 Within the Landau paradigm, generic electronic and magnetic ordered states are characterized by symmetry-breaking order parameters. The electromagnetic multipole expansion provides a powerful framework to further characterize these for local moment systems. Ordered states based on electric and magnetic dipoles are common, and the corresponding order parameters can be readily coupled to, and manipulated by, uniform electric and magnetic fields respectively. We have studied the case of electric quadrupole order extensively, for which uniform strain has the correct symmetry to act as an effective field. In centrosymmetric systems, the magnetic octupole is the next-allowed magnetic multipolar degree of freedom (Figure, courtesy Linda Ye, illustrates the magnetization density in a specific magnetic octupole, with yellow and blue representing North and South magnetic poles). Revealing the presence of magnetic octupole order and associated octupole fluctuations in solids is significantly more challenging due to the lack of simple external fields that can couple to magnetic octupoles. We accomplish this by using a product of magnetic field Hi and shear strain εjk to form a composite effective field that has the right symmetry to couple to magnetic octupole moments. Using this approach, we are able to reveal for the first time the presence of magnetic octupole fluctuations in certain candidate materials. This work has found a new significance in the wider ontext of altermagnetism, certain classes of which break all the same symmetries as octupolar order. |
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| Fisher Research Group Geballe Laboratory for Advanced Materials Dept. of Applied Physics Stanford University CA 94305-4045 |
Last Updated: Nov 25th 2024 |