${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ Spin Ice: A Test Case for Emergent Clusters in a Frustrated Magnet

${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ is a geometrically frustrated magnetic material with a strongly correlated spin ice regime that extends from 1 K down to as low as 60 mK. The diffuse elastic neutron scattering intensities in the spin ice regime can be remarkably well described by a phenomenological model of weakly interacting hexagonal spin clusters, as invoked in other geometrically frustrated magnets. We present a highly refined microscopic theory of ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ that includes long-range dipolar and exchange interactions to third nearest neighbors and which demonstrates that the clusters are purely fictitious in this material. The seeming emergence of composite spin clusters and their associated scattering pattern is instead an indicator of fine-tuning of ancillary correlations within a strongly correlated state.

Figure 1

Neutron scattering intensity $I(\mathbf{q})$ of ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ as a function of the wave vector. (a) Experimental elastic scattering intensity at 300 mK [7] in the (hhl) planes of the reciprocal space is notably amassed along the hexagonal zone boundaries. (b) $I(\mathbf{q})$ calculated using the model of uncorrelated hexagonal spin clusters (see text). (c) $I(\mathbf{q})$ obtained from MC simulations on the s-DSM of ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ [22] describes the main experimental features, but is inadequate in reproducing the ZBS [7]. (d) The g-DSM allows for an excellent match between the theoretical and experimental $I(\mathbf{q})$, and allows us to identify that correlations beyond 3rd nearest neighbors are the microscopic origin behind the ZBS. (e, f) Quantitative comparison of the experimental (a) and theoretical (b),(c),(d) data along a cut through the reciprocal space chosen to emphasize the mismatch with the s-DSM. Panels (c),(d),(e),(f) produced by MC simulations of $8192=8^3\times 16$ spins.

Figure 2

rms deviation $\sigma$ of Monte Carlo vs experimental [4] specific heat data in the $J_1-J_2$ plane at fixed value of $J_3=0.025\mathrm{K}$. The isolines are drawn at $\sigma =0.05$, 0.10, 0.15 and $0.20\mathrm{J}{\mathrm{mol}}^{-1}{\mathrm{K}}^{-2}$ outward. The two functions $\sigma$ [(a), obtained for the $T_1=0.7\mathrm{K}–1.49\mathrm{K}$ temperature interval, and (b), for $T_2=1.5\mathrm{K}–2.8\mathrm{K}$] yield candidate solutions (delineated by inner isolines) in overlapping parts of the $J_1-J_2$ plane. The determination of the $J_{\nu }$ couplings in the Hamiltonian (2) of ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ is obtained via a fitting to several bulk experimental thermodynamic data, akin to the procedure illustrated here (see text).