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We study energy gap formation at the level-crossing point due to the hyperfine interaction. In contrast to the energy gap induced by the Dzyaloshinskii-Moriya interaction, the gap induced by the hyperfine interaction is independent of the direction of the magnetic field. We also study the dynamics of the magnetization under a time dependent field that changes at a constant rate.

Directionally Independent Energy Gap Formation Due to the Hyperfine Interaction