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Recent electron spin resonance experiments on CaWO$_4$:Gd$^{3+}$ and on other magnetic impurities have demonstrated that sustained Rabi oscillations can be created by driving a magnetic moment with a microwave field frequency slightly larger than the Larmor frequency and tuned to the Floquet resonance together with another microwave field (image drive). These observations are confirmed by the new experimental results reported in this paper. We investigate several mechanisms of decoherence and dissipation by using a combination of numerical and analytical techniques. The first microscopic model describes a magnetic moment in external magnetic fields, interacting with a bath of two-level systems acting as a source of decoherence and dissipation. The second model describes a collection of the identical, interacting magnetics moments, all subject to the same magnetic fields. In this case, the many-body interactions causes a decay of the Rabi oscillations. In addition, we also study the effect of the inhomogeneity of the microwave radiation on the decay of the Rabi oscillations. Our simulation results show that the dynamics of a magnetic moment subject to the two microwave fields with different frequencies and in contact with an environment is highly nontrivial. We show that under appropriate conditions, and in particular at the Floquet resonance, the magnetization exhibits sustained Rabi oscillations, in some cases with additional beatings. Although these two microscopic models separately describe the experimental data well, a simulation study that simultaneously accounts for both types of interactions is currently prohibitively costly. To gain further insight into the microscopic dynamics of these two different models, we study the time dependence of the bath and system energy and of the correlations of the spins, data that is not readily accessible experimentally.

Macroscopic phase coherence in superconductors enables quantum interference and phase manipulation at realistic device length scales. Numerous superconducting electronic devices are based on the modulation of the supercurrent in superconducting loops. While the overall behavior of symmetric superconducting loops have been studied, the effects of asymmetries in such devices remain under-explored and poorly understood. Here we report on an experimental and theoretical study of the flux modulation of the persistent current in a doubly-connected asymmetric aluminum nanowire loop. A model considering the length and electronic cross-section asymmetries in the loop provides a quantitative account of the observations. Comparison with experiments give essential parameters such as persistent and critical currents as well as the amount of asymmetry which can provide feedback into the design of superconducting quantum devices., Comment: to appear in EPL

The properties of rare-earth elements diluted in non-magnetic crystals make them a promising candidate for a quantum memory due to their limited Hilbert space. The control and readout of the qubit states require a highly sensitive measurement and large coupling of the spin ensemble with the electro-magnetic mode of a superconducting resonator. We report sensitive detection of forbidden transitions of electronuclear states from the minority species of $^{155}$Gd and $^{157}$Gd isotopes which opens the possibility of connecting quantum states with very different spin projections. Cavity perturbation measurements seen in the reflected signal allows the detection of about 7.6$\times10^{7}$ spins and the measurement of spin decoherence rate and spin-photon coupling strength.

Precise detection of spin resonance is of paramount importance to achieve coherent spin control in quantum computing. We present a novel setup for spin resonance measurements, which uses a dc-SQUID flux detector coupled to an antenna from a coplanar waveguide. The SQUID and the waveguide are fabricated from 20~nm Nb thin film, allowing high magnetic field operation with the field applied parallel to the chip. We observe a resonance signal between the first and third excited states of Gd spins $S=7/2$ in a CaWO$_4$ crystal, relevant for state control in multi-level systems., Comment: submitted

The multi-level system $^{55}$Mn$^{2+}$ is used to generate two pseudo-harmonic level systems, as representations of the same electronic sextuplet at different nuclear spin projections. The systems are coupled using a forbidden nuclear transition induced by the crystalline anisotropy. We demonstrate Rabi oscillations between the two representations in conditions similar to two coupled quasi-harmonic quantum oscillators. Rabi oscillations are performed at a detuned pumping frequency which matches energy difference between electro-nuclear states of different oscillators. We measure a coupling stronger than the decoherence rate, to indicate the possibility fast information exchange between the systems.

