Electronic and vibrational signatures of ruthenium vacancies in Sr$_2$RuO$_4$ thin films

The synthesis of stoichiometric Sr$_2$RuO$_4$ thin films has been a challenge because of the high volatility of ruthenium oxide precursors, which gives rise to ruthenium vacancies in the films. Ru vacancies greatly affect the transport properties and electronic phase behavior of Sr$_2$RuO$_4$, but their direct detection is difficult due to their atomic dimensions and low concentration. We applied polarized X-ray absorption spectroscopy at the oxygen K-edge and confocal Raman spectroscopy to Sr$_2$RuO$_4$ thin films synthesized under different conditions. The results show that these methods can serve as sensitive probes of the electronic and vibrational properties of Ru vacancies, respectively. The intensities of the vacancy-related spectroscopic features extracted from these measurements are well correlated with the transport properties of the films. The methodology introduced here can thus help to understand and control the stoichiometry and transport properties in films of Sr$_2$RuO$_4$ and other ruthenates.