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The relaxation of Yb$^{3+}$ in YBa$_{2}$Cu$_{3}$O$_{x}$ ($6<x<7$) was studiedusing Electron Paramagnetic Resonance (EPR). It was found that both electronicand phononic processes contribute to the Yb$^{3+}$ relaxation. The phononicpart of the relaxation has an exponential temperature dependence, which can beexplained by a Raman process via the coupling to high-energy ($\sim$500 K)optical phonons or an Orbach-like process via the excited vibronic levels ofthe Cu$^{2+}$ ions (localized Slonczewski-modes). In a sample with a maximumoxygen doping $x$=6.98, the electronic part of the relaxation follows aKorringa law in the normal state and strongly decreases below $T_{c}$.Comparison of the samples with and without Zn doping proved that thesuperconducting 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 electronicpart of the Yb$^{3+}$ relaxation in the superconducting state follows the sametemperature dependence as $^{63}$Cu and $^{17}$O nuclear relaxations despitethe huge difference between the corresponding electronic and nuclear relaxationrates.

Probing the Yb$^{3+}$ spin relaxation in Y$_{0.98}$Yb$_{0.02}$Ba$_{2}$Cu$_{3}$O$_{x}$ by Electron Paramagnetic Resonance