A quantum spin liquid (QSL) is an exotic state of matter in which electrons' spins are quantum entangled over long distances, but do not show symmetry-breaking magnetic order in the zero-temperature limit [1]. The observation of QSL states is a central aim of experimental physics, because they host collective excitations that transcend our knowledge of quantum matter [2, 3]; however, examples in real materials are scarce [4]. Here, we report neutron-scattering measurements on YbMgGaO 4 , a QSL candidate in which Yb 3+ ions with effective spin-1/2 occupy a triangular lattice [5,6]. Our measurements reveal a continuum of magnetic excitations-the essential experimental hallmark of a QSL [7,8]-at very low temperature (≈ 0.06 K). The origin of this peculiar excitation spectrum is a crucial question, because isotropic nearest-neighbor interactions do not yield a QSL ground state on the triangular lattice [9]. Using measurements of the magnetic excitations close to the field-polarized state, we identify antiferromagnetic next-nearest-neighbor interactions [10,11,12,13,14] in the presence of planar anisotropy[6] as key ingredients for QSL formation in YbMgGaO 4 .1 arXiv:1607.03231v1 [cond-mat.str-el]

We present single-crystal neutron scattering measurements of the spin-1/2 equilateral triangular-lattice antiferromagnet Ba3CoSb2O9. Besides confirming that the Co 2+ magnetic moments lie in the ab plane for zero magnetic field and then determining all the exchange parameters of the minimal quasi-2D spin Hamiltonian, we provide conclusive experimental evidence of magnon decay through observation of intrinsic line-broadening. Through detailed comparisons with the linear and nonlinear spin-wave theories, we also point out that the large-S approximation, which is conventionally employed to predict magnon decay in noncollinear magnets, is inadequate to explain our experimental observation. Thus, our results call for a new theoretical framework for describing excitation spectra in low-dimensional frustrated magnets under strong quantum effects. The equilateral triangular-lattice quantum antiferromagnet Ba 3 CoSb 2 O 9 was synthesized recently [24][25][26][27][28][29]. The Co 2+ ion has a Kramers doublet ground-state due to the spin-orbit coupling, and this doublet can be described as an effective spin-1/2 moment. In addition, the high symmetry of the hexagonal crystal structure, P6 3 / mmc [24-28], forbids DM interaction for pairs up to third nearest-neighbor (NN) in the same abplane and between any pair of spins along the c-axis [25].Powder neutron diffraction measurements presented the noncollinear 120• structure with the magnetic wavevector Q = (1/3, 1/3, 1) [24]. The Néel temperature was found to be ≈ 3.8 K and a rich temperature-magnetic field phase diagram was reported up to 32 T [25][26][27][28]. Electronic spin resonance (ESR) [27] and nuclear magnetic resonance (NMR) [28] measurements suggested a spin model with small easy-plane exchange anisotropy and an exchange interaction along the caxis much weaker than the NN intralayer exchange. This observation is consistent with the alternation of magnetic (Co 2+ ) and nonmagnetic (Sb 2 O 9 bioctahedra) layers along the cdirection. While more precise determination of the model parameters requires inelastic neutron scattering (INS) measurements, such detailed information is indeed physically relevant.

Complex behavior poses challenges in extracting models from experiment. An example is spin liquid formation in frustrated magnets like Dy2Ti2O7. Understanding has been hindered by issues including disorder, glass formation, and interpretation of scattering data. Here, we use a novel automated capability to extract model Hamiltonians from data, and to identify different magnetic regimes. This involves training an autoencoder to learn a compressed representation of three-dimensional diffuse scattering, over a wide range of spin Hamiltonians. The autoencoder finds optimal matches according to scattering and heat capacity data and provides confidence intervals. Validation tests indicate that our optimal Hamiltonian accurately predicts temperature and field dependence of both magnetic structure and magnetization, as well as glass formation and irreversibility in Dy2Ti2O7. The autoencoder can also categorize different magnetic behaviors and eliminate background

