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In this work, we present a nuclear magnetic resonance (NMR) study of the spin dynamics in the rare-earth-based low-dimensional molecular magnetic chains $\mathrm{Eu}{(\mathrm{hfac})}_{3}\mathrm{NITEt}$ and $\mathrm{Gd}{(\mathrm{hfac})}_{3}\mathrm{NITEt}$ (in short, Eu-Et and Gd-Et). Although both samples are based on the same chemical building block, [(${\mathrm{hfac})}_{3}\mathrm{NITEt}]$, their magnetic properties change dramatically when the ${\mathrm{Eu}}^{3+}$ ion, which is nonmagnetic at low temperatures, is substituted by the magnetic ${\mathrm{Gd}}^{3+}$ ion. The present proton NMR investigation shows that, down to the lowest investigated temperature ($T=1.5$ K for Gd-Et and $T=3$ K for Eu-Et), the Eu-Et chain behaves as a one-dimensional Heisenberg model with antiferromagnetic exchange coupling ($J=\ensuremath{-}20$ K) between $s=1/2$ organic radicals, and has a $T$-independent exchange frequency (${\ensuremath{\omega}}_{e}=2.6\ifmmode\times\else\texttimes\fi{}{10}^{12}$ rad/s). In the Gd-Et chain, in contrast, a competition arises between nearest-neighbor ferromagnetic coupling and next-nearest-neighbor antiferromagnetic coupling; moreover, two phase transitions have previously been found, in agreement with Villain's conjecture: a first transition, at ${T}_{0}=2.2$ K, from a high temperature paramagnetic phase to a chiral spin liquid phase, and a second transition, at ${T}_{N}=1.9$ K, to a three-dimensional helical spin solid phase. Contrary to the Eu-Et chain (whose three-dimensional ordering temperature is estimated to insurge at very low, ${T}_{N}\ensuremath{\approx}0.3$ K), critical spin dynamics effects have been measured in the Gd-Et chain on approaching ${T}_{N}=1.9$ K: namely, a divergence of the proton nuclear spin-lattice relaxation rate $1/{T}_{1}$, which in turn produces a sudden wipe-out of the NMR signal in a very narrow ($\mathrm{\ensuremath{\Delta}}T\ensuremath{\sim}0.04$ K) temperature range above ${T}_{N}$. Below ${T}_{N}$, an inhomogeneous broadening of the NMR line indicates a complete spin freezing. At ${T}_{0}=2.2$ K, instead, such critical effects are not observed because NMR measurements probe the two-spin correlation function, while the chiral spin liquid phase transition is associated with a divergence of the four-spin correlation function.

The strong influence of nuclear spins on resonant quantum tunneling in the molecular cluster Fe8 is demonstrated for the first time by comparing the relaxation rate of the standard Fe8 sample with two isotopic modified samples: (i) 56Fe is replaced by 57Fe, and (ii) a fraction of 1H is replaced by 2H. By using a recently developed "hole digging" method, we measured an intrinsic broadening which is driven by the hyperfine fields. Our measurements are in good agreement with numerical hyperfine calculations. For T>1.5 K, the influence of nuclear spins on the relaxation rate is less important, suggesting that spin-phonon coupling dominates the relaxation rate.

