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The compounds A$_2$Cu$_3$O(SO$_4$)$_3$ (A=Na, K) are characterized by copper hexamers which are weakly coupled to realize antiferromagnetic order below TN=3 K. They constitute novel quantum spin systems with S=1 triplet ground-states. We investigated the energy-level splittings of the copper hexamers by inelastic neutron scattering experiments covering the entire range of the magnetic excitation spectra. The observed transitions are governed by very unusual selection rules which we ascribe to the underlying spin-coupling topology. This is rationalized by model calculations which allow an unambiguous interpretation of the magnetic excitations concerning both the peak assignments and the nature of the spin-coupling parameters., Comment: 17 pages, 4 tables, 9 figures

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.

We present results of inelastic neutron scattering experiments performed for the compound Magnetic and neutron spectroscopic properties of the tetrameric nickel compound $[Mo_{12}O_{28}(\mu_2-OH)_9(\mu_3-OH)_3{Ni(H_2O)_3}_4] $\cdot$ 13H_2O$, which is a molecular magnet with antiferromagnetically coupled Ni2+ ions forming nearly ideal tetrahedra in a diamagnetic molybdate matrix. The neutron spectroscopic data are analyzed together with high-field magnetization data (taken from the literature) which exhibit four steps at non-equidistant field intervals. The experimental data can be excellently described by antiferromagnetic Heisenberg-type exchange interactions as well as an axial single-ion anisotropy within a distorted tetrahedron of Ni2+ ions characterized by X-ray single-crystal diffraction. Our analysis contrasts to recently proposed models which are based on the existence of extremely large biquadratic (and three-ion) exchange interactions and/or on a strong field dependence of the Heisenberg coupling parameters., Comment: 39 pages, 2 tables, 12 figures

We report on inelastic neutron scattering (INS) measurements on the molecular spin ring CsFe$_8$, in which eight spin-5/2 Fe(III) ions are coupled by nearest-neighbor antiferromagnetic Heisenberg interaction. We have recorded INS data on a non-deuterated powder sample up to high energies at the time-of-flight spectrometers FOCUS at PSI and MARI at ISIS, which clearly show the excitation of spin waves in the ring. Due to the small number of spin sites, the spin-wave dispersion relation is not continuous but quantized. Furthermore, the system exhibits a gap between the ground state and the first excited state. We have modeled our data using exact diagonalization of a Heisenberg-exchange Hamiltonian together with a small single-ion anisotropy term. Due to the molecule's symmetry, only two parameters $J$ and $D$ are needed to obtain excellent agreement with the data. The results can be well described within the framework of the rotational-band model as well as antiferromagnetic spin-wave theories., Comment: 10 pages, 9 figures, REVTEX 4

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 measure by inelastic neutron scattering the spin excitation spectra as a function of applied magnetic field in the quantum spin-ladder material (C5H12N)2CuBr4. Discrete magnon modes at low fields in the quantum disordered phase and at high fields in the saturated phase contrast sharply with a spinon continuum at intermediate fields characteristic of the Luttinger-liquid phase. By tuning the magnetic field, we drive the fractionalization of magnons into spinons and, in this deconfined regime, observe both commensurate and incommensurate continua., Comment: 4 pages, 4 figures

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 1H-NMR spectrum and nuclear relaxation rate 1/T_1 in the antiferromagnetic wheel CsFe8 were measured to characterize the previously observed magnetic field-induced low-temperature phase around the level crossing at 8 T. The data show that the phase is characterized by a huge staggered transverse polarization of the electronic Fe spins, and the opening of a gap, providing microscopic evidence for the interpretation of the phase as a field-induced magneto-elastic instability., Comment: 5 pages, 4 figures, REVTEX4, to appear in PRL

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 magnetic susceptibility, and low-temperature magnetization curve, of the [3 x 3] grid [Mn(III)4Mn(II)5(2poap-2H)6](ClO4)10.10H2O is analyzed within a spin Hamiltonian approach. The Hilbert space is huge (4,860,000 states), but the consequent use of all symmetries and a two-step fitting procedure nevertheless allows the best-fit determination of the magnetic exchange parameters in this system from complete quantum mechanical calculations. The cluster exhibits a total spin S = 1/2 ground state; the implications are discussed., Comment: 28 double-spaced pages, 7 figures, 2 tables

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 magnetic torque of the antiferromagnetic molecular wheel CsFe8 was studied down to 50 mK and in fields up to 28 T. Below ca. 0.5 K phase transitions were observed at the field-induced level-crossings (LCs). Intermolecular magnetic interactions are very weak excluding an explanation in terms of field-induced magnetic ordering. A magneto-elastic coupling was considered. A generic model shows that the wheel structure is unconditionally unstable at the LCs, and the predicted torque curves explain the essential features of the data well., Comment: 4 pages, 3 figures, REVTEX4, to appear in PRL

