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Ising models on a pyrochlore oxide lattice have become associated with spin ice materials and magnetic monopoles. Ever more often, effects connecting magnetic and elastic degrees of freedom are reported on these and other related frustrated materials. Here we extend a spin-ice Hamiltonian to include coupling between spins and the O −2 ions mediating superexchange; we call it the magnetoelastic spin ice model (MeSI). There has been a long search for a model in which monopoles would spontaneously become the building blocks of new ground-states: the MeSI Hamiltonian is such a model. In spite of its simplicity and classical approach, it describes the double-layered monopole crystal observed in Tb 2 Ti 2 O 7 . Additionally, the dipolar electric moment of single monopoles emerges as a probe for magnetism. As an example we show that some Coulomb phases could, in principle, be detected through pinch points associated with O −2 -ion displacements. Pyrochlore oxide lattices are home to many geometrically frustrated magnetic systems, including the celebrated spin ice. The authors present an Ising magnetic model on this structure, with a magnetoelastic term coupling the spin lattice to the O −2  ions which mediate superexchange. This model explains the presence of exotic forms of order found in previous experiments, allows stabilisation of some long-sought phases, and signals lattice distortions as a new probe for the complex magnetism of these materials.

Monopole matter from magnetoelastic coupling in the Ising pyrochlore