Abstract
We present a general formalism of multipole descriptions under the space-time inversion group. We elucidate that two types of atomic toroidal multipoles, i.e., electric and magnetic, are fundamental pieces to express electronic order parameters in addition to ordinary electric and magnetic multipoles. By deriving quantum-mechanical operators for both toroidal multipoles, we show that electric (magnetic) toroidal multipole higher than dipole (monopole) can become a primary order parameter in a hybridized-orbital system. We also demonstrate emergent cross-correlated couplings between electric, magnetic, and elastic degrees of freedom, such as magneto-electric and magneto(electro)-elastic couplings, under toroidal multipole orders.
Highlights
Mutual interplay between fundamental degrees of freedom of electrons in solids, i.e., charge, spin, and orbital, has attracted growing interest in various context
In d-electron systems, an atomic multipole has been extended to an object that is defined over a cluster consisting of several atomic sites; magnetic monopole excitations in spin ice5,6, magnetic octupole by noncollinear/noncoplanar magnetic structures7,8, nematic order in iron-based superconductors9,10, and spin chirality accompanying Berry phase11
The magnetic toroidal (MT) dipole has been extensively investigated due to its potential role for exotic phenomena, such as magneto-electric effect and nonreciprocal directional dichroism27–35. Such a MT dipole is often identified with a vortex-type magnetic orderings over several atomic sites
Summary
The Hamiltonian inducing the Tx order in an s-p hybridized-orbital system is given by. The Hamiltonian inducing the Tyz order in an s-d hybridized-orbital system is given by. The wave functions are shown in the lower panel of Fig. 2
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
