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Thermal analogue of gimbal lock in a colloidal ferromagnetic Janus rod

We report an entropy-driven orientational hopping transition in a magnetically confined colloidal Janus rod. In a magnetic field, the sedimented rod randomly hops between horizontal and vertical states: the latter state comes at a substantial gravitational cost at no reduction of magnetic potential energy. The probability distribution over the angles of the rod shows that the presence of an external magnetic field leads to the emergence of a metastable vertical state separated from the ground state by an effective barrier. This barrier does not come from the potential energy but rather from the vast gain in phase space available to the rod as it approaches the vertical state. The loss of rotational degree of freedom that gives rise to this effect is a statistical mechanical analogue of the phenomenon of gimbal lock from classical mechanics.