Layered compounds AMnBi2 (A=Ca, Sr, Ba, or rare earth element) have been established as Dirac materials. Dirac electrons generated by the two-dimensional (2D) Bi square net in these materials are normally massive due to the presence of a spin-orbital coupling (SOC) induced gap at Dirac nodes. Here we report that the Sb square net in an isostructural compound BaMnSb2 can host nearly massless Dirac fermions. We observed strong Shubnikov-de Haas (SdH) oscillations in this material. From the analyses of the SdH oscillations, we find key signatures of Dirac fermions, including light effective mass (~0.052m0; m0, mass of free electron), high quantum mobility (1280 cm2V-1S-1) and a Pi Berry phase accumulated along cyclotron orbit. Compared with AMnBi2, BaMnSb2 also exhibits much more significant quasi two-dimensional (2D) electronic structure, with the out-of-plane transport showing nonmetallic conduction below 120K and the ratio of the out-of-plane and in-plane resistivity reaching ~670. Additionally, BaMnSb2 also exhibits an antiferromagnetic order with a weak ferromagnetic component. The combination of nearly massless Dirac fermions on quasi-2D planes with a magnetic order makes BaMnSb2 an intriguing platform for seeking novel exotic phenomena of massless Dirac electrons., Comment: crystal lattice and magnetic structure information addded; final version for publication

The chiral anomaly-induced negative magnetoresistance and non-trivial Berry phase are two fundamental transport properties associated with the topological properties of Weyl fermions. In this work, we report the quantum transport of TaP single crystals in magnetic field up to 31T. Through the analyses of our magnetotransport data, we show TaP has the signatures of a Weyl state, including light effective quasiparticle masses, ultrahigh carrier mobility, as well as negative longitudinal magnetoresistance. Furthermore, we have generalized the Lifshitz-Kosevich formula for Shubnikov-de Haas (SdH) oscillations with multi-frequencies, and determined the non-trivial Berry phase of Pi for multiple Fermi pockets in TaP through the direct fitting of the quantum oscillations. In high fields, we also probed signatures of Zeeman splitting, from which the Land\'e g-factor is extracted.

Weyl (WSMs) evolve from Dirac semimetals in the presence of broken time-reversal symmetry (TRS) or space-inversion symmetry. The WSM phases in TaAs-class materials and photonic crystals are due to the loss of space-inversion symmetry. For TRS-breaking WSMs, despite numerous theoretical and experimental efforts, few examples have been reported. In this Article, we report a new type of magnetic semimetal Sr1-yMn1-zSb2 (y,z<0.1) with nearly massless relativistic fermion behaviour (m*=0.04-0.05m0, where m0 is the free electron mass). This material exhibits a ferromagnetic order for 304K < T < 565K, but a canted antiferromagnetic order with a ferromagnetic component for T < 304K. The combination of relativistic fermion behaviour and ferromagnetism in Sr1-yMn1-zSb2 offers a rare opportunity to investigate the interplay between relativistic fermions and spontaneous TRS breaking., Comment: Accepted by Nature Materials

We performed quantum manipulations of the multi-level spin system S=5/2 of a Mn$^{2+}$ ion, by means of a two-tone pulse drive. The detuning between the excitation and readout radio frequency pulses allows one to select the number of photons involved in a Rabi oscillation as well as increase the frequency of this nutation. Thus detuning can lead to a resonant multi-photon process. Our analytical model for a two-photon process as well as a numerical generalization fit well the experimental findings, with implications in the use of multi-level spin systems as tunable solid state qubits.

We discuss a general framework to address spin decoherence resulting from fluctuations in a spin Hamiltonian. We performed a systematic study on spin decoherence in the compound K$_6$[V$_{15}$As$_6$O$_{42}$(D$_2$O)] $\cdot$ 8D$_2$O, using high-field Electron Spin Resonance (ESR). By analyzing the anisotropy of resonance linewidths as a function of orientation, temperature and field, we find that the spin-orbit term is a major decoherence source. The demonstrated mechanism can alter the lifetime of any spin qubit and we discuss how to mitigate it by sample design and field orientation., Comment: submitted

We study the dynamics of inorganic antiferroelectric nanoclusters formed during an order-disorder transition and demonstrate the coexistence of the two phases in a region of 2-3 K around the transition temperature TN~215 K. Single crystals of NH4H2AsO4, a model hydrogen-bonded compound, show an antiferroelectric-paraelectric transition studied by means of highly sensitive magic angle spinning 15N NMR at 21.1 T. The phase co-existence is demonstrated by a double-peak structure of the chemical shift. Two-dimensional chemical exchange spectroscopy and spin-lattice relaxation time (T1) measurements show that the clusters are dynamic with sizes ~50 nm and lifetimes approaching seconds as T->TN. Their occupancy increases rapidly to fill the crystal volume below $T_N$. This study provides evidence for the commonality of the phase transitions in systems with electric properties and provides an improved spectroscopic method for such studies.

