Unveiling hidden multipolar orders with magnetostriction

Area of Science:

• Condensed Matter Physics
• Materials Science
• Quantum Materials

Background:

• Higher-order multipolar degrees of freedom in solids lead to "hidden orders" that are difficult to detect with conventional methods.
• Pr-based cage compounds, such as Pr(Ti,V,Ir)₂(Al,Zn)₂₀, exhibit complex electronic behaviors driven by strongly correlated f-electrons.
• These materials possess low-energy degrees of freedom dominated by higher-order multipoles, including quadrupoles and octupoles.

Purpose of the Study:

• To theoretically propose and validate magnetostriction as a direct detection method for higher-order multipolar symmetry breaking.
• To investigate the potential of detecting elusive octupolar order in Pr-based cage compounds.
• To establish a relationship between magnetostriction and octupolar order parameters.

Main Methods:

• Development of a symmetry-based Landau theory to model the system's behavior.
• Theoretical analysis of magnetostriction, specifically the length change in response to an applied magnetic field (h).
• Focus on Pr-based cage compounds Pr(Ti,V,Ir)₂(Al,Zn)₂₀ with higher-order multipolar degrees of freedom.

Main Results:

• A distinct linear-in-h length change was theoretically predicted when a magnetic field is applied along the [111] direction.
• This specific magnetostriction effect is observed below the octupolar ordering temperature.
• The calculated magnetostriction coefficient is directly proportional to the octupolar order parameter.

Conclusions:

• Magnetostriction serves as a powerful and novel probe for directly detecting higher-order multipolar symmetry breaking, including octupolar order.
• The proposed method provides clear access to subtle octupolar order parameters in materials like Pr-based cage compounds.
• This work opens new avenues for characterizing complex magnetic orders in quantum materials.