Dynamic susceptibility and dynamic correlations in spin ice

Here we calculate the dynamic susceptibility and dynamic correlation function in spin ice using the model of emergent magnetic monopoles. Calculations are based on a method originally suggested for the description of dynamic processes in water ice (non-equilibrium thermodynamics approach). We show that for $T\rightarrow 0$ the dynamic correlation function reproduces the transverse dipole correlations (static correlation function) characteristic of spin ice in its ground state and explains in what sense spin ice is non-ergodic. At non-zero temperatures the dynamic correlation function includes an additional longitudinal component which decreases as the temperature decreases. Both terms (transverse and longitudinal) exhibit identical Debye-like dependences on frequency but with different relaxation times: the magnetic Coulomb interaction of monopoles reduces the longitudinal relaxation time with respect to the transverse one. We calculate the dielectric function analogue for the magnetic monopole gas and discuss how the non-equilibrium thermodynamics approach exposes corrections to the Debye-Hückel theory of magnetic monopoles and the concept of “entropic charge”