The molecular compound K$_6$[V$^{IV}_{15}$As$^{III}_6$O$_{42}$(H$_2$O)] $\cdot$ 8H$_2$O, in short V$_{15}$, has shown important quantum effects such as coherent spin oscillations. The details of the spin quantum dynamics depend on the exact form of the spin Hamiltonian. In this study, we present a precise analysis of the intramolecular interactions in V$_{15}$. To that purpose, we performed high-field electron spin resonance measurements at 120 GHz and extracted the resonance fields as a function of crystal orientation and temperature. The data are compared against simulations using exact diagonalization to obtain the parameters of the molecular spin Hamiltonian.

We study the quantum dynamics of a spin ensemble coupled to cavity photons. Recently, related experimental results have been reported, showing the existence of the strong coupling regime in such systems. We study the eigenenergy distribution of the multi-spin system (following the Tavis-Cummings model) which shows a peculiar structure as a function of the number of cavity photons and of spins. We study how this structure causes changes in the spectrum of the admittance in the linear response theory, and also the frequency dependence of the excited quantities in the stationary state under a probing field. In particular, we investigate how the structure of the higher excited energy levels changes the spectrum from a double-peak structure (the so-called vacuum field Rabi splitting) to a single peak structure. We also point out that the spin dynamics in the region of the double-peak structure corresponds to recent experiments using cavity ringing while in region of the single peak structure, it corresponds to the coherent Rabi oscillation in a driving electromagnetic filed. Using a standard Lindblad type mechanism, we study the effect of dissipations on the line width and separation in the computed spectra. In particular, we study the relaxation of the total spin in the general case of a spin ensemble in which the total spin of the system is not specified. The theoretical results are correlated with experimental evidence of the strong coupling regime, achieved with a spin 1/2 ensemble.

We report on multiple photon monochromatic quantum oscillations (Rabi oscillations) observed by pulsed EPR (Electron Paramagnetic Resonance) of Mn$^{2+}$ (S=5/2) impurities in MgO. We find that when the microwave magnetic field is similar or large than the anisotropy splitting, the Rabi oscillations have a spectrum made of many frequencies not predicted by the S=1/2 Rabi model. We show that these new frequencies come from multiple photon coherent manipulation of the multi-level spin impurity. We develop a model based on the crystal field theory and the rotating frame approximation, describing the observed phenomenon with a very good agreement., Comment: International Conference: Resonance in Condensed Matter Altshuler 100

We report on multi-photon Rabi oscillations and controlled tuning of a multi-level system at room temperature (S=5/2 for Mn2+:MgO) in and out of a quasi-harmonic level configuration. The anisotropy is much smaller than the Zeeman splittings, such as the six level scheme shows only a small deviation from an equidistant diagram. This allows us to tune the spin dynamics by either compensating the cubic anisotropy with a precise static field orientation, or by microwave field intensity. Using the rotating frame approximation, the experiments are very well explained by both an analytical model and a generalized numerical model. The calculated multi-photon Rabi frequencies are in excellent agreement with the experimental data.

Inelastic neutron scattering in variable magnetic field and high-field magnetization measurements, at the milikelvin temperature range, were performed to gain insight into the low-energy magnetic excitation spectrum and the field-induced level crossings in the molecular spin cluster \{Cr$_8$\}-cubane. These complementary techniques provide consistent estimates of the lowest level-crossing field. The overall features of the experimental data are explained using an isotropic Heisenberg model, based on three distinct exchange interactions linking the eight Cr$^{\text{III}}$ paramagnetic centers (spins $s = 3/2$), that is supplemented with a relatively large molecular magnetic anisotropy term for the lowest S=1 multiplet. It is noted that the existence of the anisotropy is clearly evident from the magnetic field dependence of the excitations in the INS measurements, while the magnetization measurements are not sensitive to its effects.

