Magnetic modes compatible with the symmetry of crystals

A classification of magnetic point groups is presented which gives an answer to the question: which magnetic groups can describe a given magnetic mode? There are 32 categories of magnetic point groups which describe 64 unique magnetic modes: 16 with a ferromagnetic component and 48 without. This classification focused on magnetic modes is helpful for finding the magnetic space group which can describe the magnetic symmetry of the material.

Displacement-mediated bound states in the continuum in all-dielectric superlattice metasurfaces

Bound states in the continuum (BICs) are localized states coexisting with extended waves inside the continuous spectrum range, which have infinite lifetimes without any radiation. To extract high-Q quasi-BIC resonances from the symmetry-protected BIC for practical applications, symmetry-breaking approaches are usually exploited, either by slightly breaking the excitation field symmetry or structure symmetry. Here, we introduce an all-dielectric superlattice metasurface that can symmetry-compatibly convert BIC states into high-Q quasi-BIC modes based on the guided-mode resonance coupling by relative displacement tuning. The metasurface is composed of a superlattice of multiple nanobeams, supporting both magnetic mode and toroidal mode with large tunability. Both modes can interact with the incident continuum by mediating the displacement between nanobeams, which empowers dual asymmetric Fano resonances with high Q-factors. The bandwidth of the toroidal mode under y-polarized incidences and that of the magnetic mode under x-polarized incidences can be readily tuned by the local displacement between nanobeams in each unit cell. Such displacement-mediated BIC resonance is promising for various applications such as bio-molecule sensing and low threshold lasing.

Displacement-mediated bound states in the continuum in all-dielectric superlattice metasurfaces

Bound states in the continuum (BICs) are localized states coexisting with extended waves inside the continuous spectrum range, which have infinite lifetimes without any radiation. To extract high-Q quasi-BIC resonances from the symmetry-protected BIC for practical applications, symmetry-breaking approaches are usually exploited, either by slightly breaking the excitation field symmetry or structure symmetry. Here, we introduce an all-dielectric superlattice metasurface that can symmetry-compatibly convert BIC states into high-Q quasi-BIC modes based on the guided-mode resonance coupling by relative displacement tuning. The metasurface is composed of a superlattice of multiple nanobeams, supporting both magnetic mode and toroidal mode with large tunability. Both modes can interact with the incident continuum by mediating the displacement between nanobeams, which empowers dual asymmetric Fano resonances with high Q-factors. The bandwidth of the toroidal mode under TE-polarized incidences and that of the magnetic mode under TM-polarized incidences can be readily tuned by the local displacement between nanobeams in each unit cell. Such displacement-mediated BIC resonance is promising for various applications such as bio-molecule sensing and low threshold lasing.

Constraints on the resistivity of the oceanic lithosphere and asthenosphere from seafloor ocean tidal electromagnetic measurements

SUMMARY The electromagnetic (EM) field generated by ocean tidal flow is readily detectable in both satellite magnetic field data, and in ocean-bottom measurements of electric and magnetic fields. The availability of accurate charts of tidal currents, constrained by assimilation of modern satellite altimetry data, opens the possibility of using tidal EM fields as a source to image mantle electrical resistivity beneath the ocean basins, as highlighted by the recent success in defining the globally averaged lithosphere–asthenosphere boundary (LAB) with satellite data. In fact, seafloor EM data would be expected to provide better constraints on the structure of resistive oceanic lithosphere, since the toroidal magnetic mode, which can constrain resistive features, is a significant component of the tidal EM field within the ocean, but is absent above the surface (in particular in satellite data). Here we consider this issue in more detail, using a combination of simplified theoretical analysis and 1-D and 3-D numerical modelling to provide a thorough discussion of the sensitivity of satellite and seafloor data to subsurface electrical structure. As part of this effort, and as a step toward 3-D inversion of seafloor tidal data, we have developed a new flexible 3-D spherical-coordinate finite difference scheme for both global and regional scale modelling, with higher resolution models nested in larger scale solutions. We use the new 3-D model, together with Monte Carlo simulations of errors in tidal current estimates, to provide a quantitative assessment of errors in the computed tidal EM signal caused by uncertainty in the tidal source. Over the open ocean this component of error is below 0.01 nT in Bz at satellite height and 0.05 nT in Bx on the seafloor, well below typical signal levels. However, as coastlines are approached error levels can increase substantially. Both analytical and 3-D modelling demonstrate that the seafloor magnetic field is most sensitive to the lithospheric resistance (the product of resistivity and thickness), and is more weakly influenced (primarily in the phase) by resistivity of the underlying asthenosphere. Satellite data, which contain only the poloidal magnetic mode, are more sensitive to the conductive asthenosphere, but have little sensitivity to lithospheric resistance. For both seafloor and satellite data’s changes due to plausible variations in Earth parameters are well above error levels associated with source uncertainty, at least in the ocean interior. Although the 3-D modelling results are qualitatively consistent with theoretical analysis, the presence of coastlines and bathymetric variations generates a complex response, confirming that quantitative interpretation of ocean tidal EM fields will require a 3-D treatment. As an illustration of the nested 3-D scheme, seafloor data at five magnetic and seven electric stations in the northeastern Pacific (41○N, 165○W) are fit with trial-and-error forward modelling of a local domain. The simulation results indicate that the lithospheric resistance is roughly 7 × 108 Ωm2. The phase of the seafloor data in this region are inconsistent with a sharp transition between the resistive lithosphere and conductive asthenosphere.