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Phenomenology of 63Cu Nuclear Relaxation in Cuprate Superconductors

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Abstract

Nuclear relaxation is an important thermodynamic probe of electronic excitations, in particular in conducting and superconducting systems. Here, an empirical phenomenology based on all available literature data for planar Cu in hole-doped cuprates is developed. It is found that most of the seemingly different relaxation rates among the systems are due to a temperature-independent anisotropy that affects mostly measured 1/T1∥, the rate with an external magnetic field along the crystal c-axis, while 1/T1⊥ is largely independent on doping and material above the critical temperature of superconductivity (Tc). This includes very strongly overdoped systems that show Fermi liquid behavior and obey the Korringa law. Below Tc, the relaxation rates are similar, as well, if plotted against the reduced temperature T/Tc. Thus, planar Cu nuclear relaxation is governed by a simple, dominant mechanism that couples the nuclei with varying anisotropy to a rather ubiquitous bath of electronic excitations that appear Fermi liquid-like irrespective of doping and family. In particular, there is no significant enhancement of the relaxation due to electronic spin fluctuations, different from earlier conclusions. Only the La2−xSrxCuO4 family appears to be an outlier as additional relaxation is present; however, the anisotropy remains temperature independent. Also systems with very low doping levels, for which there is a lack of data, may behave differently.

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Funding

We acknowledge the financial support from the University of Leipzig, the Free State of Saxony, the European Social Fund (ESF), and the Deutsche Forschungsgemeinschaft (DFG).

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Authors and Affiliations

  1. Felix Bloch Institute for Solid State Physics, University of Leipzig, Linnéstr. 5, 04103, Leipzig, Germany

    Michael Jurkutat, Marija Avramovska, Daniel Dernbach, Danica Pavićević & Jürgen Haase

  2. Victoria University of Wellington, The MacDiarmid Institute for Advanced Materials and Nanotechnology, SCPS, PO Box 600, Wellington, 6140, New Zealand

    Grant V. M. Williams

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  1. Michael Jurkutat
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Contributions

Data collection was performed equally by D.D and M.J.; independent verification of collected data was equally performed by M.A. and J.H.; discussion of data with equal help from D.P. and G.V.M.W.; preparation of the manuscript was equally performed by M.A., M.J., J.H.; J.H. also performed the data analysis and led the overall project.

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Correspondence to Jürgen Haase.

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Appendix: Literature data processing

Appendix: Literature data processing

For the review of relaxation data, we have collected all available literature data of 63T1 of planar Cu. That means data for two orientations of the magnetic field with respect to the crystal c-axis, c ∥B0 and c ⊥B0, i.e. 1/T1∥ and 1/T1⊥, respectively. Furthermore, nuclear quadrupole resonance (NQR) were gathered, as well. The set comprises about 54 materials for 1/T1∥. The discussion in this manuscript, however, is limited to the 24 systems listed in Table 1, for which data for both directions of the field are available. Nevertheless, this (significant) subset we are discussing is representative of all the data in terms of amplitude and different temperature dependences of relaxation, as we can judge from all 1/T1∥ data.

As remarked in the main text, the higher abundance of 1/T1∥ data is due to the use of c-axis aligned powders and NQR.

We have excluded data on electron-doped cuprates where 1/T1 in most cases is affected by rare earth magnetism in the charge reservoir layer, data on antiferromagnetic inner layers in triple and higher layered materials and data where it was unclear what definition for the T1 was used [46]. We have also excluded HgBa2CuO4+δ, for which our data are contradictory to results by Gippius et al. [43], as well as Tl2Ba2CaCu2O8−δ, since 63T1⊥ was not actually measured by Gerashenko et al. [40], but deduced from the spin-echo decay.

The data were extracted using the online software “WebPlotDigitzier”, for which screenshots from graphs from the referenced papers were imported and the data extracted using the software tools.

In Fig. 3, the temperature is an implicit parameter, owing to the limited availability of 1/T1α(T) data for both orientations at identical temperatures, we used a linear interpolation.

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Jurkutat, M., Avramovska, M., Williams, G.V.M. et al. Phenomenology of 63Cu Nuclear Relaxation in Cuprate Superconductors. J Supercond Nov Magn 32, 3369–3376 (2019). https://doi.org/10.1007/s10948-019-05275-6

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