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Dynamic interplay of nematic, magnetic, and tetrahedral order in ferromagnetic nematic phases

We consider the influence of tetrahedral/octupolar order on ferromagnetic nematic liquid-crystalline phases. The presence of tetrahedral order leads to broken parity symmetry in an achiral liquid-crystalline system, in addition to broken time-reversal symmetry associated with the existence of a spontaneous magnetization. As a consequence we find static as well as reversible and irreversible dynamic cross-coupling terms absent in usual ferromagnetic nematics. Several static and dynamic experiments are suggested to detect possible tetrahedral order. We predict that linear gradients terms in the generalized energy involving the ferromagnetic magnetization and the nematic director field lead to chiral domains of ambidextrous helicity. As a characteristic dissipative dynamic cross-coupling we point out that the rotation of the magnetization can be driven by temperature and/or concentration gradients. Conversely heat and concentration currents can be generated by rotations of the magnetization. As a characteristic example for reversible cross-coupling terms we analyze the consequences of the coupling between the molecular field of the nematic director and temperature and concentration gradients.