What's a kagome lattice, a quantum spin liquid and how are they related?

[deltasigma]

Oh, and when you’re done, if you could send me my PhD, that could be really cool. Thanks.

I understand that there are probably a few conceptual layers one needs to penetrate before you even get to ask a question like this, so if you try reach for my throat I’ll understand - it’s probably just short of asking for a mind meld. But hey, there’s always a chance.

Anyway, a little background. Physorg has literally been abuzz over this the past week so I’ll just cite this one article which seems like the best I’ve sampled thus far.

(Phys.org)—A research team including scientists from the National Institute of Standards and Technology (NIST) has confirmed long-standing suspicions among physicists that electrons in a crystalline structure called a kagome (kah-go-may) lattice can form a “spin liquid,” a novel quantum state of matter in which the electrons’ magnetic orientation remains in a constant state of change.

Read more at: For newly discovered 'quantum spin liquid', the beauty is in its simplicity

[Senegoid]

kagome lattice sounds like something I’d make a green salad out of.

With quantum spin juice on it of course.

[Nametag]

That’s a nice article. Can you elucidate what you didn’t understand about its explanation of the Kagome lattice and spin liquids, and what you already know about, say, electron spins?

[deltasigma]

Well, when you read this, it seems pretty straight forward.

Named after a mineralogist, Herbertsmithite was proposed to be a quantum spin liquid by Daniel Nocera and Young Lee of the Massachusetts Institute of Technology (MIT) in 2007. Herbertsmithite has a peculiar crystal structure in which its copper atoms lie at the corners of triangles with interactions that favor having the up-down alignment pattern of electronic spins on each corner. However, while electrons on two of the corners of a triangle can align, one up and one down, their alignment produces a quandary for the electron on the third corner, which cannot align with both. “The electronic spin on the third copper atom essentially doesn’t know what to do with itself,” says Collin Broholm, a physicist at NIST and Johns Hopkins University, who was also part of the team that previously characterized a different material with a spin-liquid-like state.** “The locations of copper atoms in Herbertsmithite suggest the material might not be able to order itself magnetically, which is interesting because it is so unusual. But testing the hypothesis of a quantum spin liquid required the right instrument and very pure crystals of Herbertsmithite, and until recently, we had neither.”

Read more at: For newly discovered 'quantum spin liquid', the beauty is in its simplicity

Some of the electrons are spin up, some spin down and then the rest are sort of caught in the middle and that’s what makes it “antiferromagnetic.”

The thing is, that when I THINK I understand something in quantum mechanics, that’s a pretty good indication that I don’t. Just take a look at the wiki entry for example.

[Half_Man_Half_Wit]

Well, there are some additional complexities, but I think you got the gist – kagome lattice is just another name for a tiling using hexagons and triangles, and not in any way intrinsically related to quantum spin liquids.

As for those QSLs, well, basically, two adjacent electron spins ‘want’ to align thenselves opposite to one another, in order to minimize total energy. However, in certain configurations, this isn’t possible: take a triangle, with spins situated at its vertices. If the spin at A is up, the spin at B is down, then what should the spin at C be? It wants to be upposite to A, so down; but it also wants to be opposite to B, so up. This is an example of what’s known as ‘frustration’; in a quantum spin liquid, now, this phenomenon occurs on a ‘large scale’ basis, i.e. all throughout the crystal lattice (it is not hard to see that a kagome lattice is a good candidate for such a situation). Because of the resulting ‘disorderedness’, the whole thing is called a liquid.

[deltasigma]

@Half_Man_Half_Wit

Because of the resulting ‘disorderedness’, the whole thing is called a liquid.

Ah, I was really getting hung up on that use of the word “liquid.” Thanks.

[robert_columbia]

@Senegoid

kagome lattice sounds like something I’d make a green salad out of…

While wearing a schoolgirl uniform.

Wot, no Inuyasha jokes yet?