Quantum aspects of fragmentation in spin ices

The apparent fragmentation of magnetic moments in spin ice systems into coexisting longitudinal, transverse and harmonic parts is a direct consequence of emergent electromagnetism in these systems. At the microscopic level, moments of fixed length act as elements of an emergent field from which magnetic monopoles can be excited. By construction, the leftover is divergence-free. In quantum spin ice systems the emergence is even more striking, as small quantum fluctuations give to the transverse part the dynamics of a compact, U(1) gauge theory. An example of fragmentation is the monopole crystal phase in classical spin ice, in which the longitudinal field has AF long-range order and the transverse part remains disordered. In this talk we identify new fragmented phases and discuss their stability with regard to quantum fluctuations, external fields, and other interactions. In particular we focus on the partially ordered topological phase of kagome spin ice. We show that the onset of the predicted long-range dimer order is explicitly reflected in the transverse part of the emergent field, accompanied by enhanced quantum fluctuations. As a consequence,the dimer ordering can be directly observed by neutron scattering. The same approach is applied to fragmented pyrochlore spin ice