Quantum Excitations in Quantum Spin Ice

Abstract

Recent work has highlighted remarkable effects of classical thermal fluctuations in the dipolar spin ice compounds, such as ''artificial magnetostatics,'' manifesting as Coulombic power-law spin correlations and particles behaving as diffusive ''magnetic monopoles.'' In this paper, we address quantum spin ice, giving a unifying framework for the study of magnetism of a large class of magnetic compounds with the pyrochlore structure, and, in particular, discuss Rare-earth pyrochlores display a diverse set of fascinating physical phenomena [1]. One of the most interesting aspects of these materials from the point of view of fundamental physics is the strong frustration experienced by coupled magnetic moments on this lattice. The best explored materials exhibiting this frustration are the ''spin ice'' compounds, Ho 2 Ti 2 O 7 , Dy 2 Ti 2 O 7 , in which the moments can be regarded as classical spins with a strong easyaxis (Ising) anisotropy [2,3]. The frustration of these moments results in a remarkable classical spin liquid regime displaying Coulombic correlations and emergent ''magnetic monopole'' excitations that have now been studied extensively in theory and experiment [4][5][6].Strong quantum effects are absent in the spin ice compounds, but can be significant in other rare-earth pyrochlores. In particular, in many materials the low-energy spin dynamics may be reduced to that of an effective spin S ¼ 1=2 moment, with the strongest possible quantum effects expected. In this case symmetry considerations reduce the exchange constant phase space of the nearestneighbor exchange Hamiltonian to a maximum of three dimensionless parameters [7] [9,10]. This makes these materials beautiful examples of highly frustrated and strongly quantum magnets on the pyrochlore lattice. They are also nearly ideal subjects for detailed experimental investigation, existing as they do in large high-purity single crystals, and with large magnetic moments amenable to neutron scattering studies. Yb 2 Ti 2 O 7 is particularly appealing because its lowest Kramers doublet is extremely well separated from the first excited one [11], and a very large single-crystal neutron scattering data set is available, allowing us to determine the full Hamiltonian quantitatively, as we will show. Although we specialize to Yb 2 Ti 2 O 7 in the present article, the theoretical considerations and parameter determination method described here will very generally apply to all pyrochlore materials where exchange interactions dominate, and whose dynamics can be described by that of a single doublet.Theoretical studies have pointed to the likelihood of unusual ground states of quantum antiferromagnets on the pyrochlore lattice [12,13]. Most exciting is the possibility of a quantum spin liquid (QSL) state, which avoids magnetic ordering and freezing even at absolute zero temperature, and whose elementary excitations carry fractional quantum numbers and are decidedly different from spin waves [14]. Although one neutron study [15] supported ferromagnetic order in Yb 2...

A two-dimensional spin liquid in quantum kagome ice

“…In contrast, we propose to concentrate the search on the quantum spin ice pyrochlore materials, subject to an external field along the 18 not considered in equation (1), our study highlights the importance of the of J ±± term, which is present for instance in Yb 2 Ti 2 O 7 (ref. 47), and promotes spinon pairing required in the formation of a Z 2 spin liquid. As the phase found in this study has a gap, it is necessarily protected against any local perturbation as long as the effective energy scale of the perturbation is smaller than the gap, and thus it may still be realized even in the presence of additional perturbations.…”

Hierarchy of Exchange Interactions in the Triangular-Lattice Spin Liquid YbMgGaO4

“…2(c) we obtain g k ¼ 3.81ð4Þ. Note that the effective g tensor here is a property of a single Yb 3þ ion and as such is independent of the exchange interactions [49]. This allows us to treat g k as a fixed parameter in the subsequent global fit.…”

“…Several perturbations from the pure TLHAF have been proposed to enhance quantum fluctuations: next-nearest neighbor (NNN) interactions [34][35][36][37][38], ring-exchange terms [39,40], and anisotropic exchange [41][42][43][44], although it remains theoretically unclear if the latter mechanism alone can stabilize a QSL [45][46][47][48]. Nevertheless, anisotropic exchange interactions [49,50] are known to generate new physics in rare-earth pyrochlores such as Yb 2 Ti 2 O 7 [49,[51][52][53], making it worthwhile to investigate their effect in other lattice geometries.…”

A novel type of splayed ferromagnetic order observed in Yb2Ti2O7

“…Indeed, the exchange interactions are highly anisotropic, with a strong ferromagnetic component akin to the Ising exchange of spin ice [18].…”