We present a magnetic study of the Gd$_3$N@C$_{80}$ molecule, consisting of a Gd-trimer via a Nitrogen atom, encapsulated in a C$_{80}$ cage. This molecular system can be an efficient contrast agent for Magnetic Resonance Imaging (MRI) applications. We used a low-temperature technique able to detect small magnetic signals by placing the sample in the vicinity of an on-chip SQUID. The technique implemented at NHMFL has the particularity to operate in high magnetic fields of up to 7 T. The Gd$_3$N@C$_{80}$ shows a paramagnetic behavior and we find a spin transition of the Gd$_3$N structure at 1.2 K. We perform quantum mechanical simulations, which indicate that one of the Gd ions changes from a $^8S_{7/2}$ state ($L=0, S=7/2$) to a $^7F_{6}$ state ($L=S=3, J=6$), likely due to a charge transfer between the C$_{80}$ cage and the ion.

We report a low temperature measurement technique and magnetization data of a quantum molecular spin, by implementing an on-chip SQUID technique. This technique enables the SQUID magnetometery in high magnetic fields, up to 7 Tesla. The main challenges and the calibration process are detailed. The measurement protocol is used to observe quantum tunneling jumps of the S=10 molecular magnet, Mn12-tBuAc. The effect of transverse field on the tunneling splitting for this molecular system is addressed as well., Comment: 7 pages, 3 figures

We study the energy level structure of the Tavis-Cumming model applied to an ensemble of independent magnetic spins $s=1/2$ coupled to a variable number of photons. Rabi splittings are calculated and their distribution is analyzed as a functin of photon number $n_{\rm max}$ and spin system size $N$. A sharp transition in the distribution of the Rabi frequency is found at $n_{\rm max}\approx N$. The width of the Rabi frequency spectrum diverges as $\sqrt{N}$ at this point. For increased number of photons $n_{\rm max}>N$, the Rabi frequencies converge to a value proportional to $\sqrt{n_{\rm max}}$. This behavior is interpreted as analogous to the classical spin resonance mechanism where the photon is treated as a classical field and one resonance peak is expected. We also present experimental data demonstrating cooperative, magnetic strong coupling between a spin system and photons, measured at room temperature. This points towards quantum computing implementation with magnetic spins, using cavity quantum-electrodynamics techniques., Comment: Received 8 April 2010; revised manuscript received 17 June 2010; published 14 July 2010

We report observation of the nonlinear Meissner effect (NLME) in Nb films by measuring the resonance frequency of a planar superconducting cavity as a function of the magnitude and the orientation of a parallel magnetic field. Use of low power rf probing in films thinner than the London penetration depth, significantly increases the field for the vortex penetration onset and enables NLME detection under true equilibrium conditions. The data agree very well with calculations based on the Usadel equations. We propose to use NLME angular spectroscopy to probe unconventional pairing symmetries in superconductors., Comment: published version

On-chip Electron Spin Resonance (ESR) of magnetic molecules requires the ability to precisely position nanosized samples in antinodes of the electro-magnetic field for maximal magnetic interaction. A method is developed to entrap micro-crystals containing spins in a well defined location on a substrate's surface. Traditional cavity ESR measurements are then performed on a mesoscopic crystal at 34 GHz. Polycrystalline diluted Cr$^{5+}$ spins were entrapped as well and measured while approaching the lower limit of the ESR sensitivity. This method suggests the feasibility of on-chip ESR measurements at dilution refrigerator temperatures by enabling the positioning of samples atop an on-chip superconducting cavity., Comment: to appear in Journal of Applied Physics

Large spin Mn2+ ions (S=5/2) diluted in a non-magnetic MgO matrix of high crystalline symmetry are used to realize a six level system that can be operated by means of multi-photon coherent Rabi oscillations. This spin system has a very small anisotropy which can be tuned in-situ to reversibly transform the system between harmonic and non-harmonic level configurations. Decoherence effects are strongly suppressed as a result of the quasi-isotropic electron interaction with the crystal field and with the 55Mn nuclear spins. These results suggest new ways of manipulating, reading and resetting spin quantum states which can be applied to encode a qubit across several quantum levels., Comment: Published version

