Debate on thermal conduction in the quantum spin liquid state of organic magnetic materials

[Introduction]  

    Quantum spin liquid is a novel magnetic state of a magnetic material proposed by P. W. Anderson. In this state, the spins do not become ordered even at cryogenic temperatures due to large quantum fluctuations caused by spin frustration [1, 2].

    One of the breakthroughs in the study of quantum spin liquids is the metallic behavior of specific heat, magnetic susceptibility, and thermal conductivity in the triangular lattice organic magnet β′-EtMe3Sb[Pd(dmit)2]2. The results have attracted much attention because they suggest the existence of a spinon Fermi surface in the quantum spin liquid state. However, among these measurements, conflicting results for the thermal conductivity have been reported by a Japanese group and groups in China and Canada since 2019, and the debate continues.

    In this article, I will try to summarize the history of this debate.

[History of the Discussion]

    The controversy over heat conduction in organic quantum spin liquids is roughly as follows. Some of the topics have been discussed at domestic and international conferences, but I have summarized them based on publicly published papers. In fact, these discussions started when the papers were first published in Arxiv, but I have cited the published papers below, so you can see how the discussions were going on in real time by looking at the differences in content between Arxiv versions.

1. Kyoto Univ. group reported in Science that β′-EtMe3Sb[Pd(dmit)2]2, one of the candidates for organic quantum spin liquids, showed metal-like thermal conductivity at cryogenic temperatures despite being an insulator.
   M. Yamashita et al., Science 328, 1246 (2010)
   

   

   Figure, Temperature dependence of the thermal conductivity of β′-EtMe3Sb[Pd(dmit)2]2.
   
   

2. 9 years later, the Chinese and Canadian groups independently conducted follow-up tests and reported to PRL and PRX, respectively, that the thermal conductivity at cryogenic temperatures was zero and that they could not reproduce the results of the Science paper.
   ・J. M. Ni et al., Phys. Rev. Lett. 123, 247204 (2019)
   ・P. Bourgeois-Hope et al., Phys. Rev. X 9, 041051 (2019)
   

   

   Figure, Comparison of the results of the Science paper with those of the Chinese and Canadian groups.
   
   

3. The first author of the Science paper, Prof. Yamashita, reported that in EtMe3Sb[Pd(dmit)2]2, there were two types of samples with different phonon components of thermal conductivity. It was thought that this was due to the presence of some impurities in the sample. The finite thermal conductivity could only be observed in samples with a large phonon component.
   The paper was published in JPSJ.
   ・M. Yamashita, J. Phys. Soc. Jpn. 88, 083702 (2019)
   

   

   Figure, Thermal Conductivity Divided into Two Groups
   
   

4. In response to this situation, Prof. Hidetoshi Fukuyama reported to the JPSJ that "it is strange that there are two results for one material, so the cause should be clarified". At the same time, Prof. Yamashita reported his response to the Fukuyama's comment to JPSJ.
   ・H. Fukuyama, J. Phys. Soc. Jpn. 89, 086001 (2020)
   ・M. Yamashita, J. Phys. Soc. Jpn. 89, 086002 (2020)
   (Note added: According to Prof. Fukuyama, "The purpose of Fukuyama's comment is "Evidence is needed to support the claim that there are two types of crystals in the Yamashita paper. In response to this, Yamashita's reply does not mention "two types of crystals" but changes the point of discussion to "cooling rate is the problem.")
5. The Canadian group responded to Prof. Yamashita's JPSJ paper.
   "The samples were provided by Kato's group at RIKEN, and we also measured the same batch as in the Science paper, so it is unlikely that there is a significant difference between the samples.
   "Synchrotron radiation X-rays show no difference in the samples measured."
   "If the comparison in the JPSJ paper is to be believed, the samples with finite thermal conductivity show no scattering of phonons at cryogenic temperatures, but how is that possible?"
   ・P. Bourgeois-Hope et al., Phys. Rev. X 9, 041051 (2019)
   

   

   Table, Difference in R-factor for each sample measured with synchrotron radiation X-rays.
   
   

6. Prof. Yamashita and his colleagues proposed the hypothesis that the reason why the Canadian and Chinese groups could not reproduce the results of the Science paper was that the cooling rate was too fast, which may have caused micro-cracks in the sample. In fact, they reported in PRB that finite thermal conductivity could be observed when cooling at extremely low speeds of 0.4 to 1.5 K/h (but one order of magnitude smaller than the value in the Science paper).
   ・M. Yamashita et al., Phys. Rev. B 101, 140407(R) (2020)
   

   

   Figure, Temperature dependence of thermal conductivity at different cooling rates.
   
   

7. In response to Prof. Yamashita's theory of micro-cracks caused by rapid cooling, a Canadian group argued that they could not observe any micro-cracks by observing the samples before and after the measurement with SEM.
   ・P. Bourgeois-Hope et al., Phys. Rev. X 9, 041051 (2019)
   ・P. Bourgeois-Hope, PhD Thesis
   

   

   Figure, SEM observation of a sample to check for microcracks.
   
   

8. Prof. Kato's group at RIKEN, which provided the samples for all the papers, verified whether the effect of quenching appeared in the crystal structure, electrical resistance, and NMR. They reported in Crystals that no difference could be observed by any of the measurement methods. They also pointed out that the cooling-rate-dependent hypothesis cannot explain the cause of the discrepancy, since the measurements in the first Science paper were made under quenching.
   ・R. Kato et al., Crystals 12, 102 (2022)
   

   

   Figure, Comparison of the relationship between cooling rate and thermal conductivity in the Science paper and the PRB paper.
   
   

9. Up to now (as of 1/23/2022)

[Summary]

    In this article, we summarize the history of the debate on the thermal conductivity problem of quantum spin liquids in organic magnetic materials, which is still controversial. The cooling-rate-dependent hypothesis is a tough one, as it requires about a month of cooling alone to reproduce the 0.4 K/h experiment, and as with the thermal Hall effect in α-RuCl3, there are many difficulties in discussing thermal measurements of quantum spin liquids. However, since the results are important enough to cause controversy, I would like to continue to pay attention to the process of discussion. It's interesting.

[References]

[1] 磯野 貴之, 宇治 進也, 有機スピン液体物質における量子臨界現象とスピン–格子デカップリング現象の発見, 日本物理学会誌 2019 年 74 巻 7 号 p. 483-488

[2] Lucile Savary and Leon Balents 2017 Rep. Prog. Phys. 80 016502