Fig. 2: Summary of the CEF states and multipoles under non-crystallographic point group symmetries for given integer values of J. | npj Quantum Materials

Fig. 2: Summary of the CEF states and multipoles under non-crystallographic point group symmetries for given integer values of J.

From: Unveiling multipole physics and frustration of icosahedral magnetic quasicrystals

Fig. 2: Summary of the CEF states and multipoles under non-crystallographic point group symmetries for given integer values of J.The alternative text for this image may have been generated using AI.

a J = 4 (Pr3+) (b) J = 6 (Tb3+) and (c) J = 8 (Ho3+). Unlike the icosahedral symmetry Ih where the CEF states are split into several multiplets. the five-fold symmetry C5v symmetry splits all the multiplets into either non-Kramers doublets or singlets. Under C5v, the z-components of the pseudospin, Σz are magnetic dipoles for each doublet. On the other hand, the x, y-components, Σx,y represent either quadrupoles or hexadecapoles. Depending on the energy scale of the breaking of mirror symmetry, the order of energy could change. d Singlet (black), quadrupoles (blue-skyblue) and hexadecapoles (violet-skyblue). See the main text for more details.

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