Electric monopoles in pyrochlore quantum spin liquids and inelastic neutron scattering signature in Ce-based compounds

Pyrochlore quantum spin liquid (QSL) is an exotic quantum state and has a strong experimental connection with the pyrochlore quantum spin ice materials such as the Ce-based pyrochlore magnets. The local moments of Ce³⁺ were identified as the dipole-octupole (DO) doublets, which leads to distinct symmetry-enriched spin liquids: the dipolar U(1) and the octupolar U(1) QSL. They have three fundamental excitations: spinons, gauge photons, and electric monopoles. Among them, the electric monopoles have purely quantum originations. Due to the special properties of the DO nature of the Ce³⁺ moment, the inelastic neutron scattering (INS) measurement in the octupolar U(1) QSL selects the gapped spinon continuum and thus has suppressed spectral weights below the energy threshold of two spinon gaps. This measurement, however, includes all other emergent excitations at lower energies in the dipolar U(1) QSL. Although the electric monopole continuum is weakly gapped compared to the larger spinon gap, the energy scale is close to the gauge photons, and the spectrum largely overlaps with the photons. Due to the background dual π flux for the electric monopoles, the density of states is enhanced at lower energies. This can be contrasted with the linearly suppressed spectral weight of the gauge photons at low energies. We propose that the electric monopole continuum should be mostly responsible for the low-energy spectrum in the INS measurement in the dipolar U(1) QSL.