# Spin Liquid

1. Jan 18, 2009

### GravityGirl

What is a spin liquid as opposed to a spin solid or a spin glass?

I know that a spin liquid is generally defined by geometric frustration in the electronic spins of that material (i.e. pryochlore structure)....but how is this different from a spin solid? Can it be that the lattice of the material is more spread out than in a solid?

2. Jan 18, 2009

### genneth

The designation of solid/liquid is a consequence of long range order. In the literal solid/liquid distinction, the relevant physical quantity is <x(0)x(r)>. In solids, this will have sharp peaks at particular r's (the lattice spacing), and in liquids there will be a rapid decay. For spin solids and liquids, the idea is the same, except the quantities measured are now spin components, e.g. <s_z(0)s_z(r)>. Note that this has nothing to do with the lattice structure. So spin solids basically have strong correlations between spins even if they are widely separated, and spin liquids don't. The glass case is more difficult, is more characterised by a plethora of nearly degenerate ground states, but which are widely separately in phase space, so tunnelling to the true ground state is kinematically disfavourable.

3. Jan 18, 2009

### GravityGirl

i don't understand.

so in a spin soild there is short range order like nearest neighbor?

so what does that mean if a spin liquid doesn't have strong spin correlations? what i understand is that a spin soild/liquid arises from two things....i am focusing on the pryochlore structure where the material is geometrically frustrated. the spins cannot align in such a way as to simultaneously minimize the energy associated with the competing spin interactions. so to me, it seems like these spins are strongly correlated.

do you mean that in a spin liquid the spins are correlated by next nearest neighbor interactions?

4. Jan 21, 2009

### hiyok

Please look at the behaviors of spin-spin correlation function for distant pairs.

5. Jan 21, 2009

### genneth

Notice that in a ferromagnet or antiferromagnet, spins very far away from each other are still correlated. These are spin solids.

In spin liquids, the correlation drops off very quickly with distance (say exponentially). The precise reason why this might occur are many and complicated. You've mentioned one possibility, where the lattice structure prevents neat ordering.

These names are given because of the similarity in lattice structures, where the location of atoms even very far away are correlated.

6. Apr 12, 2011

### wsttiger

But do the materials that are spin liquids have a normal crystalline lattice structure?

7. Apr 12, 2011

### maverick_starstrider

Most definitely. All we're ever talking about is SPIN degrees of freedom. Spin liquids are still just spins that are spatially confined to a specific lattice (the best example is probably the Kagome). They're essentially all insulators. By no means does a spin-liquid mean that the spins are actually changing position or some such.

8. Apr 12, 2011

### Physics Monkey

Just to amplify what's been said already, the term spin liquid is made by analogy with normal liquids. A normal liquid represents a phase of matter that does not break any symmetry where as a solid phase breaks translation and rotation symmetry (reducing both to discrete subgroups).

Thus, given a lattice of spins with certain symmetries, a spin liquid is any quantum phase of that system that does not break any additional symmetries. For example, the phase should not break spin rotation symmetry, lattice translation symmetry, etc. Of course, you can relax this definition and permit some symmetries to be broken, for example, time reversal.

However, this is something of a negative characterization. Spin liquids can often be positively characterized in terms of some kind of fractionalization, either topological order in fully gapped spin liquids or emergent fluctuating gauge fields in gapless spin liquids. Spin-spin correlations may decay exponentially (fully gapped case) or with a non-trivial power law (gapless case).

Examples:
1) Recent DMRG studies of kagome ladders with heisenberg interactions suggest a fully gapped ground state in two dimensions with some kind of Z2 topological order.
2) The organic salt known as dmit appears to host a gapless spin liquid. This material is a charge insulator but conducts heat like a metal.
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