A characteristic of spin reversal in the presence of phonon-bottleneck is the deviation of the magnetization cycle from a reversible function into an opened hysterezis cycle. In recent experiments on molecular magnets (e.g. V$_{15}$ and Ru$_2$), the zero-field level repulsion was sufficiently large to ensure an otherwise adiabatic passage through zero-field and the magnetization curves can be described by using only a phonon-bottleneck model. Here, we generalize the phonon-bottleneck model into a model able to blend the non-adiabatic dynamics of spins with the presence of a non-equilibrium phonon bath. In this simple phenomenological model, Bloch equations are written in the eigenbasis of the effective spin Hamiltonian, considered to be a two-level system at low temperatures. The relaxation term is given by the phonon-bottleneck mechanism. To the expense of calculus time, the method can be generalized to multi-level systems, where the notion of Bloch sphere does not apply but the density matrix formalism is still applicable., Comment: as published in EuroPhys Letters

We report coherent spin manipulation on Cr$^{5+}$ (\emph{S} = 1/2, \emph{I} = 0) doped K$_3$NbO$_8$, which constitutes a dilute two-level model relevant for use as a spin qubit. Rabi oscillations are observed for the first time in a spin system based on transition metal oxides up to room temperature. At liquid helium temperature the phase coherence relaxation time \emph{$T_2$} reaches $\sim 10$ $\mu$s and, with a Rabi frequency of 20 MHz, yields a single qubit figure of merit \emph{$Q_M$} of about 500. This shows that a diluted ensemble of Cr$^{5+}$ (\emph{S} = 1/2) doped K$_3$NbO$_8$ is a potential candidate for solid-state quantum information processing., Comment: 4 pages

The ruthenium based molecular magnet [Ru$_2$(D(3,5-Cl$_2$Ph)F)$_4$Cl(0.5H$_2$O)$\cdotp$C$_6$H$_{14}$] (hereafter Ru$_2$) behaves as a two-level system at sufficiently low temperatures. The authors performed spin detection by means of single-crystal measurements and obtained magnetic hysteresis loops around zero bias as a function of field sweeping rate. Compared to other molecular systems, Ru$_2$ presents an enhanced irreversibility as shown by ``valleys'' of negative differential susceptibility in the hysteresis curves. Simulations based on phonon bottleneck model are in good qualitative agreement and suggest an abrupt spin reversal combined with insufficient thermal coupling between sample and cryostat phonon bath., Comment: 4 pages, 3 figures

We have studied the dephasing of a superconducting flux-qubit coupled to a DC-SQUID based oscillator. By varying the bias conditions of both circuits we were able to tune their effective coupling strength. This allowed us to measure the effect of such a controllable and well-characterized environment on the qubit coherence. We can quantitatively account for our data with a simple model in which thermal fluctuations of the photon number in the oscillator are the limiting factor. In particular, we observe a strong reduction of the dephasing rate whenever the coupling is tuned to zero. At the optimal point we find a large spin-echo decay time of $4 \mu s$., Comment: New version of earlier paper arXiv/0507290 after in-depth rewriting

Decoherence in superconducting qubits is known to arise because of a variety of environmental degrees of freedom. In this article, we focus on the influence of thermal fluctuations in a weakly damped circuit resonance coupled to the qubit. Because of the coupling, the qubit frequency is shifted by an amount $n \delta \nu_0$ if the resonator contains $n$ energy quanta. Thermal fluctuations induce temporal variations $n(t)$ and thus dephasing. We give an approximate formula for the qubit dephasing time as a function of $\delta \nu_0$. We discuss the specific case of a flux-qubit coupled to the plasma mode of its DC-SQUID detector. We first derive a plasma mode-qubit interaction hamiltonian which, in addition to the usual Jaynes-Cummings term, has a coupling term quadratic in the oscillator variables coming from the flux-dependence of the SQUID Josephson inductance. Our model predicts that $\delta \nu_0$ cancels in certain non-trivial bias conditions for which dephasing due to thermal fluctuations should be suppressed.

