Theory of electric, magnetic, and toroidal polarizations in crystalline solids with applications to hexagonal lonsdaleite and cubic diamond

Abstract

Multipolar order in bulk crystalline solids is characterized by multipole densities -- denoted as polarizations in this work -- that cannot be cleanly defined using the concepts of classical electromagnetism. Here we use group theory to overcome this difficulty and present a systematic study of electric, magnetic and toroidal multipolar order in crystalline solids. Based on our symmetry analysis, we identify five categories of polarized matter, each of which is characterized by distinct features in the electronic band structure. For example, Rashba spin splitting in electropolar bulk materials like wurtzite represents the electric dipolarization in these materials. We also develop a general formalism of indicators for individual multipole densities that provide a physical interpretation and quantification of multipolar order. Our work clarifies the relation between patterns of localized multipoles and macroscopic multipole densities they give rise to. To illustrate the general theory, we discuss its application to polarized variants of hexagonal lonsdaleite and cubic diamond structures. Our work provides a general framework for classifying and expanding current understanding of multipolar order in complex materials.

26 pages, 5 figures, final version

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• Quantum Theory of Orbital Magnetization and its Generalization to Interacting Systems
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• Suppression of the D'yakonov-Perel' spin relaxation mechanism for all spin components in [111] zincblende quantum wells
• Emergent odd-parity multipoles and magnetoelectric effects on a diamond structure: implication to 5$d$ transition metal oxides $A$OsO${}_4$ ($A=$ K, Rb, and Cs)
• Magnonics vs. Ferronics
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Cited by in corpus (14)

• Landau Theory of Altermagnetism
• Magnetic octupoles as the order parameter for unconventional antiferromagnetism
• Topological transition from nodal to nodeless Zeeman splitting in altermagnets
• Dynamic paramagnon-polarons in altermagnets
• Elasto-Hall conductivity and the anomalous Hall effect in altermagnets
• Anisotropic light-tailored RKKY interaction in two-dimensional $d$-wave altermagnets
• Electric field-induced nonreciprocal directional dichroism in a time-reversal-odd antiferromagnet
• Magnetic parity violation and parity-time-reversal-symmetric magnets
• Elastic Quantum Criticality in Nematics and Altermagnets via the Elasto-Caloric Effect
• Magnetic-field-tuned randomness in inhomogeneous altermagnets
• Multipole order in two-dimensional altermagnets
• Giant non-reciprocal band structure effect in a multiferroic material
• Standard model of electromagnetism and chirality in crystals
• Micromagnetic simulations for magnetic multipoles