Three-dimensional Spin Liquid Research Articles

Pinch point singularities of tensor spin liquids

Recently, a new class of three-dimensional spin liquid models have been theoretically discovered, which feature generalized Coulomb phases of emergent symmetric tensor $U(1)$ gauge theories. These ``higher rank'' tensor models are particularly intriguing due to the presence of quasiparticles with restricted mobility, such as fractons. We investigate universal experimental signatures of tensor Coulomb phases. Most notably, we show that tensor Coulomb spin liquids (both quantum and classical) feature characteristic pinch point singularities in their spin-spin correlation functions, accessible via neutron scattering, which can be readily distinguished from pinch points in conventional $U(1)$ spin liquids. These pinch points can thus serve as a crisp experimental diagnostic for such phases. We also tabulate the low-temperature heat capacity of various tensor Coulomb phases, which serves as a useful additional diagnostic in certain cases.

Possible observation of highly itinerant quantum magnetic monopoles in the frustrated pyrochlore Yb2Ti2O7.

The low-energy elementary excitations in frustrated quantum magnets have fascinated researchers for decades. In frustrated Ising magnets on a pyrochlore lattice possessing macroscopically degenerate spin-ice ground states, the excitations have been discussed in terms of classical magnetic monopoles, which do not contain quantum fluctuations. Here we report unusual behaviours of magneto-thermal conductivity in the disordered spin-liquid regime of pyrochlore Yb2Ti2O7, which hosts frustrated spin-ice correlations with large quantum fluctuations owing to pseudospin-1/2 of Yb ions. The analysis of the temperature and magnetic field dependencies shows the presence of gapped elementary excitations. We find that the gap energy is largely suppressed from that expected in classical monopoles. Moreover, these excitations propagate a long distance without being scattered, in contrast to the diffusive nature of classical monopoles. These results suggests the emergence of highly itinerant quantum magnetic monopole, which is a heavy quasiparticle that propagates coherently in three-dimensional spin liquids.

Spin-Peierls Instability of Three-Dimensional Spin Liquids with Majorana Fermi Surfaces.

Three-dimensional (3D) variants of the Kitaev model can harbor gapless spin liquids with a Majorana Fermi surface on certain tricoordinated lattice structures such as the recently introduced hyperoctagon lattice. Here, we investigate Fermi surface instabilities arising from additional spin exchange terms (such as a Heisenberg coupling) which introduce interactions between the emergent Majorana fermion degrees of freedom. We show that independent of the sign and structure of the interactions, the Majorana surface is always unstable. Generically, the system spontaneously doubles its unit cell at exponentially small temperatures and forms a spin liquid with line nodes. Depending on the microscopics, further symmetries of the system can be broken at this transition. These spin-Peierls instabilities of a 3D spin liquid are closely related to BCS instabilities of fermions.

Hubbard Model on the Pyrochlore Lattice: A 3D Quantum Spin Liquid

We demonstrate that the insulating one-band Hubbard model on the pyrochlore lattice contains, for realistic parameters, an extended quantum spin-liquid phase. This is a three-dimensional spin liquid formed from a highly degenerate manifold of dimer-based states, which is a subset of the classical dimer coverings obeying the ice rules. It possesses spinon excitations, which are both massive and deconfined, and on doping it exhibits spin-charge separation. We discuss the realization of this state in effective S = 1/2 pyrochlore materials with and without spin-orbit coupling.

Detecting nonmagnetic excitations in quantum magnets

Many unconventional quantum phases host special nonmagnetic excitations such as photons and visons. We discuss two possible ways to detect these excitations experimentally. First, spin-lattice coupling mixes the excitations with phonons. The phonon spectral function acquires new features that can be detected by neutron or x-ray scattering. Second, valence-bond fluctuations translate into charge density fluctuations on nonbipartite lattices. Such charge fluctuations can be characterized by conventional spectroscopies such as terahertz spectroscopy. As by-products, we discuss the general mechanisms of spin-Peierls transitions in two- and three-dimensional spin liquids.

Spin-orbit coupling in the metallic and spin-liquid phases of Na4Ir3O8

It has recently been proposed that Na4Ir3O8 is a weak Mott insulator at ambient pressure, supporting a three-dimensional spin liquid phase with a spinon Fermi surface. This proposal is consistent with recent experimental findings that the material becomes a metal upon increasing pressure or doping. In this work, we investigate the effect of the spin-orbit coupling arising from 5d Ir moments both in the metallic and spin liquid phases of Na4Ir3O8. The effective Hubbard model in terms of pseudospin j=1/2 Ir states is derived and its consequences to both metallic and spin liquid phases are studied. In particular, the model leads to enhanced Wilson ratio and strong temperature dependence of the Hall coefficient.

