  The emergence of fractionalized quasiparticles in quantum spin liquids has
served a wealth of unconventional phenomena in frustrated magnets. In our work,
we explore the various domain patterns of such fractionalized quasiparticles,
especially focusing on charge defects in U(1) quantum spin liquids. We claim
that emergent long range interaction between charge defects leads to
characteristic structures with distinct length scales, where they can be
controlled via the ratio of interaction strengths. In this context, the spin
ice phase is the dilute gas of weakly interacting charges, whereas, the
macroscopic population of charge defects naturally develops charge ordering for
large Coulomb interaction limit. Interestingly, we find that the competing spin
interactions could naturally give rise to stabilize the mosaic structure of
charge defects in the absence of uniform ordering. They are characterized by
liquid-like correlations having a finite length scale. The emergence of such
intermediate order in the mosaic structure is confirmed by both dynamical and
static correlations. By establishing the microscopic spin Hamiltonian, we also
present the distinctive signatures in static spin correlation to detect such
spatial structure of charge defects. We speculate that the domain pattern of
defect population might be a potential hallmark to reveal unusual dynamical
properties observed in spin liquids.
