Geometrical frustration, spin ice and negative thermal expansion – the physics of underconstraint

The idea that some systems could have a thermodynamically large number of accessible ground states was presaged in the work of Pauling on ice (Pauling, Cornell University Press, Ithaca, NY, 1945) 1]. With the advent of spin glasses, the methodology for describing ground states changed dramatically, and in particular it was realized that the observed slow dynamics were due to relaxation among a large number of nearly degenerate ground states. Now the accepted wisdom is that both “frustration”, as well as structural disorder, is responsible for spin glass behavior. However, well before spin-glasses were identified as a distinct class of systems, it had been appreciated that even for structurally periodic systems, bond frustration could lead to a thermodynamically large number of states. There is now a well-defined class of magnets which display effects of macroscopic ground state degeneracy. This class of geometrically frustrated magnets presents some new paradigms with which to view condensed matter systems – marginal underconstraint and downward shift of spectral weight. We discuss possible realizations of these phenomena in both in spin ice and also outside the context of local-moment magnetism.