Two Spin-State Crystallizations in LaCoO$_{3}$

We report a magnetostriction study of a perovskite $\rm{LaCoO}_{3}$ above 100 T using our state-of-the-art strain gauge to investigate an interplay between electron correlations and spin crossover. There has been a controversy regarding whether two novel phases in $\rm{LaCoO}_{3}$ at high magnetic fields result from crystallizations or Bose-Einstein condensation during spin crossover as manifestations of localization and delocalization in spin states, respectively. We show that both phases are crystallizations rather than condensations, and the two crystallizations are different, based on the observations that the two phases exhibit as magnetostriction plateaux with distinct heights. The crystallizations of spin states have emerged manifesting the localizations and interactions in spin crossover with large and cooperative lattice changes.