Determination of the electronic energy spectrum of a trigonal-symmetry mononuclear Yb(3+) single-molecule magnet (SMM) by high-resolution absorption and luminescence spectroscopies reveals that the first excited electronic doublet is placed nearly 500 cm(-1) above the ground one. Fitting of the paramagnetic relaxation times of this SMM to a thermally activated (Orbach) model {τ = τ0 × exp[ΔOrbach/(kBT)]} affords an activation barrier, ΔOrbach, of only 38 cm(-1). This result is incompatible with the spectroscopic observations. Thus, we unambiguously demonstrate, solely on the basis of experimental data, that Orbach relaxation cannot a priori be considered as the main mechanism determining the spin dynamics of SMMs. This study highlights the fact that the general synthetic approach of optimizing SMM behavior by maximization of the anisotropy barrier, intimately linked to the ligand field, as the sole parameter to be tuned, is insufficient because of the complete neglect of the interaction of the magnetic moment of the molecule with its environment. The Orbach mechanism is expected dominant only in the cases in which the energy of the excited ligand field state is below the Debye temperature, which is typically low for molecular crystals and, thus, prevents the use of the anisotropy barrier as a design criterion for the realization of high-temperature SMMs. Therefore, consideration of additional design criteria that address the presence of alternative relaxation processes beyond the traditional double-well picture is required.

Spirals and helices are common motifs of long-range order in magnetic solids, and they may also be organized into more complex emergent structures such as magnetic skyrmions and vortices. A new type of spiral state, the spiral spin-liquid, in which spins fluctuate collectively as spirals, has recently been predicted to exist. Here, using neutron scattering techniques, we experimentally prove the existence of a spiral spin-liquid in MnSc2S4 by directly observing the 'spiral surface' -a continuous surface of spiral propagation vectors in reciprocal space. We elucidate the multi-step ordering behavior of the spiral spin-liquid, and discover a vortex-like triple-q phase on application of a magnetic field. Our results prove the effectiveness of the J1-J2 Hamiltonian on the diamond lattice as a model for the spiral spin-liquid state in MnSc2S4, and also demonstrate a new way to realize a magnetic vortex lattice.Magnetic frustration, where magnetic moments (spins) are coupled through competing interactions that cannot be simultaneously satisfied 1 , usually leads to highly cooperative spin fluctuations 2,3 and unconventional longrange magnetic order 4,5 . An archetypal ordering in the presence of frustration is the spin spiral. Competing interactions and spiral orders give rise to many phenomena in magnetism, including the multitudinous magnetic phases of rare earth metals 6 , domains with multiferroic properties 7,8 , and topologically non-trivial structures such as the emergent skyrmion lattice 9,10 .Recently, a new spiral state -a spiral spin-liquid in which the ground states are a massively degenerate set of coplanar spin spirals -was predicted to exist in the J 1 -J 2 model on the diamond lattice (see Fig. 1a) [11][12][13] . Although the diamond lattice is bipartite, and therefore unfrustrated at the near-neighbour (J 1 ) level, the second-neighbour coupling (J 2 ) can generate strong competition. For classical spins, mean-field calculations show that when |J 2 /J 1 | > 0.125 the spiral spin-liquid appears, and that it is signified by an unusual continuous surface of propagation vectors q in reciprocal space (see Fig. 1b for the spiral surface of |J 2 /J 1 | = 0.85). At finite temperature, thermal fluctuations might select some specific q-vectors on the spiral surface 11 , resulting in an orderby-disorder transition 14,15 .Until now, several series of A-site spinels, in which the magnetic A ions form a diamond lattice, have been investigated, including: the cobaltates Co 3 O 4 and CoRh 2 O 4 16 ; the aluminates M Al 2 O 4 with M = Fe, Co, Mn 17-20 ; and the scandium thiospinels M Sc 2 S 4 with M = Fe, Mn 21 . For the spinels with Fe 2+ at the A-site, the e g orbital angular momentum of Fe 2+ is active, making the pure spin J 1 -J 2 model inadequate 22 . Among the other compounds, CoAl 2 O 4 and MnSc 2 S 4 manifest the strongest frustration. For CoAl 2 O 4 , the ratio of |J 2 /J 1 | has been identified as 0.109 19 , which is near, but still lower than, the 0.125 threshold for the spiral spin-liquid state. Many expe...

Copies of full items can be used for personal research or study, educational, or not-for-profit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. Publisher statement: © 2016 American Physical Society A note on versions:The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher's version. Please see the 'permanent WRAP URL' above for details on accessing the published version and note that access may require a subscription. We report the low temperature magnetic properties of the pyrochlore Pr 2 Hf 2 O 7 . Polycrystalline and singlecrystal samples are investigated using time-of-flight neutron spectroscopy and macroscopic measurements, respectively. The crystal-field splitting produces a non-Kramers doublet ground state for Pr 3+ , with Ising-like anisotropy. Below 0.5 K ferromagnetic correlations develop, which suggests that the system enters a spin-ice-like state associated with the metamagnetic behavior observed at μ 0 H c ∼ 2.4 T. In this regime, the development of a discrete inelastic excitation in the neutron spectra indicates the appearance of spin dynamics that are likely related to cooperative quantum fluctuations.

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.

