Phases of matter are conventionally classified by symmetry. Liquid water and steam, for example, share the same symmetry: the line separating them on the phase diagram ends at the critical point, and by going around it, liquid can turn into vapor without ever boiling. Ice breaks this symmetry, so its boundary with the liquid has no such endpoint: one cannot turn into the other without crossing it. Yet some states cannot be told apart by symmetry alone. Ices VII, VIII, and X, which appear at high pressure, share the same oxygen framework and differ in where the hydrogen atoms sit; on average, the disordered hydrogens of ice VII respect the same symmetry as the centered hydrogens of ice X. Such states can still be distinguished at absolute zero by global, topological features, but whether these distinctions survive at finite temperature, and under what conditions, has remained unclear.
In this study, the research group addresses this question in classical pyrochlore spin ice, whose lattice sites correspond to hydrogen-bond midpoints in high-pressure ice. The group shows that the phase transitions of these magnets can be classified for an arbitrary spin size in a unified way through a single picture. The distinction between two states is carried by loop-like excitations, which must close on themselves under the local “ice rule.” At any finite temperature, however, thermally excited magnetic monopoles break the ice rule and cut these loops open, erasing the topological distinction. As a result, almost every sharp transition becomes a smooth crossover above absolute zero, with a discontinuous transition unique to spin 3/2 predicted as the sole exception. The spin-1 case corresponds to high-pressure ice, where ionic defects play the role of monopoles. These results indicate that the symmetry-based classification of phases holds broadly at finite temperature, and they sharpen the search for phases that remain topologically distinct at finite temperature.
Loop-like excitations on the pyrochlore lattice. In the absence of monopoles, the ice rule forbids the excitations from having endpoints, so they form closed loops (left). At finite temperature, magnetic monopoles that break the ice rule appear as endpoints and cut the loops open (right), erasing the topological distinction between the two states.
Papers
Journal: Physical Review X
Title: Topological Phase Transitions and Their Thermodynamic Fate in Arbitrary-S Classical Pyrochlore Spin Ice
Authors: Sena Watanabe, Yukitoshi Motome, Haruki Watanabe
DOI: 10.1103/bkkq-q1v9
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