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 $R_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ ( $R=\mathrm{rare}\mathrm{earth}$) 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.