A review on magnetic field induced spin crossover in LaCoO${}_3$ up to 600 T

\lco{} is known for its two-step spin crossover as a function of temperature. Despite efforts spanning over half a century, the origin of this phenomenon is still debated, particularly regarding how the microscopic spin states are involved in the observed macroscopic two-step spin crossover. High magnetic field studies on LaCoO${}_3$ are performed because the magnetic field-induced spin crossover is induced, where the magnetic excited states become more stable in high magnetic fields than the non-magnetic ground states. This review focuses on the findings in LaCoO${}_3$ at high magnetic fields over the last decade. A complex phase diagram has been revealed at high magnetic fields instead of solving the conventional problem of LaCoO${}_3$. It suggests that appreciable spin state correlations are in play in LaCoO${}_3$. The possibility of exciton condensation is also discussed.