Composite quadrupole order in ferroic and multiferroic materials.

Area of Science:

• Condensed matter physics
• Materials science

Background:

• Composite and intertwined orders formalism successfully explains complex phase diagrams in strongly correlated materials and high-temperature superconductors.
• Lattice anisotropy plays a crucial role in the emergence of composite orders in ferroic materials.

Purpose of the Study:

• To propose and investigate the realization of composite orders in ferroelectric and ferromagnetic materials.
• To demonstrate how composite orders are determined by lattice anisotropy and the easy axis of magnetization or polarization.
• To extend the composite order formalism to multiferroic materials and explain precursor phenomena.

Main Methods:

• Theoretical modeling based on the composite and intertwined orders formalism.
• Analysis of ferroelectric, ferromagnetic, and multiferroic materials considering lattice anisotropy.

Main Results:

• Composite orders are identified in ferroelectric and ferromagnetic materials above their respective phase transitions.
• The type of composite order is dictated by the material's easy axis.
• The formalism naturally incorporates magnetoelectric monopole, toroidal, and quadrupole orders.
• Composite orders can explain precursor phenomena in incipient ferroic materials.

Conclusions:

• The composite order formalism provides a unified framework for understanding complex orders in ferroic and multiferroic materials.
• This approach offers insights into precursor phenomena and potentially hidden orders, aiding in material characterization.