Dirac's “magnetic monopoles” in pyrochlore ice U(1) spin liquids: Spectrum and classification

Abstract

We study the $U(1)$ quantum spin liquid on the pyrochlore spin ice systems. For the non-Kramers doublets such as ${\mathrm{Pr}}^{3+}$ and ${\mathrm{Tb}}^{3+}$, we point out that the inelastic neutron scattering result not only detects the low-energy gauge photon, but also contains the continuum of the ``magnetic monopole'' excitations. Unlike spinons, these ``magnetic monopoles'' are purely of quantum origin and have no classical analog. We further point out that the ``magnetic monopole'' experiences a background dual ``$\ensuremath{\pi}$'' flux due to the spin-1/2 nature of the local moment when the ``monopole'' hops on the dual diamond lattice. We then predict that the ``monopole'' continuum has an enhanced spectral periodicity with a folded Brillouin zone. This prediction can be examined among the existing data on non-Kramers doublet spin liquid candidate materials like ${\mathrm{Pr}}_{2}{\mathrm{TM}}_{2}{\mathrm{O}}_{7}$ and ${\mathrm{Tb}}_{2}{\mathrm{TM}}_{2}{\mathrm{O}}_{7}$ (with TM = transition metal). The application to the Kramers doublet systems and numerical simulation is further discussed. Finally, we present a general classification of distinct symmetry enriched $U(1)$ quantum spin liquids based on the translation symmetry fractionalization patterns of ``monopoles'' and ``spinons.''