Quantum materials in which strong magnetic frustration exists among the magnetic ions are promising candidates for the realization of a quantum spin liquid. This exotic state is characterized by the absence of long-range magnetic order even at temperature $T = 0$, and by unusual physical properties such as strong quantum fluctuations, quantum entanglement, and fractionalized spin excitations. Due to their potential technological applications, quantum spin liquids have become an active and rapidly growing field of research in condensed matter physics. In this thesis, the antiferromagnet $\mathrm{Ba_9 Yb_2 Si_6 O_{24}}$, which is one of the candidates for the realization of such a state, is analyzed using the method of electron paramagnetic resonance. The measurements do not show any abrupt changes in the spectrum that would indicate magnetic ordering of the material down to a temperature of $T = 4 \mathrm{K}$. The energy levels of the Yb$^{3+}$ ions, which determine the magnetic properties of this quantum magnet, split into Kramers doublets in the crystal field. From the linewidths of the spectrum, which exhibit an exponential temperature dependence due to the Orbach process, the energy splitting between the ground and the first excited Kramers doublet was also determined.
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