Probing spin fluctuations in the paramagnetic phase of EuTi$O_{3}$ by muon spin rotation techniques

The muon spin rotation (${\mu}$SR) technique was used to search for theoretically predicted spin fluctuations in EuTi$O_{3}$ (ETO) deep in the paramagnetic phase. ETO is a perovskite with cubic structure above $T_{S}$=282 K, followed by a tetragonal phase below $T_{S}$ and shows antiferromagnetic (AFM) ordering at $T_{N}$=5.7 K. A strong spin-lattice coupling exists at low temperatures. Even though it is not apparent that this spin-lattice coupling continues to high temperatures, model calculations predict a strong paramagnon-phonon coupling at elevated temperatures. In order to test these predictions, ${\mu}$SR studies on ETO have been performed at temperatures above and below $T_{S}$. While the AFM phase is clearly observed in the ${\mu}$SR signal, a finite signal remains also in the paramagnetic phase, following closely the temperature dependence of the zone boundary soft mode. This unusual finding demonstrates that spin fluctuations are present deep in the paramagnetic phase and are tied to the soft zone boundary mode.