Magnetic susceptibility, ${}^{1}\mathrm{H}$ NMR and ${}^{63}\mathrm{Cu}$ NMR-NQR experiments on two slightly different species of the molecular $S=1/2$ antiferromagnetic (AF) ring Cu8, $[{\mathrm{Cu}}_{8}{(\mathrm{dmpz})}_{8}{(\mathrm{OH})}_{8}{]\mathrm{\ensuremath{\cdot}}2\mathrm{C}}_{5}{\mathrm{H}}_{5}\mathrm{N}$ (Cu8P) and $[{\mathrm{Cu}}_{8}{(\mathrm{dmpz})}_{8}{(\mathrm{OH})}_{8}{]\mathrm{\ensuremath{\cdot}}2\mathrm{C}}_{5}{\mathrm{H}}_{5}{\mathrm{NO}}_{2}$ (Cu8N), are presented. The magnetic energy levels are calculated exactly for an isotropic Heisenberg model Hamiltonian in zero magnetic field. From the magnetic susceptibility measurements we estimate the AF exchange coupling constant $J\ensuremath{\sim}1000\mathrm{K}$ and the resulting gap $\ensuremath{\Delta}\ensuremath{\sim}500\mathrm{K}$ between the ${S}_{T}=0$ ground state and the ${S}_{T}=1$ first excited state. The ${}^{63,65}\mathrm{Cu}$ NQR spectra indicate the presence of four crystallographically inequivalent copper nuclei in each ring. From the combination of the ${}^{63}\mathrm{Cu}$ NQR spectra and of the ${}^{63}\mathrm{Cu}$ NMR spectra at high magnetic field, we estimate the quadrupole coupling constant ${v}_{Q}$ of each site and the average asymmetry parameter \ensuremath{\eta} of the electric-field gradient tensor. The nuclear spin-lattice relaxation rate (NSLR) decreases exponentially on decreasing temperature for all nuclei investigated. The gap parameter extracted from ${}^{63}\mathrm{Cu}$ NQR-NSLR is the same as for the susceptibility while a smaller value is obtained from the ${}^{63}\mathrm{Cu}$ NMR-NSLR in an external magnetic field of 8.2 T.

We studied ${\mathrm{Mn}}_{12}$-acetate by inelastic neutron scattering and diffraction. We separated the energy levels corresponding to the splitting of the lowest $S$ multiplet ( $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}10$ ground state). The irregular spacing of the transition energies unambiguously shows the presence of high-order terms in the spin Hamiltonian [ $D\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}0.457(2){\mathrm{cm}}^{\ensuremath{-}1}$, ${B}_{4}^{0}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}2.33(4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}{\mathrm{cm}}^{\ensuremath{-}1}$]. The relative intensity of the lowest energy peaks is very sensitive to the small transverse term that is responsible for quantum tunneling, providing the first determination of this term in zero magnetic field $[{B}_{4}^{4}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ifmmode\pm\else\textpm\fi{}3.0(5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}{\mathrm{cm}}^{\ensuremath{-}1}]$.

We studied the low-temperature specific heat $C(T)$ and the magnetic susceptibility $\ensuremath{\chi}(T)$ of $\mathrm{Gd}(\mathrm{hfac}{)}_{3}\mathrm{NITiPr},$ a quasi-one-dimensional (1D) molecular magnetic chain with competing nearest-neighbor $(\mathrm{nn})$ and next-nearest-neighbor $(\mathrm{nnn})$ intrachain exchange interactions. The anomaly observed in $C(T)$ was reproducibly found at ${T}_{0}=2.09 \mathrm{K},$ although the $C(T)$ curves measured on different samples showed clear evidence for aging effects. For fresh, high-quality samples, the $\ensuremath{\lambda}$ shape of the anomaly and the negligible latent heat (less than $7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3} \mathrm{J}/\mathrm{m}\mathrm{o}\mathrm{l})$ strongly suggest the presence of a phase transition of order higher than the first. In the best sample at temperatures well below ${T}_{0}$ (0.2--1 K), a linear C-vs-$T$ dependence was found, which we interpreted in the framework of 1D quantum free spin-wave theory. Strong aging effects were also found in the magnetic susceptibility $\ensuremath{\chi}(T)$ which, for the best and freshest sample, exhibits a very small anomaly close to ${T}_{0}$ (at ${T}_{\ensuremath{\chi}}=2.1 \mathrm{K}),$ superimposed to a diverging paramagnetic behavior at lower temperatures. The anomaly at ${T}_{0}(\ensuremath{\sim}{T}_{\ensuremath{\chi}})$ could be due to a transition to three-dimensional (3D) helical long-range order, but this is inconsistent with the observed linear C-vs-$T$ behavior, typical of a 1D magnet with strong intrachain antiferromagnetic interactions. An alternative interpretation, capable of explaining the $C(T)$ data both in the low-temperature and in the critical region, calls for the onset, below ${T}_{0},$ of nonconventional chiral long-range order due to interchain interactions. The chiral phase can be described as a collection of parallel corkscrews, all turning clockwise (or all counterclockwise), whereas their phases are random. An estimation of ${T}_{0}$ according to this model and using the exchange constants evaluated from the linear C-vs-$T$ slope supports this interpretation. The chiral order is compatible with the breaking of the chain into finite segments, due to aging effects, while the phase coherence necessary for the onset of 3D helical long-range order is destroyed. In this framework, a qualitative account for the very small anomaly observed in the magnetic susceptibility $\ensuremath{\chi}(T)$ can also be given.

