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There exist a fair number of insulating magnetic materials where the
magnetic species is a 4f (rare-earth) element and which have been
long known to display interesting and intriguing magnetic and
thermodynamic behaviors. Examples include the three-dimensional
Gd3Ga5O12 garnet (GGG) lattice of corner-sharing tetrahedra,
the LiHo_xY_{1-x}F4 Ising material in a transverse magnetic field (TFIM),
and a number of pyrochlore systems such as the Tb2Ti2O7 spin liquid,
the spin Dy2Ti2O7 and Ho2Ti2O7 spin ices and the Gd2(Ti,Sn)2O7 long-range
ordered systems. In this talk, I will review some of the problems motivated
by experiments on these systems, discuss tentative explanations of what is
maybe going on and emphasize what we do not understand.
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- Gd3Ga5O12 (GGG): Phys. Rev. Lett. 97, 267203 (2006).
- LiHo_xY_{1-x}F4 (TFIM): Phys. Rev. Lett. 97, 237203 (2006).
- Gd2Sn2O7 (long range order): Phys. Rev. Lett. 99, 097201 (2007).
- Tb2Ti2O7 (spin liquid): Phys. Rev. Lett. 98, 157204 (2007).
- (Dy/Ho)2Ti2O7 (correlations in spin ice): Phys. Rev. B 70, 134408 (2004), or arXiv.org/0707.3477.

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