Ising Pyrochlore Magnets: Low-Temperature Properties, “Ice Rules,” and Beyond
Pyrochlore magnets are candidates for what Harris et al. [Phys. Rev. Lett. 79, 2554 (1997)] call ``spin-ice'' behavior. We present theoretical simulations of relevance for the pyrochlore family ${R}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ ( $R\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\mathrm{rare}\mathrm{earth}$) supported by magnetothermal measurements on selected systems. By considering long-ranged dipole-dipole as well as short-ranged superexchange interactions, we get three distinct behaviors: (i) an ordered doubly degenerate state, (ii) a highly disordered state with a broad transition to paramagnetism, and (iii) a partially ordered state with a sharp transition to paramagnetism. Closely corresponding behavior is seen in the real compounds.