  Artificial magnetism at optical frequencies can be realized in metamaterials
composed of periodic arrays of subwavelength elements, also called
"meta-atoms". Optically-induced magnetic moments can be arranged in both
unstaggered structures, naturally associated with ferromagnetic (FM) order, or
staggered structures, linked correspondingly to antiferromagnetic (AFM) order.
Here we demonstrate that such magnetic dipole orders of the lattices of
meta-atoms can appear in low-symmetry Mie-resonant metasurfaces where each
asymmetric dielectric (non-magnetic) meta-atom supports a localized trapped
mode. We reveal that these all-dielectric resonant metasurfaces possess not
only strong optical magnetic response but also they demonstrate a significant
polarization rotation of the propagating electromagnetic waves at both FM and
AFM resonances. We confirm these findings experimentally by measuring directly
the spectral characteristics of different modes excited in all-dielectric
metasurfaces, and mapping near-field patterns of the electromagnetic fields at
the microwave frequencies.
