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Marginal breakdown of the Fermi-liquid state on the border of metallic ferromagnetism


For the past half century, our understanding of how the interactions between electrons affect the low-temperature properties of metals has been based on the Landau theory of a Fermi liquid1. In recent times, however, there have been an increasingly large number of examples in which the predictions of the Fermi-liquid theory appear to be violated2. Although the qualitative reasons for the breakdown are generally understood, the specific quantum states that replace the Fermi liquid remain in many cases unclear. Here we describe an example of such a breakdown where the non-Fermi-liquid properties can be interpreted. We show that the thermal and electrical resistivities in high-purity samples of the d-electron metal ZrZn2 at low temperatures have T and T5/3 temperature dependences, respectively: these are the signatures of the ‘marginal’ Fermi-liquid state3,4,5,6,7, expected to arise from effective long-range spin–spin interactions in a metal on the border of metallic ferromagnetism in three dimensions3,5. The marginal Fermi liquid provides a link between the conventional Fermi liquid and more exotic non-Fermi-liquid states that are of growing interest in condensed matter physics. The idea of a marginal Fermi liquid has also arisen in other contexts—for example, in the phenomenology of the normal state of the copper oxide superconductors7, and in studies of relativistic plasmas and of nuclear matter3,4,6.

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Figure 1: Evidence for the marginal Fermi-liquid state in ZrZn2.
Figure 2: Predicted phase diagram of ZrZn2.
Figure 3: Resistivity of ZrZn 2 just below the critical pressure.
Figure 4: Pressure dependence of TC and the resistivity exponent in ZrZn2.


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We acknowledge financial support from the Royal Society, the EPSRC and St Catharine’s College, Cambridge, and the Ministry of Education, Culture, Sports, Science and Technology of Japan (Grants-in-Aid for Scientific Research on Priority Areas and (S) from MEXT, Japan). We thank S. E. Rowley and I. R. Walker for experimental help and S. E. Rowley, C. M. Varma and P. B. Littlewood for discussions.

Author Contributions R.P.S. set up, performed and analysed the resistivity measurements at ambient pressure and under pressure, and carried out the model calculations. M.S. set up, performed and analysed the thermal conductivity measurements. S.S.S. assisted with measurements under pressure. N.K., S.T., M.N. and H.T. grew the ZrZn2 crystals for the study. G.G.L and N.K. designed the study. R.P.S. and G.G.L. wrote the paper. M.S. assisted in writing the paper.

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Smith, R., Sutherland, M., Lonzarich, G. et al. Marginal breakdown of the Fermi-liquid state on the border of metallic ferromagnetism. Nature 455, 1220–1223 (2008).

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