Dimensional analysis, spin freezing and magnetization in spin ice.

Dimensional analysis is shown to give an insight into the non-ergodic behaviour of spin ice below its apparent 'spin freezing' temperature. Expressions are derived for the temperature-dependent magnetic susceptibility that are found to be highly consistent with the previously reported field cooled and zero field cooled magnetization of the spin ice dysprosium titanate, Dy(2)Ti(2)O(7), as well as with the theory of a 'magnetolyte', including Debye-Hückel screening and Wien dissociation. The spin freezing is inferred to reflect the inability of the quasi-free magnetic charges or 'monopoles' that comprise the magnetolyte to fully screen an applied magnetic field on the timescale of an experiment. The apparent freezing temperature (T(f)≈0.65 K) is identified as the point where the Debye screening length becomes greater than the Bjerrum association distance for charge pairs. Combining these dimensional arguments with Onsager's theory of the Wien effect, it is shown that magnetization data at relatively high field (Snyder et al 2004 Phys. Rev. B 69 064414) may be used to estimate the elementary magnetic charge of spin ice, as well as the temperature-dependent monopole density. Evidence is presented of a non-equilibrium population of monopoles below T≈0.2 K. It is also shown how Onsager's microscopic theory of field-induced monopole pair separation naturally suggests the 'magnetization jumps' in Dy(2)Ti(2)O(7) observed at applied fields of the order of ∼ 0.1 T. It is concluded that the results of dimensional analysis, when combined with Onsager's theory, provide an accurate, albeit approximate, description of the properties of Dy(2)Ti(2)O(7), that could be improved by the development of a lattice theory of the Wien effect, or tested on other spin ice materials.