We report detailed measurements of the relaxation and dephasing time in a flux-qubit measured by a switching DC SQUID. We studied their dependence on the two important circuit bias parameters: the externally applied magnetic flux and the bias current through the SQUID in two samples. We demonstrate two complementary strategies to protect the qubit from these decoherence sources. One consists in biasing the qubit so that its resonance frequency is stationary with respect to the control parameters ({\it optimal point}) ; the second consists in {\it decoupling} the qubit from current noise by chosing a proper bias current through the SQUID. At the decoupled optimal point, we measured long spin-echo decay times of up to $4 \mu s$., Comment: 4 pages, 4 figures, submitted to Phys. Rev. Letters

In the emerging field of quantum computation and quantum information, superconducting devices are promising candidates for the implementation of solid-state quantum bits or qubits. Single-qubit operations, direct coupling between two qubits, and the realization of a quantum gate have been reported. However, complex manipulation of entangled states - such as the coupling of a two-level system to a quantum harmonic oscillator, as demonstrated in ion/atom-trap experiments or cavity quantum electrodynamics - has yet to be achieved for superconducting devices. Here we demonstrate entanglement between a superconducting flux qubit (a two-level system) and a superconducting quantum interference device (SQUID). The latter provides the measurement system for detecting the quantum states; it is also an effective inductance that, in parallel with an external shunt capacitance, acts as a harmonic oscillator. We achieve generation and control of the entangled state by performing microwave spectroscopy and detecting the resultant Rabi oscillations of the coupled system., Comment: Nature. Received 25 May; accepted 5 July 2004. doi:10.1038/nature02831

Superconducting circuits fabricated using the widely used shadow evaporation technique can contain unintended junctions which change their quantum dynamics. We discuss a superconducting flux qubit design that exploits the symmetries of a circuit to protect the qubit from unwanted coupling to the noisy environment, in which the unintended junctions can spoil the quantum coherence. We present a theoretical model based on a recently developed circuit theory for superconducting qubits and calculate relaxation and decoherence times that can be compared with existing experiments. Furthermore, the coupling of the qubit to a circuit resonance (plasmon mode) is explained in terms of the asymmetry of the circuit. Finally, possibilities for prolonging the relaxation and decoherence times of the studied superconducting qubit are proposed on the basis of the obtained results., Comment: v.2: published version; 8 pages, 12 figures; added comparison with experiment, improved discussion of T_phi

We present the implementation of a new scheme to detect the quantum state of a persistent-current qubit. It relies on the dependency of the measuring Superconducting Quantum Interference Device (SQUID) plasma frequency on the qubit state, which we detect by resonant activation. With a measurement pulse of only 5ns, we observed Rabi oscillations with high visibility (65%)., Comment: 4 pages, 4 figures, submitted to PRB Rapid Com

We have observed coherent time evolution between two quantum states of a superconducting flux qubit comprising three Josephson junctions in a loop. The superposition of the two states carrying opposite macroscopic persistent currents is manipulated by resonant microwave pulses. Readout by means of switching-event measurement with an attached superconducting quantum interference device revealed quantum-state oscillations with high fidelity. Under strong microwave driving it was possible to induce hundreds of coherent oscillations. Pulsed operations on this first sample yielded a relaxation time of 900 nanoseconds and a free-induction dephasing time of 20 nanoseconds. These results are promising for future solid-state quantum computing., Comment: submitted 2 December 2002; accepted 4 February 2003

The spin one half molecular system V15 shows no barrier against spin reversal. This makes possible direct phonon activation between the two levels. By tuning the field sweeping rate and the thermal coupling between sample and thermal reservoir we have control over the phonon-bottleneck phenomena previously reported in this system. We demonstrate adiabatic motion of molecule spins in time dependent magnetic fields and with different thermal coupling to the cryostat bath. We also discuss the origin of the zero-field tunneling splitting for a half-integer spin., Comment: to appear in Phys. Rev. B - Rapid Communications

