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

The idea that some systems could have a thermodynamically large number of a ccessible ground states was presaged in the work of Pauling on ice (Pauling , Cornell University Press, Ithaca, NY, 1945) [I]. 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 diso rder, is responsible for spin glass behavior. However, well before spin-gla sses were identified as a distinct class of systems it had been appreciated that even for structurally periodic systems, bond frustration could lead t o a thermodynamically large number of states. There is now a well-defined c lass of magnets which display effects of macroscopic ground state degenerac y. This class of geometrically frustrated magnets presents some nca paradig ms with which to view condensed matter systems - marginal underconstraint a nd downward shift of spectral weight. We discuss possible realizations of t hese phenomena in both in spin ice and also outside the context of local-mo ment magnetism. (C) 2000 Elsevier Science B.V. All rights reserved.