Commensurate to incommensurate charge ordering and its real-space images in La_0.5Ca_0.5MnO₃

The antiferromagnetic to ferromagnetic transition in La_0.5Ca_0.5MnO₃ is accompanied by a commensurate to incommensurate charge-ordering transition. The presence of incommensurate charge correlation in the ferromagnetic phase is a remarkable interplay between charge and spin in double-exchange ferromagnets. Furthermore, a dark-field imaging technique has provided real-space images of charge-ordered domains revealing discommensurations inside the nearly commensurate domains. Local density fluctuations of discommensurations are responsible for the similar variations of the charge-ordering wave vector.