechanics. They're a strange mess of spin states and superpositions that forces magnetism and anti-magnetism to simultaneously exist in millions of different configurations.
But just what on earth is a spin liquid? Well, the term "liquid" is a bit of a misnomer - the main point of similarity between liquids and spin liquids is that they're both a form of disorder. The atoms in liquids are disordered compared to the neat arrays of atoms that make up solids, and spin liquids are basically a form of magnetic disorder on the quantum level. I suspect that doesn't make things all that much clearer, somehow.
Let's look at the "spin" part of spin liquids. We've gone into some detail on the notion of spin before (go here and here for a crash course), and for our purposes we can greatly simplify things by saying that the spin of atoms is what creates their magnetic fields. It's possible to create magnets on the macroscopic scale - say, like the ones on refrigerators around the world - if all the constituent atoms of the magnet have their spin pointing in the same direction.
Again, that's a pretty big oversimplification, but the key idea right now is that magnets are the result of huge amounts of atoms, all sharing the same spin alignment. It's also possible to create what's known as an anti-magnet, which has no net magnetic field. If we say the atoms in a magnet all have an "up" spin, then the atoms in an anti-magnet alternate between "up" and "down" spins, so that the magnetic field of half the atoms cancel out that of the other half. Anti-magnets are crucial in certain high-temperature superconductors.
Now, at last, here's how you make the jump to a spin liquid. Imagine you have a very simple atomic array, with three atoms arranged in an equilateral triangle. If you want to make a magnet out of this array, that's simple enough - you just need the three atoms to all share an "up" spin or a "down" spin. But what if you want to make an anti-magnet? The first atom needs to have an "up" spin, the second needs a "down" spin, but what about the third? Assigning either spin to that third atom will throw the anti-magnetism all out of whack.
While "all out of whack" has its charms as a scientific term, the actual word physicists use for this state of affairs is "frustration." We find frustrating situations — to use the strict scientific meaning of that term, of course — throughout nature, and the way we resolve it on the quantum level can lead to some very strange places. In this particular triangular array, the quantum solution is for the atoms to exist simultaneously in multiple spin orientations. This is known as a superposition, and the idea is that all these simultaneous values can average out to an anti-magnetic alignment.
Now researchers at the Joint Quantum Institute in College Park, Maryland have pushed things still further. They conceived of a six-sided lattice in which the atoms interact according to their spins. Even letting six atoms interact with each other entails massive calculations - the researchers calculate that there are thirty sites where the spins can "swing about", and charting all the possible interactions involves constructing a matrix with 155 million entries on each side. That's a whole lot of different spin configurations.
The researchers divided the interactions of the spins on this array into two different categories. Since the atoms are arranged in a hexagonal arrangement, each atom is directly next to two others. Interactions involving these atoms are known as J1, while interactions between non-adjacent atoms are classified as J2. The researchers found that, as you let the spins of the atoms interact with each other, the strengths of the J1 and J2 interactions would vary wildly, creating a "kaleidoscope" of phases.
And then, something pretty amazing happens when the value of J2 is between 21% and 36% of the value of J1, according to the researchers. At those values, frustration sets in on the system, and the array exists in millions of different quantum states, all simultaneously. At this point, the researchers say it doesn't even make sense to think of spin as an aspect of the atoms. Instead, the spins start behaving like particles in their own right. These spinons "bob about" in much the same way water molecules do in liquid water. And that is why it's called a spin liquid.
Like a lot of quantum phenomena, this is a pretty out-there concept. Even so, it would appear possible to put this idea to the test experimentally. The researchers examined a system operating at absolute zero, at which all non-quantum activity ceases - which means it's impossible for us to create that temperature - but it should be possible to construct and test the hexagonal lattice at temperatures slightly above absolute zero.
Right now, spin liquids are more a fascinating theoretical concern than anything else. But it's possible that harness spin liquids could allow us to construct new forms of superconductors, and they may have some applications in electronics. Until then, spin liquids are probably best left as a reminder of just how incomprehensibly vast the universe really is, even at scales that are unimaginably small.