Abstract
The purpose of this chapter is twofold. First, it is partly historical, to recount the somewhat uncertain beginnings and explain how ideas developed the way they did, and secondly, to review the early milestones which laid the foundations for the many years of study which were to follow. These agendas will unfold simultaneously in an essentially chronological recounting of the important first steps in constructing the edifice of high-\(T_c\) NMR phenomenology which exists today.
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Notes
- 1.
See, for example, the wide variety of cuprate structures reviewed by Hazen [214].
- 2.
The work of Heine [35] later revealed that it had no connection with \(\langle r^{-3}\rangle \).
- 3.
In (3.3.2) and again in (3.3.11)–(3.3.13) hyperfine (HF) terms are introduced, with expressions given in energy units. In (3.3.4) a primed notation is introduced, giving the HF constants in the more convenient kG/\(\mu _B\) units. In all subsequent discussion, the latter units will be used and the primed notation dropped. See, e.g., Tables 3.4, 3.6, and 4.1, etc.
- 4.
The difference between these two measurements is outside of error estimates, and can only be attributed to a difference in samples. The lower numbers agree with earlier measurements made on a random powder [138].
- 5.
It would have been desirable to have this effect confirmed by another experimental group. To our knowledge, no such confirmation has been reported.
- 6.
We take larger numbers for the \(^{89}\)Y NMR shift at 100Â K to be a sign of full oxygenation. Moreover, the plot reported for \(^{89}K_{\alpha }(T)\) versus T [200] shows a gradual increase from 300Â K down to a maximum at \(T\sim \) 120Â K. This is a characteristic of a fully oxygenated sample as well [179], rather than declining curves which then give smaller values of \(^{89}K_{\alpha }\) at T \(=\) 100Â K [166].
- 7.
Thus, only one axis is effectively contributing to the \(T_1\) rate.
- 8.
There were, however, two-band models proposed at the time, such as that given by Emery and Reiter [167].
- 9.
In this and chapters to follow, the summation \(\sum _{{\varvec{q}}}^{(N)}\) indicates an integration over the 2D cuprate Brillouin Zone (BZ). A convenient equivalent operator may be written \((a^2/4\pi ^2)\int _{-\pi /a}^{\pi /a}dq_x \int _{-\pi /a}^{\pi /a}dq_y\). For a \({\varvec{q}}\)-independent integrand, this BZ integral is normalized to unity.
- 10.
It is noteworthy that the parameter \(\mathcal {X}_{at}\), used in the first edition of this monograph, is being replaced here by the more intuitive quantity \((\mu _B^2/k_BT)\tau _e\).
- 11.
The essential assumption here is that any oxygen hole-band NMR shift would be isotropic.
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Walstedt, R.E. (2018). The Superconducting Cuprates: Preliminary Steps in Their Investigation via NMR. In: The NMR Probe of High-Tc Materials and Correlated Electron Systems. Springer Tracts in Modern Physics, vol 276. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55582-8_3
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