Giant Electrostatic Modification of Magnetism via Electrolyte-Gate-Induced Cluster Percolation in La$_{1-x}$Sr$_x$CoO$_{3-delta}$

Electrical control of magnetism is a long-standing goal in physics and technology, recently developed electrolyte gating techniques providing a promising route to realization. Validating a recent theoretical prediction, here we demonstrate large enhancement of electrostatic modulation of ferromagnetic order in ion-gel-gated ultrathin La$_{0.5}$Sr$_{0.5}$CoO$_{3-delta}$ by thickness-tuning to the brink of a magnetic percolation transition. Application of only 3-4 V then drives a transition from a short-range-ordered insulator to a robust long-range ferromagnetic metal, realizing giant electrostatic Curie temperature modulation over a 150 K window. In operando polarized neutron reflectometry confirms gate-controlled ferromagnetism, also demonstrating unusually deep penetration of induced magnetization, in further agreement with theory.