  How to control collectively ordered electronic states is a core interest of
condensed matter physics. We report an electric field controlled reversible
transition from superconductor to ferromagnetic insulator in (Li,Fe)OHFeSe thin
flake using solid ion conductor as the gate dielectric. By driving Li ions into
and out of the (Li,Fe)OHFeSe thin flake with electric field, we obtained a
dome-shaped superconducting region with optimal Tc ~ 43 K, which is separated
by a quantum critical point from ferromagnetically insulating phase. The
ferromagnetism arises from the long range order of the interstitial Fe ions
expelled from the (Li,Fe)OH layers by Li injection. The device can reversibly
manipulate collectively ordered electronic states and stabilize new metastable
structures by electric field.
