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

Abstract

The low-temperature picture of dipolar spin ice in terms of the Coulomb fluid of its fractionalised magnetic monopole excitations has allowed analytic and conceptual progress far beyond its original microscopic spin description. Here we develop its thermodynamic treatment as a 'magnetolyte', a fluid of singly and doubly charged monopoles, an analogue of the electrochemical system 2H2O = H3O + + OH − = H4O 2+ + O 2− , but with perfect symmetry between oppositely charged ions. For this lattice magnetolyte, we present an analysis based on Debye-Hückel theory, which is accurate at all temperatures and incorporates 'Dirac strings' imposed by the microscopic ice rule constraints at the level of Pauling's approximation. Our results are 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 study of the magnetolyte shows how electrochemistry can emerge in non-electrical systems. We also provide new experimental tests of Debye-Hückel theory and its extensions. The application of our results also yields insights into the electrochemical behaviour of water ice and liquid water, which are closely related to the spin ice magnetolyte.I.

Screening and the pinch point paradox in spin ice

“…(21) depends on n through ξ (Eqs. (11), (12) and (21)), it might be appropriate to replace n by the true equilibrium density [41]. A fit to the ensuing function is tested in Fig.…”

“…Boundary conditions and screening -To account for different boundary conditions, we add a 'self field' [66] to the dipolar field which generates the correct average when the field is summed over a ellipsoidal volume: in this way the demagnetizing factor N d (= 1/3, 0 for spherical and Ewald boundaries respectively) naturally enters the equations, obviating the need to treat surface charge explicitly. This factor is conveniently introduced by treating the dipolar integral as a sum over thermally generated monopoles and allowing these to screen each other as in a Debye-Hückel gas [41]. In this approximation, the dipolar field is not simply equal to minus M L , but in addition has a longer-range harmonic component.…”

“…4, to compute the scattering functions, we left κ small but finite, which broadens the delta function slightly to render it visible to the eye. It might seem surprising that we have to remove the screening (κ → 0) in order to describe the numerical data: after all, it is well established from analysis of the specific heat, that monopoles are screened with a finite κ [41]. In fact, it was shown in Ref.…”

“…Hence Debye-Hückel theory can only describe the pinch point if the screening length κ −1 is set to be infinite, recovering the Poisson equation. In contrast, to calculate the specific heat [41], it incurs negligible error to neglect the power law tail of the potential, and equate κ with the Debye length of the monopole fluid.…”

“…In particular, we find that the pinch point profile, that summarizes the long ranged correlations in spin ice, presents a clear contradiction between theory and experiment. Motivations for studying the pinch points in classical spin ices like Ho 2 Ti 2 O 7 and Dy 2 Ti 2 O 7 include not only their above-mentioned status as model representatives of a large class of condensed matter, but also their more recently-established status as model Coulomb fluids [37,[40][41][42][43][44]. Here they afford perhaps unique examples of a model lattice Coulomb fluid (of magnetic monopoles) that quantitatively obeys Debye-Hückel theory in both the dilute and concentrated regimes [41].…”