Electrostatic~\textit{vs.}~Electrochemical Doping and Control of Ferromagnetism in Ion-Gel-Gated La$_{\mathrm{0.5}}$Sr$_{\mathrm{0.5}}$CoO$_{\mathrm{3-\delta }}$.*

Recently developed ionic liquid/gel gating techniques have proven remarkably expedient in the study of charge density effects in a variety of conductors. Much remains to be learned, however, about the exact gating mechanisms ($i.e., $electrostatic \textit{vs}. electrochemical), particularly in oxides, where oxygen vacancy formation and diffusion is facile. In this work we demonstrate that in ion-gel-gated La$_{\mathrm{0.5}}$Sr$_{\mathrm{0.5}}$CoO$_{\mathrm{3-\delta }}$ (LSCO) films, transport, AFM, and XPS measurements indicate that negative gate biases induce reversible electrostatic hole accumulation, whereas positive biases irreversibly induce oxygen vacancies [1]. This is rationalized in terms of the known redox stability of LSCO, with broad implications for electrolyte gating of hole- \textit{vs}. electron-doped oxides. Clear voltage-control of magnetic and transport properties is then demonstrated under hole accumulation, including a 12 K shift in $T_{C} $probed \textit{via} anomalous Hall effect [1]. Further to this, \textit{in operando} probes have also been applied, including synchrotron X-ray diffraction directly revealing expansion in unit cell volume due to oxygen vacancy formation under positive bias, and polarized neutron reflectometry to probe the gate-voltage-dependent depth-profile of chemistry and magnetization. [1] Walter \textit{et al}. ACS Nano. (2016).