Generalised Longitudinal Susceptibility for Magnetic Monopoles in Spin Ice

Abstract

The generalised longitudinal susceptibility $\chi (\mathbf{q},\omega )$ affords a sensitive measure of the spatial and temporal correlations of magnetic monopoles in spin ice. Starting with the monopole model, a mean field expression for $\chi (\mathbf{q},\omega )$ is derived as well as expressions for the mean square longitudinal field and induction at a point. Monopole motion is shown to be strongly correlated, and both spatial and temporal correlations are controlled by the dimensionless monopole density $x$ which defines the ratio of the magnetization relaxation rate and the monopole hop rate. Thermal effects and spin lattice relaxation are also considered. The derived equations are applicable in the temperature range where the Wien effect for magnetic monopoles is negligible. They are discussed in the context of existing theories of spin ice and the following experimental techniques: dc and ac-magnetization, neutron scattering, neutron spin echo, and longitudinal and transverse field $\mu$SR. The monopole theory is found to unify diverse experimental results, but several discrepancies between theory and experiment are identified. One of these, concerning the neutron scattering line shape, is explained by means of a phenomenological modification to the theory.

29 pages, 4 figures; to be published in Phil. Trans A, special issue for Royal Society Theo Murphy Meeting on Magnetic Monopoles in Spin Ice (Nov. 2011, UK). Second version, significantly revised after helpful referee comments. Many typos corrected

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• Far from equilibrium monopole dynamics in spin ice
• New physics in frustrated magnets: Spin ices, monopoles, etc
• Dynamical fractal and anomalous noise in a clean magnetic crystal
• Experimental signature of the attractive Coulomb force between positive and negative magnetic monopoles in spin ice
• Coulomb phase diagnostics as function of temperature, interaction range and disorder
• Dynamic susceptibility and dynamic correlations in spin ice
• Acoustic signatures of the phases and phase transitions in Yb${}_2$Ti${}_2$O${}_7$
• Low-temperature muon spin rotation studies of the monopole charges and currents in Y doped Ho2Ti2O7
• Screening and the Pinch Point Paradox in Spin Ice
• Symmetry, Superposition and Fragmentation in Classical Spin Liquids: A General Framework and Applications to Square Kagome Magnets
• Gauge-Free Duality in Pure Square Spin Ice: Topological Currents and Monopoles
• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands
• Controlling degeneracy and magnetization switching in an artificial spin ice system of peanut-shaped nanomagnets