The Coulomb phase, with its dipolar correlations and pinch-point-scattering patterns, is central to discussions of geometrically frustrated systems, from water ice to binary and mixed-valence alloys, as well as numerous examples of frustrated magnets. The emergent Coulomb phase of lattice-based systems has been associated with divergence-free fields and the absence of long-range order. Here, we go beyond this paradigm, demonstrating that a Coulomb phase can emerge naturally as a persistent fluctuating background in an otherwise ordered system. To explain this behavior, we introduce the concept of the fragmentation of the field of magnetic moments into two parts, one giving rise to a magnetic monopole crystal, the other a magnetic fluid with all the characteristics of an emergent Coulomb phase. Our theory is backed up by numerical simulations, and we discuss its importance with regard to the interpretation of a number of experimental results

Low-dimensional magnetic heterostructures are a key element of spintronics, where magnetic interactions between different materials often define the functionality of devices. Although some interlayer exchange coupling mechanisms are by now well established, the possibility of direct exchange coupling via proximity-induced magnetization through non-magnetic layers is typically ignored due to the presumed short range of such proximity effects. Here we show that magnetic order can be induced throughout a 40-nm-thick amorphous paramagnetic layer through proximity to ferromagnets, mediating both exchange-spring magnet behaviour and exchange bias. Furthermore, Monte Carlo simulations show that nearest-neighbour magnetic interactions fall short in describing the observed effects and long-range magnetic interactions are needed to capture the extent of the induced magnetization. The results highlight the importance of considering the range of interactions in low-dimensional heterostructures and how magnetic proximity effects can be used to obtain new functionality.