de Haas-van Alphen studies of electron doped Sr$_2$RuO$_4$

We present the results of a highly sensitive de Haas-van Alphen (dHvA) rotation study of La$_x$Sr$_{2-x}$RuO$_4$, for $x = 0.02$, 0.06 and 0.10. By substituting Sr$^{2+}$ with La$^{3+}$, we are effectively doping the unconventional superconductor Sr$_2$RuO$_4$ with electrons without gross distortions to the crystal structure. According to band structure calculations, the resultant rigid band shift should push the Fermi level towards a van Hove singularity at $x = 0.20$, which has important consequences for theories of spin-fluctuation mediated superconductivity. In this study, due to extremely high quality samples and a low noise experimental set-up, we have been able to extract information about changes in the Fermi surface warping, electronic effective masses and spin susceptibility up to $x = 0.10$. The experimental runs were carried out in fields up to 18\,T, and the samples were rotated in the [001] to [100] plane. We have determined the field-dependent dHvA amplitude and compared it with numerically calculated results from a model Fermi surface. Effective masses were calculated from the temperature dependence of the oscillation amplitudes.