Dirty spin ice: The effect of dilution on spin freezing inDy2Ti2O

Abstract

We have studied spin freezing in the diluted spin ice compound Although geometrical magnetic frustration has been most extensively studied in materials with antiferromagnetic nearest-neighbor interactions, the effects of strong frustration have also been found in the so-called "spin ice" materials (such as Dy 2 Ti 2 O 7 , Ho 2 Ti 2 O 7 , and Ho 2 Sn 2 O 7 ) [ 3,4,5,6,7,8,9,10,11,12] in which ferromagnetic and dipolar interactions can be frustrated [13,14,15,16]. The spins in these compounds are governed by the same statistical mechanics as the hydrogen atoms in the ground state of ordinary hexagonal ice (Ih) [17,18,19]. In ice, oxygen ions reside at the center of tetrahedra with two of the four nearest hydrogen ions (protons) situated closer to it that the remaining two, as shown in figure 1a. In spin ice materials, the magnetic rare-earth ions are situated on a lattice of corner-sharing tetrahedra, and their spins are constrained by crystal field interactions to point either directly toward or directly away from the centers of the tetrahedra as shown in figure 1b. To minimize the dipole and ferromagnetic exchange interactions, the spins on each tetrahedron must be oriented such that two spins point inward and two point outward in exact analogy to the protons in ice.The spin ice state has been demonstrated experimentally through neutron scattering studies [5,12,20] and also through measurements of the magnetic specific heat, which yield a measured ground state entropy in good agreement with the theoretical prediction for the "ice rules" (first codified by Pauling) and experimental results for ice [7,17,19]. While the spin entropy only freezes out below T ~ 3 K in Dy 2 Ti 2 O 7 , magnetic susceptibility studies show a strongly frequency dependent cooperative spin-freezing at T 3 16 K [8,9], and then a sharp drop at T ~ 2 K [21]. In contrast to traditional spin glasses, the T ~ 16K spin-freezing transition is associated with a very narrow range of relaxation times, and, rather than quenching the spin-freezing as in spin glasses, application of a magnetic field is found to enhance the spin ice freezing. The dynamic spin-ice freezing in Dy 2 Ti 2 O 7 is therefore a rather unusual example of glassiness in a magnetic system. Due to the purity of the system, it provides an excellent venue in which to study a simplified model of the complex thermodynamics of ice as well as the more general consequences of frustration in the limit of low disorder.Here we report a study of this spin freezing in the diluted spin ice compound Dy 2-x Y x Ti 2 O 7 where we introduce controlled disorder by substituting non-magnetic Y ions for the J = 15/2 Dy 3+ ions on the frustrated pyrochlore lattice. We find that such dilution decreases the relative number of spins participating in the ice-like freezing while leaving the freezing temperature, T f ~ 16 K, and its frequency dependence unchanged.Correspondingly the distribution of relaxation times associated with the freezing is broadened only slightly with increasing dilution, suggest...

Magnetocaloric study of spin relaxation in dipolar spin iceDy2Ti2O7

“…The data presented here enable one to study the relaxation process in spin ice at temperatures lower than those for which ac-susceptibility data are available 20,34 and to compare the influence of magnetic dilution on spin relaxation in the milikelvin temperature range with the detailed investigations reported for T > T ice 21 . The thermal response of Dy 2 Ti 2 O 7 on decreasing magnetic field suggests that above ∼ 0.4 K the magnetic and lattice/thermometer subsystems are in thermal equilibrium during the demagnetization.…”

“…Acsusceptibility studies of powdered Dy 2 Ti 2 O 7 up to 20 K suggest rather a wide distribution of relaxation times 18 , but other studies 19 suggest that spin ice responds to external magnetic field in a very limited range of relaxation times, an effect that has been ascribed to the high degree of chemical and structural order. In addition, acsusceptibility data for Dy 2 Ti 2 O 7 indicate strongly frequency dependent spin freezing at about 16 K. This was initially discussed in terms of collective dynamics, 19,20 , but subsequently, on the basis of systematic studies of Dy 2−x Y x Ti 2 O 7 in wide range of dilutions x 21 as well as neutron scattering 22 , ascribed to a single spin flip process.…”

Symmetry and light stuffing ofHo2Ti2O7, EBaroudi1, Gaulin2, Lapidus3 et al. 2015Phys. Rev. BSelf Cite384320View full textAdd to dashboardCite

“…Because there has been no indication of a structural phase transition at low temperatures in the small rare earth titanate pyrochlores (magnetic ordering at low temperatures has been observed of course) in any of the many characterization experiments performed previously [see, e.g. 2,18,19], the Fd-3m symmetry must by inference be maintained to very low temperatures. However, to be sure about this, here we confirm this inference through performing a high-sensitivity synchrotron X-ray diffraction measurement on Ho 2 Ti 2 O 7 at 10 K.…”

Structural disorder and properties of the stuffed pyrochloreHo2TiO5

“…Dilution studies on spin ice materials, [15][16][17] where magnetic rare earth moments are replaced with a nonmagnetic species, reveal that decreasing the spin interactions does not destroy the icelike state, but does suppress the magnitude of the freezing signature. It was recently shown that "stuffed spin ice"-the opposite case where additional magnetic atoms are stuffed into the nonmagnetic Ti sites creating, for example, the series Ho 2 ͑Ti 2−x Ho x ͒O 7−x/2 , 0 ഛ x ഛ 0.67-retains the same zero-point entropy as undoped spin ice and may possess accelerated spin dynamics.…”