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The search for two dimensional quantum spin liquids, exotic magnetic states with an entangled ground state remaining disordered down to zero temperature, has been a great challenge in frustrated magnetism during the last decades. Recently, fractionalized excitations, called spinons, emerging from these states, have been evidenced in kagome and triangular antiferromagnets. In contrast, quantum ferromagnetic spin liquids in two dimensions, namely quantum kagome ices, have been less investigated, yet their classical counterparts exhibit amazing properties, magnetic monopole crystals as well as magnetic fragmentation. Here we show that, by applying a magnetic field on the pyrochlore oxide Nd$_2$Zr$_2$O$_7$, which has been shown to develop three dimensional quantum magnetic fragmentation in zero field, we are able to reduce the dimension of the system and to create a dynamic kagome ice state. Our results open the way to the observation of the quantum kagome ice state which was recently investigated theoretically., Comment: 7 pages, 4 figures + Supplementary information

We explore the field-temperature phase diagram of the XY pyrochlore antiferromagnet Er$_2$Ti$_2$O$_7$, by means of magnetization and neutron diffraction experiments. Depending on the field strength and direction relative to the high symmetry cubic directions $[001], [1\bar{1}0]$ and $[111]$, the refined field induced magnetic structures are derived from the zero field $\psi_2$ and $\psi_3$ states of the $\Gamma_5$ irreducible representation which describes the ground state of XY pyrochlore antiferromagnets. At low field, domain selection effects are systematically at play. In addition, for $[001]$, a phase transition is reported towards a $\psi_3$ structure at a characteristic field $H_c^{001}=$ 43 mT. For $[1\bar{1}0]$ and $[111]$, the spins are continuously tilted by the field from the $\psi_2$ state, and no phase transition is found while domain selection gives rise to sharp anomalies in the field dependence of the Bragg peaks intensity. For $[1\bar{1}0]$, these results are confirmed by high resolution inelastic neutron scattering experiments, which in addition allow us to determine the field dependence of the spin gap. This study agrees qualitatively with the scenario proposed theoretically by Maryasin {\it et al.} [Phys. Rev. B {\bf 93}, 100406(R) (2016)], yet the strength of the field induced anisotropies is significantly different from theory., Comment: 14 pages, 10 figures

We present an experimental study of the quantum spin ice candidate pyrochlore coumpound \przr\ by means of magnetization measurements, specific heat and neutron scattering up to 12 T and down to 60 mK. When the field is applied along the $[111]$ and $[1\bar{1}0]$ directions, ${\bf k}=0$ field induced structures settle in. We find that the ordered moment rises slowly, even at very low temperature, in agreement with macroscopic magnetization. Interestingly, for $H \parallel [1\bar{1}0]$, the ordered moment appears on the so called $\alpha$ chains only. The spin excitation spectrum is essentially {\it inelastic} and consists in a broad flat mode centered at about 0.4 meV with a magnetic structure factor which resembles the spin ice pattern. For $H \parallel [1\bar{1}0]$ (at least up to 2.5 T), we find that a well defined mode forms from this broad response, whose energy increases with $H$, in the same way as the temperature of the specific heat anomaly. We finally discuss these results in the light of mean field calculations and propose a new interpretation where quadrupolar interactions play a major role, overcoming the magnetic exchange. In this picture, the spin ice pattern appears shifted up to finite energy because of those new interactions. We then propose a range of acceptable parameters for \przr\, that allow to reproduce several experimental features observed under field. With these parameters, the actual ground state of this material would be an antiferroquadrupolar liquid with spin-ice like excitations.