Thermal measurements of single microcrystals of ${\mathrm{Mn}}_{12}$ acetate have been performed with a particularly sensitive nanocalorimeter. Heat-capacity measurements as a function of applied magnetic field demonstrate magnetization quantum tunneling at the crossing of crystal-field levels. We present a theoretical model of the magnetic heat capacity of ${\mathrm{Mn}}_{12}$ acetate that approximately agrees with experimental results. Temperature measurements as a function of a slowly scanned magnetic field confirm earlier magnetization measurements and suggest that the thermal coupling between bath and sample, as well as the thermal conductivity of the crystals, play a major role in the magnetization reversal.

We present specific-heat and ac-susceptibility measurements providing more evidence that magnetic quantum tunneling occurs in ${\mathrm{Mn}}_{12}$Ac spin clusters. The total anisotropy energy barrier determined by fitting an Arrhenius law to the magnetic relaxation time is underestimated when compared to the specific-heat data. The expected magnetic contribution using a quadratic spin Hamiltonian needs higher-order terms to improve the agreement with the experiments, as recently done for electron-paramagnetic-resonance spectra. In addition, another interesting effect was observed in the specific-heat measurements when a dc magnetic field is applied. The extra magnetic contribution due to Zeeman splitting is suppressed below the expected superparamagnetic blocking temperature in the time scale of the measurements.

Neutron diffraction and inelastic neutron scattering in zero field have been performed on mesoscopic magnetic Mn{sub 12}O{sub 12} clusters, well known for their macroscopic quantum effects observed at low temperature. In addition to the static spin correlations of the cluster in its ground state, we have observed some energy levels related both to the anisotropy and to the exchange energies of the cluster, with their respective dynamical form factor. The temperature and Q dependences of the anisotropy energy levels can be qualitatively explained using a quantum model. Besides these expected modes, the most striking result is the observation of extended energy modes at energy values below those related to anisotropy. Their temperature and Q dependences differ from those expected for the energy levels of usual magnetic clusters. They indicate an additional spin coupling which must play a role in tunneling properties. {copyright} {ital 1997} {ital The American Physical Society}

A particularly sensitive heat capacity measuring device has allowed us to measure the tunneling process of ${\mathrm{Mn}}_{12}{\mathrm{O}}_{12}$-acetate single crystals (mass: $1$ and $20\ensuremath{\mu}\mathrm{g}$) from the irreversible tunneling process below the blocking temperature ${T}_{B}$ to the reversible resonant tunneling process above ${T}_{B}$. Above the ${T}_{B}$ (typically $3.5\mathrm{K}$) we find specific heat anomalies at the magnetic field values that correspond to the crossing of spin up and spin down levels of different magnetic quantum numbers. Below ${T}_{B}$, heat relaxation pulses at the crossing of crystal field levels are observed for fields applied antiparallel to the initial magnetization. These measurements give a new scope to ${\mathrm{Mn}}_{12}{\mathrm{O}}_{12}$-acetate investigations and show the great interest of nanocalorimetry for studies of big magnetic molecules.

We present the results of high-resolution inelastic neutron scattering experiments in the energy region below $85 \ensuremath{\mu}\mathrm{eV}$ for the octanuclear iron molecular cluster ${\mathrm{Fe}}_{8},$ which are relevant to the problem of determining the zero-field splitting parameters of the $S=10$ spin ground state. By using a cold-neutron backscattering spectrometer, we observed two magnetic peaks at $14.5$ and at $7.5 \ensuremath{\mu}\mathrm{eV}.$ Their position and intensity support a previous determination of the zero-field splitting parameters by neutron spectroscopy. The experimental findings are discussed in relation to very recent quantum phase interference and single-crystal electron paramagnetic resonance measurements.

