Nutation versus angular-dependent NQR spectroscopy and impact of underdoping on charge inhomogeneities in ${\text{YBa}}_2{\text{Cu}}_3{\text{O}}_y$

We describe two different nuclear quadrupole resonance (NQR) based techniques, designed to measure the local asymmetry of the internal electric field gradient $\eta$ and the tilt angle $\alpha$ of the main NQR principal axis $\hat{\mathbf{z}}$ from the crystallographic axis $\hat{\mathbf{c}}$. These techniques use the dependence of the NQR signal on the duration of the radio frequency (rf) pulse and on the direction of the rf field $H_1$ with respect to the crystal axis. The techniques are applied to oriented powder of ${\text{YBa}}_2{\text{Cu}}_3{\text{O}}_y$ fully enriched with ${}^{63}\text{C}\text{u}$. Measurements were performed at different frequencies, corresponding to different in-plane copper sites with respect to the dopant. Combining the results from both techniques, we conclude that oxygen deficiency in the chain layer lead to a rotation of the NQR main principal axis at the nearby Cu on the ${\text{CuO}}_2$ planes by $\alpha \simeq 20°\pm 5°$. This occurs with no change to $\eta$. The axis rotation associated with oxygen deficiency means that there must be electric field inhomogeneities in the ${\text{CuO}}_2$ planes only in the vicinity of the missing oxygen.

Figure 1

(Color online) Calculated on-resonance nutation spectra for: (a) powder samples. (b) Perfectly oriented powder where $\hat{\mathbf{z}}\parallel \hat{\mathbf{c}}$. (c) Oriented powder where $\hat{\mathbf{z}}$ has up to $20°$ angle from $\hat{\mathbf{c}}$ (d) Perfectly oriented powder where $\hat{\mathbf{z}}\parallel \hat{\mathbf{b}}$. For the oriented powders the rf transmission is perpendicular to the $\hat{\mathbf{c}}$ direction.

Figure 2

(Color online) The unit cell of YBCO. An illustration of the rotation of the EFG main principal axis from the crystallographic directions due to the missing oxygen atoms in the chains. The angle between $\hat{\mathbf{z}}$ and $\hat{\mathbf{c}}$ is $\alpha$. The $\hat{\mathbf{x}}$ direction is in the $a\text{−}b$ plane making an angle $\phi$ with $\hat{\mathbf{a}}$.

Figure 3

(Color online) Theoretical echo intensity curves for various values of $\eta$ calculated from Eq. (15). $\theta$ is the polar angle between the rf field and the $\hat{\mathbf{c}}$ direction of the lattice in an oriented powder. In this case the $\hat{\mathbf{z}}$ direction of the EFG is assumed to be parallel to $\hat{\mathbf{c}}$. Inset: basic angle dependent NQR configuration. A sample with a preferred direction is inserted into the coil. The angle $\theta$ between them can be varied with a motor.

Figure 4

(Color online) Theoretical echo intensity curves for $\eta =0$ and various values of $\alpha$ calculated from Eq. (19). $\theta$ is the polar angle between the rf field and the $c$ direction of the lattice in an oriented powder.

Figure 5

(Color online) NQR frequency sweep on ${\text{YBCO}}_y$. The solid lines are Gaussian fits performed in order to determine the resonance frequencies.

Figure 6

(Color online) (a) The oxygen doping for different YBCO samples as a function of the NQR frequencies. (b) The superconducting transition temperature of these samples as a function of the NQR frequencies. The blue circular symbols are resonance frequencies coming from the Cu(1) site. The red lines are a fit to three parallel lines, for the three different Cu(2) sites.

Figure 7

(Color online) Schematic illustration of the Cu site in YBCO with locally different oxygen coordinations.

Figure 8

Inset: the pulse sequence of a nutation experiment. (a) An example of raw data of a nutation experiment for $y=7-\delta$ at 31.5 MHz. The refocusing pulse $t_r$ was $4.4\mu \text{s}$ and $\tau$ was $32\mu \text{s}$. (b) The data after Fourier transform.

Figure 9

(Color online) (a) Nutation spectra for ${\text{YBCO}}_{7-\delta }$ with natural abundance of ${}^{65}\text{C}\text{u}$ and ${}^{63}\text{C}\text{u}$. [(b) and (c)] Nutation spectra for ${\text{YBCO}}_{6.73}$ and ${\text{YBCO}}_{6.68}$ enriched with ${}^{63}\text{C}\text{u}$. [(d)–(f)] Cu NQR line shape for these three samples, extracted from Fig. 5. The arrows show the frequencies where nutation spectroscopy is applied.

Figure 10

(Color online) Right panels: Cu NQR line shape for ${\text{YBCO}}_{7-\delta }$ with natural abundance of ${}^{65}\text{C}\text{u}$ and ${}^{63}\text{C}\text{u}$, and for ${\text{YBCO}}_{6.68}$ enriched with ${}^{63}\text{C}\text{u}$. The arrows show the frequencies where ADNQR is applied. Left panels: the echo intensity as a function of the angle $\theta$ between the rf field and the $\hat{\mathbf{c}}$ direction of the lattice for the two samples. The solid lines are fits to Eq. (19).