Fractionalised excitations that emerge from a many body system have revealed rich physics and concepts, from composite fermions in two-dimensional electron systems, revealed through the fractional quantum Hall effect, to spinons in antiferromagnetic chains and, more recently, fractionalisation of Dirac electrons in graphene and magnetic monopoles in spin ice. Even more surprising is the fragmentation of the degrees of freedom themselves, leading to coexisting and a priori independent ground states. This puzzling phenomenon was recently put forward in the context of spin ice, in which the magnetic moment field can fragment, resulting in a dual ground state consisting of a fluctuating spin liquid, a so-called Coulomb phase, on top of a magnetic monopole crystal. Here we show, by means of neutron scattering measurements, that such fragmentation occurs in the spin ice candidate Nd$_2$Zr$_2$O$_7$. We observe the spectacular coexistence of an antiferromagnetic order induced by the monopole crystallisation and a fluctuating state with ferromagnetic correlations. Experimentally, this fragmentation manifests itself via the superposition of magnetic Bragg peaks, characteristic of the ordered phase, and a pinch point pattern, characteristic of the Coulomb phase. These results highlight the relevance of the fragmentation concept to describe the physics of systems that are simultaneously ordered and fluctuating., Comment: accepted in Nature Physics

We report the results of neutron scattering on a powder sample of Gd3Ga5O12 at high magnetic fields. We find that in high fields (B>1.8 T) the system is not fully polarized, but has a small canting of the moments induced by the dipolar interaction. We show that the degree of canting is accurately predicted by the standard Hamiltonian which includes the dipolar interaction. The inelastic scattering is dominated at large momentum transfers by a band of almost dispersionless excitations. We show that these correspond to the spin waves localized on ten site rings, expected for a system described by a nearest neighbor interaction, and that the spectrum at high fields B>1.8 T is well-described by a spin wave theory. The phase for fields <1.8 T is characterized by an antiferromagnetic Bragg peak at (210) and an incommensurate peak., Comment: 5 pages, 4 figures

Examples of materials where an "order by disorder" mechanism is at play to select a particular ground state are scarce. It has recently been proposed, however, that the antiferromagnetic XY pyrochlore Er2Ti2O7, reveals a most convincing case of this mechanism. Observation of a spin gap at zone centers has recently been interpreted as a corroboration of this physics. In this paper, we argue, however, that the anisotropy generated by the interaction-induced admixing between the crystal-field ground and excited levels provides for an alternative mechanism. It especially predicts the opening of a spin gap of about 15 micro-eV, which is of the same order of magnitude as the one observed experimentally. We report new high resolution inelastic neutron scattering data which can be well understood within this scenario., Comment: This version corrects a mistake on the numerical values of the exchange couplings $J$ in relation to the published version

At low temperatures, Tb$_2$Ti$_2$O$_7$ enters a spin liquid state, despite expectations of magnetic order and/or a structural distortion. Using neutron scattering, we have discovered that in this spin liquid state an excited crystal field level is coupled to a transverse acoustic phonon, forming a hybrid excitation. Magnetic and phononlike branches with identical dispersion relations can be identified, and the hybridization vanishes in the paramagnetic state. We suggest that Tb$_2$Ti$_2$O$_7$ is aptly named a "magnetoelastic spin liquid" and that the hybridization of the excitations suppresses both magnetic ordering and the structural distortion. The spin liquid phase of Tb$_2$Ti$_2$O$_7$ can now be regarded as a Coulomb phase with propagating bosonic spin excitations., Comment: 10 pages, 6 figures, supplementary information included

Molecular nanomagnets are among the first examples of spin systems of finite size and have been test-beds for addressing a range of elusive but important phenomena in quantum dynamics. In fact, for short-enough timescales the spin wavefunctions evolve coherently according to the an appropriate cluster spin-Hamiltonian, whose structure can be tailored at the synthetic level to meet specific requirements. Unfortunately, to this point it has been impossible to determine the spin dynamics directly. If the molecule is sufficiently simple, the spin motion can be indirectly assessed by an approximate model Hamiltonian fitted to experimental measurements of various types. Here we show that recently-developed instrumentation yields the four-dimensional inelastic-neutron scattering function S(Q,E) in vast portions of reciprocal space and enables the spin dynamics to be determined with no need of any model Hamiltonian. We exploit the Cr8 antiferromagnetic ring as a benchmark to demonstrate the potential of this new approach. For the first time we extract a model-free picture of the quantum dynamics of a molecular nanomagnet. This allows us, for example, to examine how a quantum fluctuation propagates along the ring and to directly test the degree of validity of the N\'{e}el-vector-tunneling description of the spin dynamics.

