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Spin ice in a magnetic field in the [111] direction displays twomagnetization plateaux, one at saturation and an intermediate one with finiteentropy. We study the crossovers between the different regimes from a point ofview of (entropically) interacting defects. We develop an analytical theory forthe nearest-neighbor spin ice model, which covers most of the magnetizationcurve. We find that the entropy is non-monotonic, exhibiting a giant spikebetween the two plateaux. This regime is described by a monomer-dimer modelwith tunable fugacities. At low fields, we develop an RG treatment for theextended string defects, and we compare our results to extensive Monte Carlosimulations. We address the implications of our results for cooling byadiabatic (de)magnetization.Comment: 13 pages, 13 figure

Magnetization curve of spin ice in a [111] magnetic field