The spin-1=2 triangular lattice antiferromagnet YbMgGaO 4 has attracted attention recently as a quantum spin-liquid candidate with the possible presence of off-diagonal anisotropic exchange interactions induced by spin-orbit coupling. Whether a quantum spin liquid is stabilized or not depends on the interplay of various exchange interactions with chemical disorder that is inherent to the layered structure of the compound. We combine time-domain terahertz spectroscopy and inelastic neutron scattering measurements in the field-polarized state of YbMgGaO 4 to obtain better insight of its exchange interactions. Terahertz spectroscopy in this fashion functions as a high-field electron spin resonance and probes the spin-wave excitations at the Brillouin zone center, ideally complementing neutron scattering. A global spin-wave fit to all our spectroscopic data at fields over 4 T, informed by the analysis of the terahertz spectroscopy linewidths, yields constraints on the disorder-averaged g factors and exchange interactions. Our results paint YbMgGaO 4 as an easy-plane XXZ antiferromagnet with the combined and necessary presence of subleading next-nearest neighbor and weak anisotropic off-diagonal nearest-neighbor interactions. Moreover, the obtained g factors are substantially different from previous reports. This work establishes the hierarchy of exchange interactions in YbMgGaO 4 from high-field data alone and thus strongly constrains possible mechanisms responsible for the observed spin-liquid phenomenology.

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We present the structural and magnetic properties of a new compound family, Mg2RE3Sb3O14 (RE = Gd, Dy, Er), with a hitherto unstudied frustrating lattice, the "tripod kagome" structure. Susceptibility (ac, dc) and specific heat exhibit features that are understood within a simple Luttinger-Tisza type theory. For RE = Gd, we found long ranged order (LRO) at 1.65 K, which is consistent with a 120• structure, demonstrating the importance of diople interactions for this 2D Heisenberg system. For RE = Dy, LRO at 0.37 K is related to the "kagome spin ice (KSI)" physics for a 2D system. This result shows that the tripod kagome structure accelerates the transition to LRO predicted for the related pyrochlore systems. For RE = Er, two transitions, at 80 mK and 2.1 K are observed, suggesting the importance of quantum fluctuations for this putative XY system. Introduction.-The two-dimensional (2D) kagome lattice magnet (KLM) has been a favorite in the theoretical condensed matter community since the experimental work on SCGO [1], due to the strong frustration associated with its network of corner-shared triangles. [15]. From a materials standpoint, however, these two systems are limited by (i) known defect prone structures [14,16], and (ii) the inability to substitute facilely on the magnetic site (e.g with non-Heisenberg spins) to realize states other than the QSL. Clearly then, finding new KLM-containing compounds with spin-type variability is a challenge of the highest order.Intriguingly, a 2D KLM is naturally contained in the frustrated 3D pyrochlore structure. In pyrochlores RE 2 X 2 O 7 (RE = rare earth element, X = transition metal element), both the RE 3+ and X 4+ sublattices form alternating kagome and triangular layers along the [111] axis as a result of corner-shared tetrahedrons ( Fig. 1(a)) [17]. However, the strong inter-layer interaction enforces three-dimensionality. An exception is found in studies of Dy 2 Ti 2 O 7 in a [111] magnetic field, which polarizes the triangular layer spins, effectively decoupling the kagome planes, leading to a KSI state [17].Obviously, if one can remove the magnetic moment of the triangular layers in the pyrochlore lattice, a RE-kagome-

We present a systematic study of the structural and magnetic properties of two branches of the rare earth Tripod Kagome Lattice (TKL) family A2RE3Sb3O14 (A = Mg, Zn; RE = Pr, Nd, Gd, Tb, Dy, Ho, Er, Yb; here, we use abbreviation A-RE, as in MgPr for Mg2Pr3Sb3O14), which complements our previously reported work on MgDy, MgGd, and MgEr 15 . The present susceptibility (χ dc , χac) and specific heat measurements reveal various magnetic ground states, including the non-magnetic singlet state for MgPr, ZnPr; long range orderings (LROs) for MgGd, ZnGd, MgNd, ZnNd, and MgYb; a long range magnetic charge ordered state for MgDy, ZnDy, and potentially for MgHo; possible spin glass states for ZnEr, ZnHo; the absence of spin ordering down to 80 mK for MgEr, MgTb, ZnTb, and ZnYb compounds. The ground states observed here bear both similarities as well as striking differences from the states found in the parent pyrochlore systems. In particular, while the TKLs display a greater tendency towards LRO, the lack of LRO in MgHo, MgTb and ZnTb can be viewed from the standpoint of a balance among spin-spin interactions, anisotropies and non-Kramers nature of single ion state. While substituting Zn for Mg changes the chemical pressure, and subtly modifies the interaction energies for compounds with larger RE ions, this substitution introduces structural disorder and modifies the ground states for compounds with smaller RE ions (Ho, Er, Yb).