The low-temperature elementary spin excitations in the AFM molecular wheel Fe18 were studied experimentally by inelastic neutron scattering and theoretically by modern numerical methods, such as dynamical density matrix renormalization group or quantum Monte Carlo techniques, and analytical spin-wave theory calculations. Fe18 involves eighteen spin-5/2 Fe(III) ions with a Hilbert space dimension of 10^14, constituting a physical system that is situated in a region between microscopic and macroscopic. The combined experimental and theoretical approach allowed us to characterize and discuss the magnetic properties of Fe18 in great detail. It is demonstrated that physical concepts such as the rotational-band or L&E-band concepts developed for smaller rings are still applicable. In particular, the higher-lying low-temperature elementary spin excitations in Fe18 or AFM wheels in general are of discrete antiferromagnetic spin-wave character., Comment: 16 pages, 10 figures

Y0.5Ca0.5BaCo4O7 was recently introduced as a possible candidate for capturing some of the predicted classical spin kagome ground state features. Stimulated by this conjecture we have taken up a more complete study of the spin correlations in this compound with neutron scattering methods on a powder sample characterized with high-resolution neutron diffraction and the temperature dependence of magnetic susceptibility and specific heat. We have found that the frustrated near neighbor magnetic correlations involve not only the kagome planes but concern the full Co sub-lattice as evidenced by the analysis of the wavevector-dependence of the short range order. We conclude from our results that the magnetic moments are located on the Co sub-lattice as a whole and that correlations extend beyond the two-dimensional kagome planes. We identify intriguing dynamical properties, observing high-frequency fluctuations with a lorentzian line-width {\Gamma} <= 20 meV at ambient temperature. On cooling a low-frequency (~ 1 meV) dynamical component develops alongside the high-frequency fluctuations, which eventually becomes static at temperatures below T ~ 50 K. The high-frequency response with an overall line-width of ~ 10 meV prevails at T <= 2 K coincident with a fully elastic short-range ordered contribution.

We present the first neutron inelastic scattering results on the low temperature magnetic state of the three dimensional hyperkagom\'e compound Gd$_{3}$Ga$_{5}$O$_{12}$ (GGG). GGG is often classified as a strongly frustrated system with a manifold of continuously connected states. However, in contrast to the expectation of a continuum of gap-less excitations above a spin liquid-like ground state our results reveal three distinct inelastic modes found at 0.04(1), 0.12(2) an 0.58(3) meV at 0.06 K. The inelastic modes can be attributed to the magnetic ground state with the lowest and highest energy excitations showing spatial dependencies indicative of dimerized short range antiferromagnetic correlations. Short range correlations, reminiscent of spin liquid-like order, are static within the instrumental resolution (50 $\mu$eV) and represent 82% of the spectral weight. Longer range correlations, first observed by Petrenko, et al.\cite{Petrenko1998, develop below 0.14 ~K within the elastic cross section. The short range static correlations and dynamic components survive to high temperatures, comparable to the nearest neighbor exchange interactions. Our results suggest that the ground state of a three dimensional hyperkagom\'e compound differs distinctly from its frustrated counterparts on a pyrochlore lattice and reveals a juxtaposition of spin liquid order and strong dimerised coupling.

We investigate the magnetic properties of three Mn$_6$ single molecule magnets by means of inelastic neutron scattering and frequency domain magnetic resonance spectroscopy. The experimental data reveal that small structural distortions of the molecular geometry produce a significant effect on the energy level diagram and therefore on the magnetic properties of the molecule. We show that the giant spin model completely fails to describe the spin level structure of the ground spin multiplets. We analyze theoretically the spin Hamiltonian for the low spin Mn$_6$ molecule (S=4) and we show that the excited $S$ multiplets play a key role in determining the effective energy barrier for the magnetization reversal, in analogy to what was previously found for the two high spin Mn6 (S=12) molecules [S. Carretta et al., Phys. Rev. Lett. 100, 157203 (2008)]., Comment: 12 pages, 13 figures, 2 tables

