Peter C. W. Holdsworth

Using the Dirac string formalism for monopoles, we expose an extensive analogy between magnetic monopole excitations in the dumbbell model of spin ice and those of the vacuum. In both cases, the Dirac strings are defined in the space-time of monopole trajectories, which are simulated in spin ice using transition graphs between initial and final configurations. The Stanford experiment for Dirac monopole detection is reconstructed in spin ice using the fragmentation procedure. The setup is then extended to simulate magnetic noise experiments using stochastic dynamics. It is shown that the noise from the monopoles and their constraining strings can be separated and that the correlated signal over long times comes largely from the constraining strings rather than from the monopoles themselves.

We test the fluctuation-dissipation relation (FDR) in spin ice materials Dy_{2}Ti_{2}O_{7} and Ho_{2}Ti_{2}O_{7} by measuring both the magnetic noise and the out-of-phase part of the susceptibility and comparing their ratio. We show that it is satisfied at temperatures well into the nonergodic region below 600 mK, indicating local equilibrium. In both materials, below 400 mK, low frequency violations develop, showing an excess of noise as in spin glasses, with a frequency threshold of 0.1 Hz. New relaxation pathways and aging properties are unveiled in this frequency range in the ac susceptibility. The FDR remains valid at higher frequencies down to 150 mK.