Emergent electrochemistry in spin ice: Debye-Hückel theory and beyond

We present a detailed theoretical and experimental study to show how a model system for the investigation of classic electrolyte theory emerges in a nonelectrical context. In particular we develop the thermodynamic treatment of spin ice as a “magnetolyte,” a fluid of singly and doubly charged magnetic monopoles. This is equivalent to the electrochemical system 2H2O=H3O++OH−=H4O2++O2−, but with perfect symmetry between oppositely charged ions. For this lattice magnetolyte, we present an analysis going beyond Debye-Hückel theory to include Bjerrum pairs. This is accurate at all temperatures and incorporates “Dirac strings” imposed by the microscopic ice rule constraints at the level of Pauling's approximation. Our theory is in close agreement with the specific heat from numerical simulations as well as new experimental measurements with an improved lattice correction, which we present here, on the spin ice materials Ho2Ti2O7 and Dy2Ti2O7. Our results provide new experimental tests of Debye-Hückel theory and its extensions and yield insights into the electrochemical behavior of water ice and liquid water, which are closely related to the spin ice magnetolyte.