Inelastic neutron scattering is used to study excited spin multiplets and low-energy phonons in the ${\mathrm{Fe}}_{8}$ nanomagnet. The energies of the three lowest-lying excited multiplets are determined. In addition, we find weakly dispersive optical phonons with energies lower than the anisotropy splitting of the ground $S=10$ spin multiplet. We show that these optical phonons may produce sharp minima in the field dependence of the relaxation time. The positions of the calculated minima agree with those that had been inferred from frequency-dependent specific heat and ac-susceptibility measurements.

The static and dynamic magnetic properties of an $[{\mathrm{Fe}}_{13}]$ cluster were investigated using several experimental techniques. The cluster crystallizes in a cubic space group, but careful investigation of the crystallographic data revealed that the symmetry is distorted locally. dc magnetic susceptibility measurements showed the presence of competing antiferromagnetic isotropic exchange interactions leading to a high-spin ground state and many low-lying excited spin states, which was confirmed by inelastic neutron scattering measurements. From high-field electron paramagnetic resonance measurements a small zero-field splitting of the spin ground state was inferred, which supports the local symmetry distortion found in the crystallographic studies. The spin dynamics slows down at sub-kelvin temperatures, where ac susceptibility measurements indicated that part of the sample shows superparamagnetic-like behavior and the other part relaxes through magnetization tunneling. The M\"ossbauer data confirmed the slowing down of the spin dynamics, indicating that this occurs mainly in the peripheral spins.

We present a study of the spin dynamics of the magnetic dimer $[\mathrm{Fe}(\mathrm{OMe})(\mathrm{dpm}{)}_{2}{]}_{2},$ using M\"ossbauer spectroscopy. In this cluster, the two iron(III) ions are antiferromagnetically coupled so that the dimer presents a $S=0$ spin ground state. Spin multiplets with values of S ranging from 1 to 5 follow in order of increasing energy. Axial anisotropy ${\mathrm{DS}}_{z}^{2}$ is also present with D of the order of a few kelvin. Spectra were collected over a range from 6.5 K to room temperature. They consist of doublets in which any magnetic structure is lacking, but the line widths of which increase with the temperature, due to relaxation effects. We performed their fits by assuming a fast-fluctuating hyperfine field which stochastically inverts its direction along the anisotropy axis. The zero-frequency Fourier transform ${J}_{z}$ of the hyperfine-field correlation function versus the temperature was obtained from the spectrum fittings. The trend of ${J}_{z}$ suggests that the basic mechanisms of the spin dynamics consist of a tunnel effect due to magnetic-anisotropy transversal terms, as well as of spin-thermal bath interactions. By assuming this, the following parameters were estimated from the fitting of ${J}_{z}(T):$ $D(1)\ensuremath{\approx}8.1\mathrm{K},$ $E/D(1)\ensuremath{\approx}8.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4},$ and ${w=w}_{0}\mathrm{exp}(\ensuremath{-}{2T}_{0}/T)$ with ${w}_{0}\ensuremath{\approx}9.2\ifmmode\times\else\texttimes\fi{}{10}^{8}{\mathrm{s}}^{\ensuremath{-}1}$ and ${T}_{0}\ensuremath{\approx}732\mathrm{K}.$ Lastly, similarities in spin dynamics between the dimer and the ring shaped clusters were discussed.

The dependence of the magnetic susceptibility on the magnetic field is investigated for the ferrimagnetic ring $[\mathrm{Mn}(\mathrm{hfac}{)}_{2}\mathrm{NITPh}{]}_{6}.$ The spikes of the susceptibility detected in a magnetic field ranging from 90 T to 285 T are interpreted as a manifestation of magnetic quantum jumps under spin reorientation from ferrimagnetic to ferromagnetic structure. The characteristic feature of the molecular ferrimagnetic ring ${\mathrm{Mn}}_{6}{R}_{6}$ is a deficiency of pair Heisenberg exchange interactions for the description of its magnetic properties in high magnetic fields. The comparison of the experimental data with the results of theoretical calculations allows us to prove the existence of a strong three-spin interaction in this molecular cluster and to determine the values of exchange constants. Constant of the Heisenberg exchange interaction is $J=39.8{\mathrm{cm}}^{\ensuremath{-}1}$ and the constant of the three-spin interaction is ${J}_{3}/J=0.14.$ For the calculation of the ground-state spin structure, the modified Lanczos method has been used.

