A quantum liquid of magnetic octupoles on the pyrochlore lattice

Abstract

Spin liquids are highly correlated yet disordered states formed by the entanglement of magnetic dipoles 1 .Theories typically define such states using gauge fields and deconfined quasiparticle excitations that emerge from a simple rule governing the local ground state of a frustrated magnet. For example, the '2-in-2-out' ice rule for dipole moments on a tetrahedron can lead to a quantum spin ice in rare-earth pyrochlores -a state described by a lattice gauge theory of quantum electrodynamics 2-4 . However, f-electron ions often carry multipole degrees of freedom of higher rank than dipoles, leading to intriguing behaviours and 'hidden' orders 5-6 . Here we show that the correlated ground state of a Ce 3+based pyrochlore, Ce2Sn2O7, is a quantum liquid of magnetic octupoles. Our neutron scattering results are consistent with the formation of a fluid-like state of matter, but the intensity distribution is weighted to larger scattering vectors, which indicates that the correlated degrees of freedom have a more complex magnetization density than that typical of magnetic dipoles in a spin liquid. The temperature evolution of the bulk properties in the correlated regime below 1 Kelvin is well reproduced using a model of dipoleoctupole doublets on a pyrochlore lattice 7-8 . The nature and strength of the octupole-octupole couplings, together with the existence of a continuum of excitations attributed to spinons, provides further evidence for a quantum ice of octupoles governed by a '2-plus-2-minus' rule. Our work identifies Ce2Sn2O7 as a unique example of a material where frustrated multipoles form a 'hidden' topological order, thus generalizing observations on quantum spin liquids to multipolar phases that can support novel types of emergent fields and excitations. The composite 'dipole-octupole' nature of the degrees of freedom and their evolution as a function of temperature or magnetic field provide new ways of controlling emergent phenomena in quantum materials.

Ground-state phase diagram of dipolar-octupolar pyrochlores

“…The Ce pyrochlores in particular seem promising with recent neutron scattering results on Ce 2 Zr 2 O 7 bearing similarity to predictions for emergent photons [30]. Low-energy correlations in Ce 2 Sn 2 O 7 seem to be dominantly octupolar in nature [28], which would be consistent with either of the two octupolar spin liquids on the phase diagram (Fig. 1).…”

“…Amongst materials, Ce 2 Zr 2 O 7 [29,30], Ce 2 Sn 2 O 7 [27,28], and Sm 2 Zr 2 O 7 [35] stand out as lacking low-temperature order. The Ce pyrochlores in particular seem promising with recent neutron scattering results on Ce 2 Zr 2 O 7 bearing similarity to predictions for emergent photons [30].…”

“…"Dipolar-octupolar" (DO) pyrochlores R 2 M 2 O 7 (R=Ce, Sm, Nd; M=Zr, Hf, Ti, Sn, Pb) [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44] constitute an opportunity in this context, with their low-energy physics being described by a simple XY Z Hamiltonian [45,46]. Out of this family, Ce 2 Sn 2 O 7 [27,28] and Ce 2 Zr 2 O 7 [29,30] have been highlighted recently as showing evidence of QSL physics. Notably, neutron scattering results for Ce 2 Zr 2 O 7 bear encouraging similarity to predictions for a U (1) quantum spin liquid [30,47].…”

“…There are strong crystal electric fields (CEFs) acting on each magnetic site, resulting in a Kramers doublet at the bottom of the CEF spectrum, separated from higher states by a large gap CEF ∼ 100 K [30,37,40]. With the scale of exchange interactions being ∼1 K [28,39], this motivates a description of the system in terms of pseudospin-1/2 operators τ x i , τ y i , τ z i . The thing which sets DO pyrochlores apart from other pyrochlore oxides is the transformation properties of these operators under timereversal and lattice symmetries [45,46].…”

Pyrochlore U(1) spin liquid of mixed-symmetry enrichments in magnetic fields

“…This is a clear indication that the system is not in the spin-ice regime. Another interesting aspect is that the Ce 3+ local moment in both Ce 2 Sn 2 O 7 [50][51][52] and Ce 2 Zr 2 O 7 is a dipole-octupole doublet [33,53,54]. It is thus natural for us to consider the possibility of pyrochlore U(1) QSL beyond the spin-ice regime with the dipole-octupole doublets.…”