The interplay between strong electronic correlations and spin–orbit coupling produces a variety of unconventional quantum phenomena and remains a central theme in condensed-matter physics. A key example can be observed in f-electron materials, where spin–orbit coupling combined with a highly symmetric crystalline electric field (CEF) can give rise to a degenerate ground state with multiple degrees of freedom.

These electronic degrees of freedom are naturally classified using the concept of multipoles, according to the symmetry of charge and magnetization distributions. While most experimentally established ordered phases involve magnetic dipoles, higher-rank multipoles, such as electric quadrupoles and magnetic octupoles, are difficult to observe directly.

In most f-electron materials, symmetry breaking occurs in magnetic dipole sectors. However, in some non-Kramers ions such as Praseodymium (Pr³⁺), where the CEF ground state carries no magnetic dipoles, high-rank multipoles play a primary role.

In a recent study published in the Journal of the Physical Society of Japan, researchers reported clear experimental evidence of magnetic-field-induced transitions in the ferro-quadrupole (FQ) ordered state of the Pr-based cage compound PrTi₂Al₂₀. The study demonstrated discontinuous switching of the FQ order depending on the direction of external magnetic field.

To directly probe the symmetry of the FQ order, the authors performed high-precision aluminum nuclear magnetic resonance measurements, complemented by magnetization studies. Notably, to explain the field-induced switching, this study presented a novel theoretical model in which the quadrupole interaction itself depends on magnetic-field direction. This model consistently reproduces the experimental observations.

This work establishes an important framework for identifying and characterizing multipolar ordered phases, providing valuable insight into the role of higher-rank multipoles. Recognizing the novelty and potential of this work, this paper was awarded the Outstanding Paper Award of the Physical Society of Japan in 2026.

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