Spin dynamics of the two magnetic molecular clusters Fe4 and Fe8, with four and eight Fe(III) ions, respectively, was studied by means of Mossbauer spectroscopy. The transition probabilities W's between the spin states of the ground multiplet were obtained from the fitting of the spectra. For the Fe4 cluster we found that, in the range from 1.38 to 77 K, the trend of W's versus the temperature corresponds to an Orbach's process involving an excited state with energy of about 160 K. For the Fe8, which, due to the presence of a low-energy excited state, could not be studied at temperatures greater than 20 K. the trend of W's in the range from 4 to 18 K seems to correspond to a direct process. The correlation functions of the magnetization were then calculated in terms of the W's. They have an exponential trend for the Fe4 cluster, while a small oscillating component is also present for the Felt cluster. For the first of the clusters, Τ vs T ( Τ is the decay time of the magnetization) has a trend which, at low temperatures (T 15 K. Τ follows the trend of W - 1 . For the Fe8, Τ follows an Arrhenius law, but with a prefactor which is smaller than the one obtained susceptibility measurements.

Inelastic neutron scattering has been used to determine the anisotropic spin Hamiltonian that splits the S = 10 ground multiplet of the cluster (tacn) 6 Fe 8 O 2 (OH) 1 2 Br 4 . 3 (ClO 4 ) 3 . 7 6H 2 O (Fe 8 PCl), where (tacn) is the organic ligand 1,4,7-triazacyclononane. This single-molecule magnet, which is obtained from the well known Fe 8 Br cluster, by partial replacement of the bromide ions by perchlorate anions, presents a larger transverse anisotropy than the parent compound, the E/D ratio being 0.22 instead of 0.16. This is in agreement with the relaxation measurements in the pure quantum tunneling regime. The details of the neutron spectra detected at three different temperatures (2, 10, and 15 K) allowed us to determine the spin Hamiltonian parameters up to fourth order and to identify the main source of the transition linewidth broadening with the occupational disorder of the bromide and perchlorate ions, rather than with the random internal dipolar field distribution.

X-ray magnetic-circular-dichroism (XMCD) spectra on the molecular superparamagnets $[{\mathrm{Mn}}_{12}{\mathrm{O}}_{12}{(\mathrm{C}\mathrm{H}}_{3}{\mathrm{C}\mathrm{O}\mathrm{O})}_{16}{(\mathrm{H}}_{2}{\mathrm{O})}_{24}]\ensuremath{\cdot}{2\mathrm{C}\mathrm{H}}_{3}{\mathrm{COOH}\mathrm{\ensuremath{\cdot}}4\mathrm{H}}_{2}\mathrm{O}$ (in short Mn12) and $[{\mathrm{Fe}}_{8}{\mathrm{O}}_{2}{(\mathrm{OH})}_{12}{(\mathrm{tacn})}_{6}{]\mathrm{Br}}_{2}{\mathrm{\ensuremath{\cdot}}9\mathrm{H}}_{2}\mathrm{O}$ (in short Fe8) are presented. The XMCD measurements have been performed at the ${\mathrm{M}\mathrm{n}\ensuremath{-}\mathrm{L}}_{\mathrm{I}\mathrm{I}\mathrm{I},\mathrm{I}\mathrm{I}}$ edges in the Mn12 compound and at the ${\mathrm{F}\mathrm{e}\ensuremath{-}\mathrm{L}}_{\mathrm{I}\mathrm{I}\mathrm{I},\mathrm{I}\mathrm{I}}$ edges in the Fe8 compound. For Fe8 the typical two-peak structure of Fe(III) compounds is found. For Mn12 and Fe8, from the dichroic signals a very low or negligible $〈{L}_{z}〉$ was obtained: to the best of our knowledge, this is the first direct experimental evidence of the quenching of the angular momentum by the crystal field in these systems. Quantitative analysis of the dichroic spectra for Fe8 yielded $〈{L}_{z}〉/〈{S}_{z}〉=0.02(1).$