  The phenomenon of phase separation into antiferromagnetic (AFM) and
superconducting (SC) or normal-state regions has great implication for the
origin of high-temperature (high-Tc) superconductivity. However, the occurrence
of an intrinsic antiferromagnetism above the Tc of (Li, Fe)OHFeSe
superconductor is questioned. Here we report a systematic study on a series of
(Li, Fe)OHFeSe single crystal samples with Tc up to ~41 K. We observe an
evident drop in the static magnetization at Tafm ~125 K, in some of the SC (Tc
< ~38 K, cell parameter c < ~9.27 {\AA}) and non-SC samples. We verify that
this AFM signal is intrinsic to (Li, Fe)OHFeSe. Thus, our observations indicate
mesoscopic-to-macroscopic coexistence of an AFM state with the normal (below
Tafm) or SC (below Tc) state in (Li, Fe)OHFeSe. We explain such coexistence by
electronic phase separation, similar to that in high-Tc cuprates and iron
arsenides. However, such an AFM signal can be absent in some other samples of
(Li, Fe)OHFeSe, particularly it is never observed in the SC samples of Tc > ~38
K, owing to a spatial scale of the phase separation too small for the
macroscopic magnetic probe. For this case, we propose a microscopic electronic
phase separation. It is suggested that the microscopic static phase separation
reaches vanishing point in high-Tc (Li, Fe)OHFeSe, by the occurrence of
two-dimensional AFM spin fluctuations below nearly the same temperature as Tafm
reported previously for a (Li, Fe)OHFeSe (Tc ~42 K) single crystal. A complete
phase diagram is thus established. Our study provides key information of the
underlying physics for high-Tc superconductivity.
