Water ice and spin ice are important model systems in which theory can directly account for "zero point" entropy associated with quenched configurational disorder.Spin ice differs from water ice in the important respect that its fundamental constituents, the spins of the magnetic ions, can be removed through replacement with non-magnetic ions while keeping the lattice structure intact. In order to investigate the interplay of frustrated interactions and quenched disorder, we have performed systematic heat capacity measurements on spin ice materials which have been thus diluted up to 90%.Investigations of both Ho and Dy spin ices reveal that the zero point entropy depends non-monotonically on dilution and approaches the value of Rln2 in the limit of high dilution. The data are in good agreement with a generalization of Pauling's theory for the entropy of ice. 2Entropy is one of the most important concepts in thermodynamics, but it is rarely directly connected through experiment to its statistical definition rooted in the number of available states. One such connection is found in the case of water ice wherein each oxygen atom is bonded to four hydrogen atoms. The lowest energy state has two hydrogens located closer to the oxygen with the other two further away, establishing the so-called 'ice rules ' [1]. This arrangement allows for a high degeneracy of states, and a resultant 'zero point entropy' has been measured thermodynamically and can be associated with the disordered states frozen in place asA high degeneracy of states also leads to a range of exotic physics in geometrically frustrated magnets, including 'spin ice' materials [3,4,5,6] in which the low temperature behavior is closely analogous to that of water ice. In these materials, the magnetic ions (Ho 3+ or Dy 3+ ) occupy a pyrochlore lattice of corner-sharing tetrahedra, and the local crystal field environment causes the magnetic moments to point along the lines connecting the centers of two tetrahedra at low temperatures [5,6]. This strong single-ion Ising anisotropy, combined with dipolar and exchange interactions [7], results in a highly degenerate two-in/two-out spin configuration for the ground states of these materials [3,5] -locally equivalent to the situation for hydrogen atoms in water ice.Although numerical calculations [8] suggest the existence of a long range ordered state for these systems which would have no zero point entropy, the spins in these materials freeze into a non-equilibrium low temperature state with approximately the same zero point entropy as water ice [4,9 ], and no long range ordering has been observed experimentally in zero magnetic field. 3Here we examine experimentally how dilution of the spin ice lattice affects the zero point entropy over a broad range of dilution in both Ho and Dy spin ice materials --a measurement which would not be possible in water ice. We find that the zero point entropy of diluted spin ice depends non-monotonically on the level of dilution, with the zero point entropy per spin approaching th...
We report systematic low temperature measurements of the DC magnetization, AC susceptibility, and heat capacity of dysprosium pyrogermanate (Dy 2 Ge 2 O 7 ) single crystal and powder samples. Our results confirm that Dy 2 Ge 2 O 7 is an anisotropic antiferromagnet. The isothermal field dependent magnetization and the integrated magnetic entropy both indicate that the Dy 3+ ions behave as Ising-like spins, analogous to those in the pyrochlore spin ice materials. Both single-spin and collective spin relaxation phenomena appear to lead to spin freezing in this material, again in analogy to observations in the spin ice materials, suggesting that such phenomena may be generic to a broader class of magnetic materials.
We report the anisotropic magnetic properties of Ho 2 Ge 2 O 7 determined from dc and ac magnetization, specific heat and powder neutron diffraction experiments. The magnetic lanthanide sublattice, seen in our refinement of the tetragonal pyrogermanate crystal structure, is a right-handed spiral of edge-sharing and corner-sharing triangles; the local Ho-O coordination indicates that the crystal field is anisotropic. Susceptibility and magnetization data indeed show that the magnetism is highly anisotropic, and the magnetic structure has the Ho moments
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