Abstract
The generalized longitudinal susceptibility χ(q,ω) 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 χ(q,ω) 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 μSR. 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.
Highlights
Following the paper of Castelnovo, Moessner and Sondhi [1] on emergent magnetic monopoles, there has been renewed interest in the properties of spin ice [2,3,4,5]
Magnetic monopole currents were first envisaged by Ryzhkin [6], while Jaubert & Holdsworth [7,8] studied the closely related problem of magnetic relaxation in spin ice by means of numerical simulations of the dipolar spin-ice model [9,10] and of a dual monopole electrolyte
Experimental evidence indicates that magnetic monopoles afford an economical description of spin ice at temperatures below approximately 10 K [13,14,15]
Summary
Following the paper of Castelnovo, Moessner and Sondhi [1] on emergent magnetic monopoles, there has been renewed interest in the properties of spin ice [2,3,4,5]. The simplest approach to treating the monopole correlations is a ‘magnetolyte’ model of freely diffusing magnetic charges, in which the effect of Dirac strings is subsumed into the transport coefficients, and electrolyte properties such as Debye–Hückel screening [17], Bjerrum pairing [11,16,17] and the Wien effect [11,12] may be naturally formulated Another (and earlier) approach [6] accounts for the ignored spin degrees of freedom in the form of an effective reaction field, and this approach has recently been developed to include magnetic charge screening [38]. The results of the present paper are applicable to zero and weak applied field (m0H 1 T).
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