Unified description of electronic orderings and cross correlations by complete multipole representation

Abstract

We overview recent developments of electronic orderings and associated cross correlations in condensed matter physics based on a complete set of multipole representations (electric, magnetic, electric toroidal, and magnetic toroidal multipoles) with distinct space-time inversion symmetries. By means of the symmetry-adapted complete basis set in any physical Hilbert space including atomic and cluster degrees of freedom, it provides a unified description of electronic orderings, deformations of band structures, cross correlations, and transport properties in solids. We review that a multipole representation is a powerful tool to attain a comprehensive understanding of various electronic properties and physical phenomena observed in materials. We also demonstrate how to identify active multipoles and expected physical phenomena in real materials with several examples. Our review would serve as a solid foundation for future studies toward observations and identifications of unknown electronic phases and their related physical phenomena.

41 pages, 30 figures, 14 tables

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• Cluster Toroidal Multipoles Formed by Electric-Quadrupole and Magnetic-Octupole Trimers: A Possible Scenario for Hidden Orders in Ca${}_5$Ir${}_3$O${}_{12}$
• Spin Conductivity Based on Magnetic Toroidal Quadrupole Hidden in Antiferromagnets
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• Electric Quadrupolar Contributions in the Magnetic Phases of UNi${}_4$B
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Cited by in corpus (32)

• Emergence of chirality by multipole interconversion
• Purely Electronic Chirality without Structural Chirality
• Symmetry-adapted closest Wannier modeling based on complete multipole basis set
• Nonlinear Piezomagnetic Effects in $g$-wave Altermagnets
• Anisotropic Piezomagnetism in Noncollinear Antiferromagnets
• Intrinsic low-temperature magnetic properties on the ultra-clean UTe${}_2$ with $T_{\mathrm{c}}$ = 2.1 K revealed by ${}^{125}$Te NMR
• Quantification of electronic asymmetry: chirality and axiality in solids
• Sum rules for x-ray circular and linear dichroism based on complete magnetic multipole basis
• Relativistic Spin-momentum locking in altermagnets
• Predominant Electronic Order Parameter for Structural Chirality -- Role of Spinless Electronic Toroidal Multipoles
• Finite-$q$ antiferrotoroidal and ferritoroidal order in a distorted kagome structure
• Chirality/Axiality-Induced Axiality/Chirality via Surface Polarization
• TbPt6Al3: A rare-earth-based g-wave altermagnet with a honeycomb structure
• Electron chirality and hydrodynamic helicity: Analysis in the atomic limit
• Multipole analysis of spin currents in altermagnetic MnTe
• X-ray magnetic circular dichroism originating from the $T_z$ term in collinear altermagnets under trigonal crystal field
• DiracBilinears.jl: A package for computing Dirac bilinears in solids
• Spin-flip Scattering at a Chiral Interface of Helical Chains
• Analysis of Spin Current Generation by Elastic Waves in $f$-wave Altermagnets
• Theory of Many-Body Multipole Operators in Single-Centered Electron Systems: Two-Body Toroidal Monopoles in Spinless Orbitals
• Relativistic spin-momentum locking in ferromagnets
• Nonlinear frequency-asymmetric optical response in chiral systems
• Superzone gap formation induced by ferroic orders
• Microscopic Determination of the c-axis-Oriented Antiferromagnetic Structure in LaMnSi by ${}^{55}$Mn and ${}^{139}$La NMR
• Nonrelativistic Functional Properties in Collinear Antiferromagnets Based on Multipole Representation Theory
• Light-induced nonlinear Edelstein effect under ferroaxial ordering
• Piezomagnetic effect of a rare-earth-based altermagnet TbPt6Al3
• Multipolar fluctuations from localized 4f electrons in CeRh2As2
• Effects of crystal field and momentum-based frustrated exchange interactions on multiorbital square skyrmion lattice
• Detection of ferroic octupole ordering in $d$-wave altermagnetic rutile-type compounds
• Symmetry Rules on Multipole Interactions under Crystallographic Point Groups and Application to Multiple-$Q$ Multipole States
• Ferroaxial order of the monolayer ice in martyite