  The residual entropy of spin ice and other frustrated magnets is a property
of considerable interest, yet the usual way of determining it, by integrating
the heat capacity, is generally ambiguous. Here we note that a straightforward
alternative method based on Maxwell's thermodynamic relations can yield the
residual entropy on an absolute scale. The method utilises magnetization
measurements only and hence is a useful alternative to calorimetry. We confirm
that it works for spin ice, Dy2Ti2O7, which recommends its application to other
systems. The analysis described here also gives an insight into the dependence
of entropy on magnetic moment, which plays an important role in the theory of
magnetic monopoles in spin ice. Finally, we present evidence of a field-induced
crossover from correlated spin ice behaviour to ordinary paramagnetic behaviour
with increasing applied field, as signalled by a change in the effective Curie
constant.
