Interplay of uniform U (1) quantum spin liquid and magnetic phases in rare-earth pyrochlore magnets: A fermionic parton approach

We study the uniform time-reversal-invariant $U(1)$ quantum spin liquid (QSL) with low-energy fermionic quasiparticles for rare-earth pyrochlore magnets and explore its magnetic instability, employing an augmented fermionic parton mean field theory approach. Self-consistent calculations stabilize a uniform $U(1)$ QSL with both gapped and gapless parton excitations as well as fractionalized magnetically ordered phases in an experimentally relevant part of the phase diagram near the classical phase boundaries of the magnetically ordered phases. The gapped QSL has a band structure with a nonzero ${Z}₂$ topological invariant. The fractionalized magnetically ordered phases bear signatures of both QSL through fermionic excitations as well as magnetic order. Thus, this provides a possible way to understand the unconventional diffuse neutron scattering in rare-earth pyrochlores such as ${\mathrm{Yb}}₂{\mathrm{Ti}}₂{\mathrm{O}}₇$, ${\mathrm{Er}}₂{\mathrm{Sn}}₂{\mathrm{O}}₇$, and ${\mathrm{Er}}₂{\mathrm{Pt}}₂{\mathrm{O}}₇$ at low or zero external magnetic fields. We calculate the dynamic spin structure factor to understand the nature of the diffuse two-particle continuum.