A spin liquid is a state of matter where there is no magnetic order (spontaneous breaking of spin rotational symmetry) at zero temperature. The past few decades has seen a desperate search for both real materials and Heisenberg spin models in two spatial dimensions that have this property. I have written many posts on the subject. An important question is what is a definitive experimental signature of such a system.

Strong candidate materials are the Mott insulating phase of several organic charge transfer salts, which was reviewed in detail in 2011 by Ben Powell and I.

One experimental signature is the temperature dependence of the specific heat. In particular, some theories predict spin liquid states with spinon excitations with a Fermi surface. This would lead to a linear term in the temperature dependence of the specific heat, as one sees in a simple metal that is a Landau Fermi liquid. This paper is one of several that claims to observe this signature.

However, it is important to bear in mind two subtle issues with interpreting these experiments.

First, one always have to subtract off the large contribution to the specific heat from lattice vibrations. There are two main ways to do this. One is to fit the data, including a cubic term, T^3 in the temperature dependence. The second method is to subtract the data from a different compound (e.g. a deuterated one) which has a different electronic (magnetic) ground state but a similar crystal structure. Due to subtle isotope effects and hydrogen bonding, sometimes deuterated compounds are argued to meet this requirement for the magnetic contributions to be different and the phonon contributions to be the same.

However, there are

**problems**with both of these subtraction methods.
First,

**curve fitting**with many parameters can be getting the tail of the elephant to wiggle, as discussed more below. Second, changing the chemistry does change the phonon spectrum and so also changes the lattice contribution.
Finally, what about the linear in T term?

In a News and Views about a 2008 Nature Physics paper claiming to observe this linear in T term, Art Ramirez showed one could take the same experimental data and fit it to an alternative expression involving T^(2/3) which was proposed by an alternative theory.

This is shown in the Figure below.

I also worry about how the low T specific heat is dominated by the 1/T^2 term associated with the Schottky anomaly from two level systems.

Unfortunately,

We really need more direct experimental probes of spin liquid behaviour. Unfortunately, there is a paucity of realistic ones.

**Ramirez's concerns seem to have been ignored in following papers.**We really need more direct experimental probes of spin liquid behaviour. Unfortunately, there is a paucity of realistic ones.

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