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We investigated the fundamental physical properties in the ultra-quantum limit state of bismuth through measurements of magnetoresistance, magnetization, magnetostriction, and ultrasound attenuation in magnetic fields up to 60T. For magnetic fields applied along the bisectrix direction of a single crystal, a drastic sign reversal in magnetostriction was observed at approximately 39T, which could be ascribed to the complete valley polarization in the electron Fermi pockets. The application of magnetic fields along the binary direction presented an anomalous feature at approximately 50T only in the magnetoresistance. The emergence of a field-induced splitting of a valley was proposed as a possible origin of this anomaly.

Thermodynamic evidence of magnetic-field-induced complete valley polarization in bismuth