Magnetic Fragmentation in Spin Ice Systems
The apparent fragmentation [1,2] of magnetic moments in spin ice-like systems into coexisting longitudinal, transverse and harmonic parts is a direct consequence of emergent electromagnetism in these systems. At the microscopic level, the moments act as elements of this emergent lattice field from which topological defects, monopoles  can be excited. By construction, the left over is made up of a divergence free, or transverse component and a harmonic component controlled by the boundaries. The fragmentation process therefore provides a continuous fractionalisation of the moments allowing for novel magnetic phases and topological phase transitions. In this seminar I will review some of these including the partially ordered monopole crystal phase in which a Coulomb spin liquid coexists with antiferromagnetic order, as well as two fluid phases and topological aspects related to the harmonic component. I will also show how fragmentation leads naturally to the emergence of classical Dirac strings and how it can be used as a tool for the analysis of neutron scattering data in the presence of quantum spin fluctuations . Several experimental examples of fragmented systems will be discussed.
 M. E. Brooks-Bartlett, S. T. Banks, L. D. C. Jaubert, A. Harman-Clarke, P. C. W. Holdsworth. “Magnetic-Moment Fragmentation and Monopole Crystallization”. Physical Review X, 2014, 4, 011007.
 E. Lhotel, L.D.C. Jaubert, P.C.W. Holdsworth, J. Low. Temp. Physics 201, 710 (2020)
 Castelnovo, C., Moessner, R. & Sondhi, S. Magnetic monopoles in spin ice. Nature 451, 42–45 (2008). https://doi.org/10.1038/nature06433
 F. Museur, E. Lhotel, P. C. W. Holdsworth, arXiv:2209.10239, 2022