Electrostatic doping limits and control of magnetism in electrolyte gated LaAlO$_{\mathrm{3}}$(001)/La$_{\mathrm{0.5}}$Sr$_{\mathrm{0.5}}$CoO$_{\mathrm{3-\delta }}$ thin films

Recently developed ionic liquid/gel gating techniques have proven remarkably expedient in the study of charge density effects in a variety of conductors, ranging from organics to complex oxides. Here we present electrolyte gate control of magnetism in ultrathin (8 u.c.) La$_{\mathrm{0.5}}$Sr$_{\mathrm{0.5}}$CoO$_{\mathrm{3-\delta }}$ (LSCO) films, using ion gels in electric double layer transistors. The LSCO films are initially metallic and ferromagnetic ($T_{c}\approx $ 170 K), with anomalous Hall conductivity up to 40 S/cm, and strong perpendicular magnetic anisotropy. Based on extensive temperature and gate voltage dependences we first determined the limits for electrostatic \textit{vs}. electrochemical operation, concluding that negative bias enables reversible hole accumulation, whereas positive bias irreversibly induces oxygen vacancies. Following this we demonstrated clear voltage-control of resistivity, magnetoresistance, and$ T_{c}$. Utilizing the anomalous Hall conductivity as an exceptional probe of the magnetic order parameter in the gated surface region, a 12 K shift in $T_{c}$ is obtained. This compares favorably to the state-of-the-art and exhibits potential for much larger modulation in films of lower Sr content. Work supported by NSF MRSEC.