Composite (multi)ferroic order

The formalism of composite and intertwined orders has been remarkably successful in discussing the complex phase diagrams of strongly correlated materials and high-T_c superconductors. A generalization of the formalism to other ordered states of matter has remained largely unexplored. Here, we show that conventional ferromagnetic and ferroelectric materials can exhibit composite orders, emerging above the critical temperature for the transition into the ferroic phase. The existence of this transition depends on the anisotropy of the ferroic phase. We show that the quadrupole magnetic and electric orders couple to the shear elastic constant, which explains experimental findings for elastic precursors of ferromagnetic and ferroelectric phase transitions, showing a softening of shear modes in various materials. Furthermore, we extend our formalism to strongly coupled multiferroic materials, which can form composites of magnetic and ferroelectric orders. This gives rise to novel kinds of "hidden orders", not interacting with electric, magnetic, or strain as well as insights into the formation of toroidal moments in multiferroics. As the multipolar and composite orders discussed here are emerging above the ferroic transition temperatures, they might be relevant for explaining precursor phenomena in incipient (multi)ferroic materials.

[1] R. M. Geilhufe, Hidden composite (multi)ferroic order, arXiv:2309.03312 (2023)