Imaging the formation and surface phase separation of the CE phase.

The CE phase is an extraordinary phase exhibiting the simultaneous spin, charge, and orbital ordering due to strong electron correlation. It is an ideal platform to investigate the role of the multiple orderings in the phase transitions and discover emergent properties. Here, we use a cryogenic high-field magnetic force microscope to image the phase transitions and properties of the CE phase in a Pr_0.5Ca_0.5MnO₃ thin film. In a high magnetic field, we observed a clear suppression of magnetic susceptibility at the charge-ordering insulator transition temperature (T_COI), whereas, at the Néel temperature (T_N), no significant change is observed. This observation favors the scenario of strong antiferromagnetic correlation developed below T_COI but raises questions about the Zener polaron paramagnetic phase picture. Besides, we discoverd a phase-separated surface state in the CE phase regime. Ferromagnetic phase domains residing at the surface already exist in zero magnetic field and show ultra-high magnetic anisotropy. Our results provide microscopic insights into the unconventional spin- and charge-ordering transitions and revealed essential attributes of the CE phase, highlighting unusual behaviors when multiple electronic orderings are involved. [ABSTRACT FROM AUTHOR]