Tuesday, August 4, 2009

Can we see visons?

The organic charge transfer salt kappa-(ET)2Cu2(CN)3 has attracted a lot of attention the past few years because there is significant experimental evidence that the ground state of the Mott insulating phase is a spin liquid.

I have been reading a very interesting theoretical paper by Qi, Xu, and Sachdev that presents a highly original (and exotic) explanation for thermal conductivity and nuclear magnetic resonance experiments on this material.

At low temperatures the NMR relaxation rate 1/T1 goes to zero as T^\eta with eta ~1.5 and the thermal conductivity kappa(T)/T goes to zero in an activated fashion with a gap of about 0.5 K.

The authors propose the ground state is a Z2 spin liquid close to a quantum critical point with quasiparticles that are spin-1/2 bosons (spinons) and spinless bosons (visons).
It is shown that spinons dominate the nmr and visons the thermal conductivity.
The visons form a dilute Boltzmann gas with a bandwidth of about 8 K, which the authors claim corresponds to the peak observed in the heat capacity and thermal conductivity. Note that this bandwidth is only about 3 per cent of the exchange interaction J, which sets the energy scale for the spinons.

The visons correspond to low-energy singlet excitations and can be viewed as vortices in the Z2 gauge field
associated with a liquid of resonating valence bonds.

These are bold hypotheses.

I worry how robust the thermal conductivity data is. Is there any chance that at these low temperatures the suppression is due to a decoupling of the magnetic excitations from the phonons, as was observed in cuprates and explained by Mike Smith. The experimentalists claim not.
The thermal conductivity data is inconsistent with the heat capacity data, i.e.,
kappa(T)/T does not extrapolate to a non-zero value. So at least one of them must be wrong.


  1. Thanks for the plug Ross. At first glance I share your concerns.

    I read the experimentalists' argument against the occurence of phonon thermal decoupling (PTD) and am unconvinced.

    Their first piece of evidence is that they measured the data for a range of contact resistances (from 1 to 20 Ohms) and saw no change in the measured kappa/T. However, if a 1 Ohm contact resistance WERE sufficient to effect a complete downturn like that observed (i.e. kappa/T -> 0 at T -> 0)
    then one wouldn't expect any dependence on contact resistance upon raising it even further.

    (It is interesting that the complete downturn seen in the cuprate PCCO occured for contact resistance of about 1 Ohm. The value of kappa/T above the downturn in PCCO looks to be roughly the same as that in this organic as well. However, to make a fair comparison we would have to know the size of the measured sample and the spinon-phonon coupling.)

    Their second piece of evidence is that turning on a field has no effect on the data. Since a field should reduce the number of spinons, they argue that this would be seen as a more pronounced downturn. I'm not sure whether that claim is true for a downtown that is already complete. But in any case, I would have thought that a reduction in spinon number should lower the spinon contribution to kappa/T even if the data is NOT contaminated by PTD (though maybe the theory paper explains the H dependence of spinon kappa/T).

  2. Dear Prof. McKenzie and colleagues,

    Thanks for posting blog and please allow my delayed posting. I was actually in Queens land (Goldcoast and Hamilton Is) with my family when you posted the blog and we were really enjoying great & beautiful nature in Australia.

    It is really exciting that Qi, Xu, and Sachdev propose that excitations of spinons and visons play role in the organic compound. We really hope that following-up experiments to check our result and to prove the vison excitations come up in future.

    As for the concern about thermal decoupling that you and Dr. Smith share, we’d like to emphasize that the strongest evidence, we believe, is that we’ve measured enhancement of kappa by magnetic field even at the lowest temperature. Although we don’t know the precise origin of the excitations, it must be a magnetic excitation and the enhancement is even larger in lower temperature. This enhancement means that our contact is capable of detecting magnetic excitations even at the lowest temperatures.

    On the other hand, as Dr. Smith pointed out, contact resistance of 1 Ohm would be not good enough in sense of studying superconductivity. It should be less than 100 mOhm as discussed in Dr Smith’s paper and as we found in our recent work in Fe-As (arXiv:0907.4399). However, in case of our study, what we need to know is a contact resistance to spin systems, not electrons. So electric contact resistances might mean nothing. Also, we need to know how strong the phonon-spinons coupling that is not known. Frankly speaking, therefore, i’m not sure how good the contact resistance should be and how to make sure by contact resistance measurements prior to experiments.

    I believe that it is the first challenge to detect spin excitations in organic compound by thermal transport measurements and we would need further experiments in different materials. We are currently working on Pd(dmit)-salts by similar measurement technique and it seems that we are detecting very interesting magnetic excitations as well as in kappa-Et salts. In future, we are also hoping to measure thermal conductivity in kagomé materials if a single crystal available.

    We really don’t think it is possible to extract gamma term from the heat capacity measurements which are suffering from huge Schottky anomaly (one order of magnitude larger than the gamma-term they propose). 1/T1 measurements also have problem of non-uniform spins. Their stretched-exponential fittings with the exponent less than 0.5 mean that spins are awfully inhomogeneous in microscopic length scale. Thermal transport measurements, we believe therefore, should be the best to detect the low-lying excitations.


    Minoru Yamashita

  3. Dear Prof. Yamishita

    I now understand your argument regarding the low-T field dependence of the thermal conductivity data. My apologies for missing your point previously.

    I agree that the enhancement in field appears difficult to explain within a el-ph decoupling scenario, and is suggestive that you are seeing electronic (spinonic) thermal current.

    As for the contacts, to avoid a significant downturn in the thermal conductivity: the contacts have to be less resistive to electronic heat flow than the sample itself.
    One could check whether this condition is met for the spinons: knowing the sample size and spinonic thermal conductivity you could determine the thermal resistance of the sample and compare it to the electronic heat resistance of the contacts (obtained from electrical contact resistance via Wiedemann-Franz).

    But, even if the contacts are more resistive to electronic heat flow than the sample, this does not necessarily mean that a downturn will be seen. For, if the phonon-spinon heat transfer rate in the sample is sufficiently large then temperature below which the downturn occurs would be immeasurably small.

    Mike Smith