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Nutation versus angular dependent NQR spectroscopy and the impact of underdoping on charge inhomogeneities in YBa$_2$Cu$_3$O$_y$

We describe two different nuclear quadrupole resonance (NQR) based techniques, designed to measure the local asymmetry of the internal electric field gradient, and the tilt angle of the main NQR principal axis z from the crystallographic axis 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 H1 with respect to the crystal axis. The techniques are applied to oriented powder of YBa$_{2}$Cu$%_{3}$O$_{y}$ fully enriched with 63Cu. 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 CuO2 planes by 20+-degrees. This occurs with no change to the asymmetry. The axis rotation associated with oxygen deficiency means that there must be electric field inhomogeneities in the CuO2 planes only in the vicinity of the missing oxygen.