Thursday, December 20, 2012

Quantum spin liquids - neat stuff!

There is a new result in this week's issue of Nature that is very neat (and my college classmate Young Lee is the PI - small world!).  The experiment is an inelastic neutron scattering measurement that looks at a material with the unusual name herbertsmithite, and reports evidence that this material is a "quantum spin liquid".  I'll try to break down the physics here into reasonably accessible bite-sized chunks.

First, what is a spin liquid?  Imagine having a bunch of localized spins on a lattice.  You can picture these like little bar magnets.  In this case, the spins are the unpaired d electrons of the copper atoms in the herbertsmithite structure.   In general, the spins in a solid (this particular one is an insulator) "talk" to each other via the exchange interaction.  What this really means is that there are interactions between the spins so that the spins prefer a particular relative orientation to each other.  In this case, the interaction between the electron spins is antiferromagnetic, meaning that for spins on two neighboring Cu atoms, having the spins be oppositely directed saves some energy (17 meV) compared to having the spins aligned.  As the temperature is lowered, an ensemble of spins will tend to find whatever configuration minimizes the total energy (the ground state).  In a ferromagnet, that will be a state with the spins all aligned with their neighbors.  In a perfect antiferromagnet, that would be a state where the spins are all antialigned with their neighbors.  Both of these are ordered ground states, in that there is some global arrangement of the spins (with a particular symmetry) that wins at T = 0.   The problem in herbertsmithite is, because of the spatial arrangement of the Cu atoms (in a Kagome lattice), it's impossible to have every spin antialigned with all of its neighbors.  This is an example of geometric frustration.   As a result, even as T gets very low, it would appear that the spins in herbertsmithite never order, even though they interact with their neighbors very strongly.  This is an analog to the liquid state, where the molecules of a liquid clearly interact very strongly with their neighbors (they bump right into each other!), but they do not form a spatially ordered arrangement (that would be a solid).

Why a quantum spin liquid?  Two reasons.  First, I cheated in my description above.  While we can talk classically about antialigned spins, we really should say that pairs of spins want to form singlets, meaning quantum mechanically entangled antialigned states with net spin zero.  So, you can think of this spin liquid state as involving a big entangled mess of spins, where each spin is somehow trying to be entangled in a singlet state with each of its nearest neighbors.  This is very complicated to treat theoretically.  Second, the fluctuations that dominate in this situation are quantum fluctuations, rather than thermally driven fluctuations.  Quantum fluctuations will persist all the way down to T = 0. 

What's special about a quantum spin liquid?  Well, the low energy excitations of a quantum spin liquid can be very weird.  If you imagine reaching into the material and flipping one spin so that it's now energetically "unhappy" in terms of its neighbors, what you find is that you can start flipping spins and end up with "spinon" excitations that travel through the material, having spin-1/2 but no charge, and other exotic properties.  This is described reasonably well here.  Importantly, these excitations have effects that are seen in measurable properties, like heat capacity and how the system can take up and lose energy.

So what did the experimenters do?  They grew large, very pure single crystals of herbertsmithite, and fired neutrons at them.  Knowing the energies and momenta of the incident neutrons, and measuring the energies and momenta of the scattered neutrons, they were able to map out the properties of the excitations, showing that they really do look like what one expects for a quantum spin liquid. 

Why should you care?  This is a great example of seeing exotic properties (like these weird spin excitations) that emerge because of the collective response of a large number of particles.  A single Cu ion or unit cell of the crystal doesn't do this stuff - you need lots of spins.  Moreover, this is now a system where we can study what this weird, highly quantum-entangled does - I think it's very very far from practical applications, but you never know.   Looks like a very nice piece of work.


paris cox said...

this is fantastic! i can't wait until there is a killer app for this. sure it is at low T, but big things start out small.
give it time and something will become great of it!

Anonymous said...

My impression is that QSLs aren't the real goal of people who study QSLs; the next trick is to dope it and see high-temperature superconductivity, isn't it?

(of course, doping is the hard problem -- ever thus for science)

Anonymous said...

Is this the first example of an experimental quantum spin liquid?

rob said...

i wonder how long it will take some homepath to say their concoctrions are quantum spin liquids?

Douglas Natelson said...

Anon12:19, certainly some people are interested in doping some spin liquids to look for superconductivity. I recall that Anderson and others put about the idea that some of the physics of the cuprates may be spin liquid stuff (resonating valence bonds, etc.). In the case of herbersmithite, though, I don't think that's credible, because the stuff has a big gap (a couple of eV).

Anon2:20, it's the first experimental system that's been probed like this and really seems to have the characteristic excitation spectrum.

joelhelton said...

I'd like to add a comment to Doug's response to Anonymous 2:20.

A good point made very well by Leon Balents (Nature 464, 199) is that experimental signatures of a QSL are difficult to come by since the state is often defined primarily by what it ISN'T (not an ordered magnet, not a spin glass, not a valence bond solid). Therefore there are plenty of reports in the literature of new frustrated magnets with antiferromagnetic interactions that are measured to low temperatures without any evidence of magnetic Bragg peaks, spin glassiness, or muon oscillations. These may well be described as a spin liquid, but in those cases the data really only show a lack of any evidence that it isn't a QSL. This paper is a step forward in the search for experimental signatures of QSLs because the relatively large single crystal samples and new advances in neutron spectroscopy instruments allow for positive evidence in the form of the measured excitation spectrum.

(typo in original post corrected)

Anonymous said...

thanks for posting..