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 [3] 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 [4]. Several experimental examples of fragmented systems will be discussed.
[1] 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. 
[2] E. Lhotel, L.D.C. Jaubert, P.C.W. Holdsworth, J. Low. Temp. Physics 201, 710 (2020) 
[3] Castelnovo, C., Moessner, R. & Sondhi, S. Magnetic monopoles in spin ice. Nature 451, 42–45 (2008). https://doi.org/10.1038/nature06433
[4] F. Museur, E. Lhotel, P. C. W. Holdsworth, arXiv:2209.10239, 2022