$\mathrm{LuC}{\mathrm{o}}_3$ is an itinerant ferromagnet whose magnetic properties strongly depend on the position of the $3d$ electronic states relative to the Fermi level. Here, we report on the magnetization of a $\mathrm{LuC}{\mathrm{o}}_3$ single crystal in pulsed magnetic fields up to 58 T. We find a field-induced phase transition just below 50 T from a low-spin to a high-spin state. The transition shows a pronounced anisotropy of the magnetization jump and hysteresis. A series of ab initio calculations based on the density functional theory show that the transition is due to a significant change in the occupancies of the Co $3d$ electronic states. At the same time, some features in the majority spin density of the Co $3d$ states are slightly modified and pass through the Fermi level when the spin state is changed, which leads to the instability of the $3d$-electron subsystem. Thereby, the applied magnetic field causes a significant redistribution in the majority and minority spin states in the Co $3d$ subsystem, which results in the sharp change in the magnetization.

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• Metamagnetism
• Spin state transition
• Intermetallic compounds
• Single crystal materials
• Density functional calculations
• Magnetization measurements