Probing the Yb$^{3+}$ spin relaxation in Y$_{0.98}$Yb$_{0.02}$Ba$_{2}$Cu$_{3}$O$_{x}$ by Electron Paramagnetic Resonance
The relaxation of Yb$^{3+}$ in YBa$_{2}$Cu$_{3}$O$_{x}$ ($6<x<7$) was studied using Electron Paramagnetic Resonance (EPR). It was found that both electronic and phononic processes contribute to the Yb$^{3+}$ relaxation. The phononic part of the relaxation has an exponential temperature dependence, which can be explained by a Raman process via the coupling to high-energy ($\sim$500 K) optical phonons or an Orbach-like process via the excited vibronic levels of the Cu$^{2+}$ ions (localized Slonczewski-modes). In a sample with a maximum oxygen doping $x$=6.98, the electronic part of the relaxation follows a Korringa law in the normal state and strongly decreases below $T_{c}$. Comparison of the samples with and without Zn doping proved that the superconducting gap opening is responsible for the sharp decrease of Yb$^{3+}$ relaxation in YBa$_{2}$Cu$_{3}$O$_{6.98}$. It was shown that the electronic part of the Yb$^{3+}$ relaxation in the superconducting state follows the same temperature dependence as $^{63}$Cu and $^{17}$O nuclear relaxations despite the huge difference between the corresponding electronic and nuclear relaxation rates.