We use neutron scattering to show that ferromagnetic (FM) phase transition in the two-dimensional (2D) honeycomb lattice CrI 3 is a weakly first order transition and controlled by spin-orbit coupling (SOC) induced magnetic anisotropy, instead of magnetic exchange coupling as in a conventional ferromagnet. With increasing temperature, the magnitude of magnetic anisotropy, seen as a spin gap at the Brillouin zone center, decreases in a power law fashion and vanishes at T C , while the in-plane and c-axis spin-wave stiffnesses associated with magnetic exchange couplings remain robust at T C. We also compare parameter regimes where spin waves in CrI 3 can be described by a Heisenberg Hamiltonian with Dzyaloshinskii-Moriya interaction or a Heisenberg-Kitaev Hamiltonian. These results suggest that the SOC induced magnetic anisotropy plays a dominant role in stabilizing the FM order in single layer 2D van der Waals ferromagnets.

dc-magnetization data measured down to 40 mK speak against conventional freezing and reinstate YbMgGaO4 as a triangular spin-liquid candidate. Magnetic susceptibility measured parallel and perpendicular to the c-axis reaches constant values below 0.1 and 0.2 K, respectively, thus indicating the presence of gapless low-energy spin excitations. We elucidate their nature in the triple-axis inelastic neutron scattering experiment that pinpoints the low-energy (E ≤ J0 ∼ 0.2 meV) part of the excitation continuum present at low temperatures (T < J0/kB), but completely disappearing upon warming the system above T J0/kB. In contrast to the high-energy part at E > J0 that is rooted in the breaking of nearest-neighbor valence bonds and persists to temperatures well above J0/kB, the low-energy one originates from the rearrangement of the valence bonds and thus from the propagation of unpaired spins. We further extend this picture to herbertsmithite, the spin-liquid candidate on the kagome lattice, and argue that such a hierarchy of magnetic excitations may be a universal feature of quantum spin liquids.Introduction.-Quantum spin liquids (QSLs) have a special place in condensed-matter physics as states with unconventional excitations solely driven by spin degrees of freedom in the absence of charge and orbital fluctuations. The QSL physics may be behind many intriguing phenomena studied over the last decades, including the high-temperature superconductivity [1,2]. Exotic properties of the QSLs are also central to new technologies, such as topological quantum computing [3]. The prototype of a QSL was proposed by Anderson back in 1973 as a resonating-valence-bond (RVB) state, a superposition of many different partitions of the triangular spin network into valence bonds (VBs, spin-0 singlets), 1

In contrast to magnetic order formed by electrons' dipolar moments, ordering phenomena associated with higher-order multipoles (quadrupoles, octupoles, etc.) are more difficult to characterize because of the limited choice of experimental probes that can distinguish different multipolar moments. The heavy-fermion compound CeB 6 and its La-diluted alloys are among the best-studied realizations of the long-range-ordered multipolar phases, often referred to as "hidden order". Previously the hidden order in phase II was identified as primary antiferroquadrupolar (AFQ) and field-induced octupolar (AFO) order. Here we present a combined experimental and theoretical investigation of collective excitations in the phase II of CeB 6 . Inelastic neutron scattering (INS) in fields up to 16.5 T reveals a new high-energy mode above 14 T in addition to the lowenergy magnetic excitations. The experimental dependence of their energy on the magnitude and angle of the applied magnetic field is compared to the results of a multipolar interaction model. The magnetic excitation spectrum in rotating field is calculated within a localized approach using the pseudo-spin presentation for the Γ 8 states. We show that the rotating-field technique at fixed momentum can complement conventional INS measurements of the dispersion at constant field and holds great promise for identifying the symmetry of multipolar order parameters and the details of inter-multipolar interactions that stabilize hidden-order phases.