We report the low temperature magnetic properties of Ce2Sn2O7, a rare-earth pyrochlore. Our susceptibility and magnetization measurements show that due to the thermal isolation of a Kramers doublet ground state, Ce2Sn2O7 has Ising-like magnetic moments of ∼ 1.18 µB. The magnetic moments are confined to the local trigonal axes, as in a spin ice, but the exchange interactions are antiferromagnetic. Below 1 K the system enters a regime with antiferromagnetic correlations. In contrast to predictions for classical 111 -Ising spins on the pyrochlore lattice, there is no sign of longrange ordering down to 0.02 K. Our results suggest that Ce2Sn2O7 features an antiferromagnetic liquid ground state with strong quantum fluctuations. [5,6], which have no conventional order parameter associated with a broken symmetry, but whose defining character is a longrange entangled groundstate wavefunction [7,8]. Spin liquids are of great interest thanks to the remarkable collective phenomena that they can present, such as emergent gauge fields and fractional quasiparticle excitations [9,10]. Such states may also offer the possible application of coherent or topologically protected ground states in quantum information processing devices [11].Quantum coherence of a spin system lacking symmetry-breaking order is well established in onedimensional spin chains forming a spin fluid with a quantum coherence length almost an order of magnitude larger than the classical antiferromagnetic correlation length [12]. In higher dimensions two paradigms are employed, often simultaneously, to try to obtain a quantum spin liquid (QSL). Firstly, for Heisenberg spins with S=1/2, where quantum mechanical corrections are most significant compared to classical states, quantum melting of the Néel ground state may be possible when spins pair into valence bond singlets [13]. The result may be a valence bond crystal (translationally ordered valence bonds) [14], a resonating valence bond state (singlet configurations resonate around a plaquette) [15], or a true spin liquid when valence bonds can be formed at all lengthscales so that the ground state wavefunction has a genuine long-range entanglement [5,16]. Secondly, geometrically frustrated magnets are a natural landscape for liquid-like states of magnetic moments. In two dimensions, the triangular and kagome lattices are important examples [17][18][19][20], and neutron scattering experiments on the S=1/2 kagome lattice antiferromagnet ZnCu 3 (OH) 6 Cl 2 (herbertsmithite) have provided evidence of fractionalized excitations in a 2D QSL [21,22] [27] have illustrated how quantum effects can become important in materials where they may not be expected, i.e. in rare earth materials where crystal field effects lead to highly anisotropic magnetic moments.The spin system of a pyrochlore with a thermally isolated doublet ground state can be described by a generalized Hamiltonian for effective S = 1/2 spins [24,28]. This Hamiltonian includes all symmetry-allowed near neighbour magnetic exchange interactions, with a lea...

In a quantum spin liquid, the magnetic moments of the constituent electron spins evade classical longrange order to form an exotic state that is quantum entangled and coherent over macroscopic length scales 1-2 . Such phases offer promising perspectives for device applications in quantum information technologies, and their study can reveal fundamentally novel physics in quantum matter. Quantum spin ice is an appealing proposal of one such state, in which the fundamental ground state properties and excitations are described by an emergent U(1) lattice gauge theory 3-7 . This quantum-coherent regime has quasiparticles that are predicted to behave like magnetic and electric monopoles, along with a gauge boson playing the role of an artificial photon. However, this emergent lattice quantum electrodynamics has proved elusive in experiments. Here we report neutron scattering measurements of the rare-earth pyrochlore magnet Pr 2 Hf 2 O 7 that provide evidence for a quantum spin ice ground state. We find a quasielastic structure factor with pinch points -a signature of a classical spin ice -that are partially suppressed, as expected in the quantum-coherent regime of the lattice field theory at finite temperature.Our result allows an estimate for the speed of light associated with magnetic photon excitations. We also reveal a continuum of inelastic spin excitations, which resemble predictions for the fractionalized, topological excitations of a quantum spin ice. Taken together, these two signatures suggest that the low-energy physics of Pr 2 Hf 2 O 7 can be described by emergent quantum electrodynamics. If confirmed, the observation of a quantum spin ice ground state would constitute a concrete example of a threedimensional quantum spin liquid -a topical state of matter which has so far mostly been explored in lower dimensionalities.

Dehydration of the hybrid compound [Ni3(OH)2(tp)2(H2O)4] (1) upon heating led to the sequential removal of coordinated water molecules to give [Ni3(OH)2(tp)2(H2O)2] (2) at T1 = 433 K and thereafter anhydrous [Ni2(OH)2(tp)] (3) at T2 = 483 K. These two successive structural transformations were thoroughly characterized by powder X-ray diffraction assisted by density functional theory calculations. The crystal structures of the two new compounds 2 and 3 were determined. It was shown that at T1 (433 K) the infinite nickel oxide chains built of the repeating structural unit [Ni3(μ3-OH)2](4+) in 1 collapse and lead to infinite porous layers, forming compound 2. The second transformation at T2 (483 K) gave the expected anhydrous compound 3, which is isostructural with Co2(OH)2(tp). These irreversible transitions directly affect the magnetic behavior of each phase. Hence, 1 was found to be antiferromagnetic at TN = 4.11 K, with metamagnetic behavior with a threshold field Hc of ca. 0.6 T. Compound 2 exhibits canted antiferromagnetism below TN = 3.19 K, and 3 is ferromagnetic below TC = 4.5 K.

The charge ordered structure of ions and vacancies characterizing rare-earth pyrochlore oxides serves as a model for the study of geometrically frustrated magnetism. The organization of magnetic ions into networks of corner-sharing tetrahedra gives rise to highly correlated magnetic phases with strong fluctuations, including spin liquids and spin ices. It is an open question how these ground states governed by local rules are affected by disorder. Here we demonstrate in the pyrochlore Tb2Hf2O7, that the vicinity of the disordering transition towards a defective fluorite structure translates into a tunable density of anion Frenkel disorder while cations remain ordered. Quenched random crystal fields and disordered exchange interactions can therefore be introduced into otherwise perfect pyrochlore lattices of magnetic ions. We show that disorder can play a crucial role in preventing long-range magnetic order at low temperatures, and instead induces a strongly fluctuating Coulomb spin liquid with defect-induced frozen magnetic degrees of freedom.