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

Many molecular magnetic clusters, such as single-molecule magnets, are characterized by spin ground states with defined total spin S exhibiting zero-field-splittings. In this work, the spectroscopic intensities of the transitions within the ground-state multiplet are analyzed. In particular, the effects of a mixing with higher-lying spin multiplets, which is produced by anisotropic interactions and is neglected in the standard single-spin description, are investigated systematically for the two experimental techniques of inelastic neutron scattering (INS) and electron paramagnetic resonance (EPR), with emphasis on the former technique. The spectroscopic transition intensities are calculated analytically by constructing corresponding effective spin operators perturbationally up to second order and consequently using irreducible tensor operator techniques. Three main effects of spin mixing are observed. Firstly, a pronounced dependence of the INS intensities on the momentum transfer Q, with a typical oscillatory behavior, emerges in first order, signaling the many-spin nature of the wave functions in exchange-coupled clusters. Secondly, as compared to the results of a first-order calculation, the intensities of the transitions within the spin multiplet are affected differently by spin mixing. This allows one, thirdly, to differentiate the higher-order contributions to the cluster magnetic anisotropy which come from the single-ion ligand-field terms and spin mixing, respectively. The analytical results are illustrated by means of the three examples of an antiferromagnetic heteronuclear dimer, the Mn-[3 x 3] grid molecule, and the single-molecule magnet Mn12., Comment: 18 pages, 3 figures, REVTEX4, to appear in PRB

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 have obtained new inelastic neutron scattering (INS) data for the molecular magnet Mn12-acetate which exhibit at least six magnetic peaks in the energy range 5-35 meV. These are compared with a microscopic Heisenberg model for the 12 quantum spins localised on the Mn ions, coupled by four inequivalent magnetic exchange constants. A fit to the magnetic susceptibility under the constraint that the spin of the ground state be S=10 yields two dominant exchange constants of very similar value, J1 ~ J2 ~ 65 K (~ 5.5 meV), and two smaller exchange constants J3 and J4. We compute the low-lying excitations by exact numerical diagonalisation and demonstrate that the parameters determined from the ground state and susceptibility fit provide qualitative agreement with the excitations observed by INS., Comment: 3 pages including 3 figures, uses elsart style files (included); to appear in JMMM (proceedings of JEMS'04)

We perform inelastic neutron scattering measurements on the molecular nanomagnet Mn_12-acetate to measure the excitation spectrum up to 45meV (500K). We isolate magnetic excitations in two groups at 5-6.5meV (60-75K) and 8-10.5meV (95-120K), with higher levels appearing only at 27meV (310K) and 31meV (360K). From a detailed characterization of the transition peaks we show that all of the low-energy modes appear to be separate S = 9 excitations above the S = 10 ground state, with the peak at 27meV (310K) corresponding to the first S = 11 excitation. We consider a general model for the four exchange interaction parameters of the molecule. The static susceptibility is computed by high-temperature series expansion and the energy spectrum, matrix elements and ground-state spin configuration by exact diagonalization. The theoretical results are matched with experimental observation by inclusion of cluster anisotropy parameters, revealing strong constraints on possible parameter sets. We conclude that only a model with dominant exchange couplings J_1 ~ J_2 ~ 5.5meV (65K) and small couplings J_3 ~ J_4 ~ 0.6meV (7K) is consistent with the experimental data., Comment: 17 pages, 12 figures

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 report an Inelastic Neutron Scattering (INS) study of the fully deuterated molecular compound K6[V15As6O42].9(D2O) (V15). Due to geometrical frustration, the essential physics at low temperatures of the V15 cluster containing 15 coupled V4+ (S=1/2) is determined by three weakly coupled spin-1/2 on a triangle. The INS spectra at low-energy allow us to directly determine the effective exchange coupling J0 = 0.211 meV within the triangle and the gap 2 \Delta = 0.035(2)meV between the two spin-1/2 doublets of the ground state. Results are discussed in terms of deviations from trigonal symmetry and Dzyaloshinskii-Moriya (DM) interactions., Comment: 8 pages, 4 figures. to appear in Europhysics Letters

We performed high resolution diffraction and inelastic neutron scattering measurements of Mn_{12}-acetate. Using a very high energy resolution, we could separate the energy levels corresponding to the splitting of the lowest S multiplet. Data were analyzed within a single spin model (S=10 ground state), using a spin Hamiltonian with parameters up to 4^{th} order. The non regular spacing of the transition energies unambiguously shows the presence of high order terms in the anisotropy (D= -0.457(2) cm^{-1}, B_4^0 = -2.33(4) 10^{-5}cm^{-1}). The relative intensity of the lowest energy peaks is very sensitive to the small transverse term, supposed to be mainly responsible for quantum tunneling. This allows an accurate determination of this term in zero magnetic field (B_4^4 = \pm 3.0(5) 10^{-5} cm^{-1}). The neutron results are discussed in view of recent experiments and theories., Comment: 4 pages ? 3 figures, submitted to Physical Review Letter