Anyonic loops in three-dimensional spin liquid and chiral spin liquid

We established a large class of exactly soluble spin liquids and chiral spin liquids on three-dimensional helix lattices by introducing Kitaev-type's spin coupling. In the chiral spin liquids, exact stable ground states with spontaneous breaking of the time reversal symmetry are found. The fractionalized loop excitations in both the spin and chiral spin liquids obey non-Abelian statistics. We characterize this kind of statistics by non-Abelian Berry phase and quantum algebra relation. The topological correlation of loops is independent of local order parameter and it measures the intrinsic global quantum entanglement of degenerate ground states.

TRIPLET MODES IN A QUANTUM SPIN LIQUID ACROSS THE CRITICAL FIELD

S = 1/2 TlCuCl3 is a magnetic insulator with a singlet ground state and a finite spin gap to triplet excited states. At finite fields, the degeneracy of the triplet states is lifted according to the Zeeman interaction term. Field-induced magnetic ordering occurs in TlCuCl3 at the critical field Hc ~ 6 T , when the Zeeman interaction overcomes the spin gap at the antiferromagnetic zone center. A detailed characterization of the elementary excitations realized at H > Hc is obtained by means of inelastic neutron scattering on single crystals. The general framework of field-induced quantum criticality in a three-dimensional spin liquid is illustrated on the complete dynamic range for the first time.

Thermodynamic study of excitations in a three-dimensional spin liquid

In order to characterize thermal excitations in a frustrated spin liquid, we have examined the magnetothermodynamics of a model geometrically frustrated magnet. Our data demonstrate a crossover in the nature of the spin excitations between the spin liquid phase and the high-temperature paramagnetic state. The temperature dependence of both the specific heat and magnetization in the spin liquid phase can be fit within a simple model which assumes that the spin excitations have a gapped quadratic dispersion relation.

Study of the low temperature thermal properties of the geometrically frustrated magnet: Gadolinium gallium garnet

Gadolinium gallium garnet, Gd3Ga5O12 (GGG) has an extraordinary low temperature phase diagram. Although the Curie–Weiss temperature of GGG is about −2 K, GGG shows no long-range order down to T∼0.4 K. At low temperatures GGG has a spin glass phase at low fields (⩽0.1 T) and a field-induced long-range order antiferromagnetic state at fields of between 0.7 and 1.3 T [P. Schiffer et al., Phys. Rev. Lett. 73, 2500 (1994), S. Hov, H. Bratsberg, and A. T. Skjeltorp, J. Magn. Magn. Mater. 15–18, 455 (1980); S. Hov, Ph.D. thesis, University of Oslo, 1979 (unpublished), A. P. Ramirez and R. N. Kleiman, J. Appl. Phys. 69, 5252 (1991)]. However, the nature of the ground state at intermediate fields is still unknown, and has been hypothesized to be a three-dimensional spin liquid. We have measured the thermal conductivity (κ) and heat capacity (C) of a high-quality single crystal of GGG in the low temperature regime in order to study the nature of this state. The field dependence of κ shows that phonons are the predominant heat carriers and are scattered by spin fluctuations. We observe indications in κ(H) and C(H) of both the field induced ordering and the spin glass phase at low temperatures (T⩽200 mK).

Properties of the chiral-spin-liquid state.

It is shown that one of the class of variational spin-liquid wave functions recently derived by Wen, Wilczek, and Zee [Phys. Rev. B 39, 11413 (1989)] is identical to the fractional-quantum-Hall analog state proposed by Kalmeyer and Laughlin [Phys. Rev. Lett. 59, 2095 (1987); Phys. Rev. B 39, 11 879 (1989)] and Laughlin [Ann. Phys. (N.Y.) 191, 163 (1989)], and that the neutral spin-1/2 excitations of the two states are also the same. The 1/2 fractional statistics obeyed by these particles is demonstrated explicitly. The spin-spin correlation function and quasiparticle profile for the Wen-Wilczek-Zee states are calculated both numerically and by a hypernetted-chain procedure. Both are consistent with the idea that spontaneous breaking of time-reversal symmetry is an essential feature of any spin state lacking magnetic order. A version of this state for a three-dimensional spin system is reported and shown to have similar properties. A case is made that the neutral spin-1/2 excitations of the three-dimensional spin liquid behave like anisotropic monopoles.