The tetrameric Ni(II) spin cluster Ni4Mo12 has been studied by INS. The data were analyzed extensively in terms of a very general spin Hamiltonian, which includes antiferromagnetic Heisenberg interactions, biquadratic 2-spin and 3-spin interactions, a single-ion magnetic anisotropy, and Dzyaloshinsky-Moriya interactions. Some of the experimentally observed features in the INS spectra could be reproduced, however, one feature at 1.65 meV resisted all efforts. This supports the conclusion that the spin Hamiltonian approach is not adequate to describe the magnetism in Ni4Mo12. The isotropic terms in the spin Hamiltonian can be obtained in a strong-coupling expansion of the Hubbard model at half-filling. Therefore detailed theoretical studies of the Hubbard model were undertaken, using analytical as well as numerical techniques. We carefully analyzed its abilities and restrictions in applications to molecular spin clusters. As a main result it was found that the Hubbard model is also unable to appropriately explain the magnetism in Ni4Mo12. Extensions of the model are also discussed., Comment: 12 pages, 12 figures

The antiferromagnetic molecular wheel Fe18 of eighteen exchange-coupled Fe(III) ions has been studied by measurements of the magnetic torque, the magnetization, and the inelastic neutron scattering spectra. The combined data show that the low-temperature magnetism of Fe18 is very accurately described by the Neel-vector tunneling (NVT) scenario, as unfolded by semiclassical theory. In addition, the magnetic torque as a function of applied field exhibits oscillations that reflect the oscillations in the NVT tunnel splitting with field due to quantum phase interference., Comment: 5 pages, 4 figures, REVTEX4, to appear in PRL

We are interested in the phonon response in the frustrated magnets SrCr$_{9x}$Ga$_{12-9x}$O$_{19}$ (SCGO) and Ba$_{2}$Sn$_{2}$ZnCr$_{7x}$Ga$_{10-7x}$O$_{22}$ (BSZCGO). The motivation of the study is the recently discovered, phonon-driven, magnetic relaxation in the SCGO compound [Mutka et al. PRL {\bf 97} 047203 (2006)] pointing out the importance of a low-energy ($\hbar\omega\sim$7 meV) phonon mode. In neutron scattering experiments on these compounds the phonon signal is partly masked by the magnetic signal from the Cr moments and we have therefore examined in detail the non-magnetic isostructural counterparts SrGa$_{12}$O$_{19}$ (SGO) and Ba$_{2}$Sn$_{2}$ZnGa$_{10}$O$_{22}$ (BSZGO). Our {\it ab-initio} lattice dynamics calculations on SGO reveal a peak in the vibrational density of states matching with the neutron observations on SGO and SCGO. A strong contribution in the vibrational density of states comes from the partial contribution of the Ga atoms on the 2b and 12k sites, involving modes at the M--point of the hexagonal system. These modes comprise dynamics of the kagom\'e planes of the pyrochlore slab magnetic sub-lattice, 12k sites, and therefore can drive magnetic relaxation via spin-phonon coupling. Both BSZCGO and BSZGO show a similar low-energy Raman peak but no corresponding peak in the neutron determined density of states of BSZGO is seen. However, a strong non-Debye enhancement of low-energy phonon response is observed. We attribute this particular feature to the Zn/Ga disorder on the 2$d$ -site, already evoked earlier to affect the magnetic properties of BSZCGO. We propose that this disorder-induced phonon response explains the absence of a characteristic energy scale and the much faster magnetic relaxation observed in BSZCGO., Comment: This version is a fully improved revision of the previous one. New results are added and additional relevant arguments are provided to support the discussion

