Recently, the electric and magnetic multipoles due to the orbital degrees of freedom are considered to be important for the study on new functional physical properties. In principle, no quadrupolar ordering occurs in a magnetically ordered state because the degeneracy of multipoles is lifted by a magnetic ordering.

However, our experimental and calculated results revealed that a novel multipolar ordering occurs in a magnetically ordered state in the rare-earth compound ErNiAl. Why does a multipolar ordering occur in a condition of no multipole degree of freedom of which the degeneracy of multipoles is lifted by a local internal magnetic field of magnetic ordering? Understanding of its origin is significant and is expected to contribute to development of functional materials, such as new switching devices using the multipoles.

The rare-earth compound ErNiAl shows an antiferromagnetic ordering at TN = 6 K. We performed the ultrasonic measurement which is a great tool for investigating the electric quadrupole, one of the multipoles. Generally the elastic modulus increases monotonically with decreasing the temperature. In ErNiAl, however, the transverse modulus C66 shows a significant elastic softening due to a quadrupole mediated interaction below TN. The softening continues toward an as-yet-unidentified phase transition at TQ = 3.4 K. Our quantum-mechanical analysis indicates occurrence of a spontaneous quadrupolar order parameter at TQ and a positive coupling constant between the quadrupoles. From these results, we revealed that the phase transition at TQ is driven by the Oxy-type ferroquadrupolar ordering, making ErNiAl a unique compound because it exists in an electronic environment where quadrupolar ordering is impossible in principle. We also pointed out that the magnetic octupoles may facilitate a cross correlation between ordered spins and spontaneous strains.

In principle, multipolar ordering should not occur in a magnetically ordered state, however, ErNiAl clearly shows a novel multipolar ordering in the magnetically ordered state. We continue to investigate the mechanism why the multipolar ordering occurs in a magnetically ordered state. In addition, we are studying novel multiferroics with cross-correlation of a multipolar ordering in isomorphic compounds.

Reference
Ferroquadrupolar ordering in a magnetically ordered state in ErNiAl I. Ishii, Y. Kurata, Y. Wada, M. Nohara, T. Suzuki, K. Araki, and A. V. Andreev Physical Review B 105, 165147 (2022). DOI: 10.1103/PhysRevB.105.165147