We have studied magnetically frustrated Tb$_2$Sn$_2$O$_7$ by neutron diffraction and high resolution energy-resolved neutron scattering. At 0.1 K, we observe short range magnetic correlations with a typical scale of 4 \AA, close to the near neighbor distance between Tb$^{3+}$ ions. %(3.686 \AA), This short range order coexists with ferromagnetic correlations and long range spin ice order at the scales of 18 and 190 \AA, respectively. Spin dynamics was investigated at a time scale down to 10$^{-9}$s, by energy-resolved experiments on a backscattering spectrometer. We observe a freezing of the spin dynamics for all length-scales, with a strong slowing down of the spin fluctuations when long range order settles in. We discuss the spin fluctuations remaining in the ground state in comparison with previous data obtained by muon spectroscopy., Comment: 6 pages, 5 figures

Inelastic neutron scattering has been used to determine the microscopic Hamiltonian describing two high-spin variants of the high-anisotropy Mn$_6$ nanomagnet. The energy spectrum of both systems is characterized by the presence of several excited total-spin multiplets partially overlapping the S=12 ground multiplet. This implies that the relaxation processes of these molecules are different from those occurring in prototype giant-spin nanomagnets. In particular, we show that both the height of the energy barrier and resonant tunnelling processes are greatly influenced by low-lying excited total-spin multiplets.

We follow the evolution of the elementary excitations of the quantum antiferromagnet TlCuCl3 through the pressure-induced quantum critical point, which separates a dimer-based quantum disordered phase from a phase of long-ranged magnetic order. We demonstrate by neutron spectroscopy the continuous emergence in the weakly ordered state of a low-lying but massive excitation corresponding to longitudinal fluctuations of the magnetic moment. This mode is not present in a classical description of ordered magnets, but is a direct consequence of the quantum critical point., Comment: 4 pages, 4 figures

The Cudaca system composed of isolated Cu2+ S=1/2 tetrahedra with antiferromagnetic exchange should exhibit properties of a frustrated quantum spin system. ab initio density functional theory calculations for electronic structure and molecular dynamics computations suggest a complex interplay between magnetic exchange, electron delocalization and molecular vibrations. Yet, extensive experimental characterization of Cudaca by means of synchrotron x-ray diffraction, magnetization, specific heat and inelastic neutron scattering reveal that properties of the real material can be only partly explained by proposed theoretical models as the low temperature properties seem to be governed by a manifold of molecular configurations coexisting at high temperatures., Comment: 15 figures

The antiferromagnetic molecular finite chain Cr6 was studied by inelastic neutron scattering. The observed magnetic excitations at 2.6 and 4.3 meV correspond, due to the open boundaries of a finite chain, to standing spin waves. The determined energy spectrum revealed an essentially classical spin structure. Hence, various spin-wave theories were investigated in order to assess their potential for describing the elementary excitations of finite spin systems., Comment: 6 pages, 6 figures, accepted for publication in Europhysics Letters

The Q dependence of the inelastic neutron scattering (INS) intensity of transitions within the ground-state spin multiplet of single-molecule magnets (SMMs) is considered. For these transitions, the Q dependence is related to the spin density map in the ground state, which in turn is governed by the Heisenberg exchange interactions in the cluster. This provides the possibility to infer the exchange-coupling constants from the Q dependence of the INS transitions within the spin ground state. The potential of this strategy is explored for the M = +-10 -> +- 9 transition within the S = 10 multiplet of the molecule Mn12 as an example. The Q dependence is calculated for powder as well as single-crystal Mn12 samples for various exchange-coupling situations discussed in the literature. The results are compared to literature data on a powder sample of Mn12 and to measurements on an oriented array of about 500 single-crystals of Mn12. The calculated Q dependence exhibits significant variation with the exchange-coupling constants, in particular for a single-crystal sample, but the experimental findings did not permit an unambiguous determination. However, although challenging, suitable experiments are within the reach of today's instruments., Comment: 11 pages, 6 figures, REVTEX4, to appear in PRB

The inelastic neutron scattering (INS) spectrum is studied for the antiferromagnetic molecular wheel CsFe8, in the temperature range 2 - 60 K, and for transfer energies up 3.6 meV. A qualitative analysis shows that the observed peaks correspond to the transitions between the L-band states, from the ground state up to the S = 5 multiplet. For a quantitative analysis, the wheel is described by a microscopic spin Hamiltonian (SH), which includes the nearest-neighbor Heisenberg exchange interactions and uniaxial easy-axis single-ion anisotropy, characterized by the constants J and D, respectively. For a best-fit determination of J and D, the L band is modeled by an effective SH, and the effective SH concept extended such as to facilitate an accurate calculation of INS scattering intensities, overcoming difficulties with the dimension of the Hilbert space. The low-energy magnetism in CsFe8 is excellently described by the generic SH used. The two lowest states are characterized by a tunneling of the Neel vector, as found previously, while the higher-lying states are well described as rotational modes of the Neel vector., Comment: 12 pages, 10 figures, REVTEX4, to appear in PRB

The low-lying magnetic excitations in the dimer of single-molecule magnets (Mn4)2 are studied by inelastic neutron scattering as a function of hydrostatic pressure. The anisotropy parameters D and B04, which describe each Mn4 subunit, are essentially pressure independent, while the antiferromagnetic exchange coupling J between the two Mn4 subunits strongly depends on pressure, with an increase of 42% at 17 kbar. Additional pressure dependent powder X-ray measurements allow a structural interpretation of the findings., Comment: 4 pages, 4 figures, REVTEX4, to be published in PRB

Time-resolved inelastic neutron scattering measurements on an array of single-crystals of the single-molecule magnet Mn12ac are presented. The data facilitate a spectroscopic investigation of the slow relaxation of the magnetization in this compound in the time domain., Comment: 3 pages, 4 figures, REVTEX4, to appear in Appl. Phys. Lett., for an animation see also http://www.dcb.unibe.ch/groups/guedel/members/ow2/trins.htm

The compound TlCuCl3 represents a model system of dimerized quantum spins with strong interdimer interactions. We investigate the triplet dispersion as a function of temperature by inelastic neutron scattering experiments on single crystals. By comparison with a number of theoretical approaches we demonstrate that the description of Troyer, Tsunetsugu, and Wuertz [Phys. Rev. B 50, 13515 (1994)] provides an appropriate quantum statistical model for dimer spin systems at finite temperatures, where many-body correlations become particularly important., Comment: 4 pages, 4 figures, to appear in Physical Review Letters

From inelastic neutron scattering experiments, we demonstrate quantum tunneling of the Neel vector in the antiferromagnetic molecular ferric wheel CsFe8. Analysis of the linewidth of the tunneling transition evidences coherent tunneling., Comment: 4 pages, 4 figure, REVTEX4

We report an inelastic neutron scattering (INS) study under a magnetic field on the frustrated molecular spin cluster $V_{15}$. Several field-dependent transitions are observed and provide a comprehensive understanding of the low-energy quantum spin states. The energy gap $2 \Delta_{0}\approx 27(3)\mu$eV between the two lowest $S=1/2$ Kramers doublets is unambiguously attributed to a symmetry lowering of the cluster. The INS data are mapped onto an S=1/2 Antiferromagnetic Heisenberg triangle with scalene distortion. A quantitative description of the wavefunction mixing within the ground state is derived., Comment: To be published in Europhysics Letters 7 pages, 3 figures

We present an extensive gallium NMR study of the geometrically frustrated kagome bi-layer compound SrCr_(9p)Ga_(12-9p)O_(19) (Cr^3+, S=3/2) over a broad Cr-concentration range (.72

We report a high-$T$ Ga-NMR study in the kagome-based antiferromagnetic compound SrCr$_{9p}$Ga$_{12-9p}$O$_{19}$ ($.81\leq p\leq .96$), and present a refined mean-field analysis of the high T local NMR susceptibility of Cr frustrated moments. We find that the intralayer kagome coupling is $J=86(6)$ K, and the interlayer coupling through non-kagome Cr moments is $J^{\prime }=69(7)$ K. The $J^{\prime}/J=0.80(1)$ ratio confirms the common belief that the frustrated entity is a pyrochlore slab., Comment: 8 pages, 4 figures Conference paper: Highly Frustrated Magnetism 2000, Waterloo (Canada) Submitted to Canadian Journal of Physics