The so-called V15 molecule is formed of 15 spins 1/2 antiferromagnetically coupled. The resultant spin is equal to 1/2. Contrary to what is expected at first sight, this half-integer spin is gapped. We show that this is a consequence of the multi-spin character of the molecule. Time reversal symmetry (Kramers theorem) is preserved due to the existence of a groundstate degeneracy larger than 2. Magnetization experiments have been performed at different temperatures, sweeping-field rates and couplings with the cryostat. Their interpretation in terms of the Landau-Zener-Stuckelberg model gives evidence for adiabatic LZS spin reversal with and without dissipation., Comment: to be published in the supplement of the Progress of Theoretical Physics, proceedings of the 16th Nishinomiya-Yukawa Memorial Symposium held in the city of Nishinomiya, Japan, Nov. 13-14, 2001

Longitudinal or transverse magnetic fields applied on a crystal of Mn12-ac allows to observe independent tunnel transitions between m=-S+p and m=S-n-p (n=6-10, p=0-2 in longitudinal field and n=p=0 in transverse field). We observe a smooth transition (in longitudinal) from coherent ground-state to thermally activated tunneling. Furthermore two ground-state relaxation regimes showing a crossover between quantum spin relaxation far from equilibrium and near equilibrium, when the environment destroys multimolecule correlations. Finally, we stress that the complete Hamiltonian of Mn12 should contain odd spin operators of low order.

The phenomenon of Quantum Tunneling of Mesoscopic Spins is reviewed in the light of the behavior of the archetype of these systems: the molecular complex Mn12-ac. Most observations can be understood in the framework of the reduced Hilbert space dimension 2S+1=21. Due to the large spin S=10, the energy barrier preventing spin rotation is large, and as a consequence, quantum relaxation is very slow. The application of a magnetic field of a few Tesla below 1 K allows to observe tunneling (i) between the states m=-10 and m=10-n with n=8 to 11 if the field is longitudinal, or (ii) between the two ground-states m~-10 and m~10 if the field is transverse. The crossover temperature between ground-state and thermally assisted tunneling in a longitudinal field extrapolates in zero field at ~1.7 K. The observation of square root relaxation at short-times/low-temperatures and of exponential relaxation at long-times/high-temperatures, as observed previously above 1.5 K, confirms the important role of the spin bath dynamics which is out of equilibrium in the first regime and at equilibrium in the second one. In a second part of this paper a new molecule, so-called V15, with resultant spin S=1/2 is investigated. Contrary to high spin molecules, the energy barrier of low spin molecules is small or null, and the splitting between the symmetrical and anti-symmetrical states is sufficiently large to allow spin-phonon transitions during spin rotation. In low spin molecules the coupling to the environment is quite different from the one found in large spin molecules in low fields., Comment: 12 pages, 13 figures, to appear in The J. of Phys. Soc. of Japan, proc. of The Workshop on Frontiers in Magnetism, October 4-7, 1999, Kyoto, Japan

The Landau Zener model has recently been used to measure very small tunnel splittings in molecular clusters of Fe8, which at low temperature behaves like a nanomagnet with a spin ground state of S = 10. The observed oscillations of the tunnel splittings as a function of the magnetic field applied along the hard anisotropy axis are due to topological quantum interference of two tunnel paths of opposite windings. Transitions between quantum numbers M = -S and (S - n), with n even or odd, revealed a parity effect which is analogous to the suppression of tunnelling predicted for half integer spins. This observation is the first direct evidence of the topological part of the quantum spin phase (Berry or Haldane phase) in a magnetic system. We show here that the quantum interference can also be measured by ac susceptibility measurements in the thermal activated regime., Comment: 3 pages, 2 figures, conference proceedings of LT22 (Helsinki, Finland, August 4-11, 1999

The V_{15} polyoxovanadate molecule is made of 15 spins 1/2 with antiferromagnetic couplings. It belongs to the class of molecules with very large Hilbert space dimension (2^{15} in V_{15}, 10^8 in Mn_{12}-ac). It is a low-spin/big-molecule with spin S=1/2. Contrary large-spins/big-molecules of the Mn_{12}-ac type, V_{15} has no energy barrier against spin rotation. Magnetization measurements have been performed and despite the absence of a barrier, magnetic hysteresis is observed over a timescale of several seconds. This new phenomenon characterized by a "butterfly" hysteresis loop is due to the effect of the environment on the quantum rotation of the entangled 15 spins of the molecule, in which the phonon density of states is not at its equilibrium (phonon bottleneck)., Comment: REVTeX/LaTeX, 5 figures

Time resolved magnetization measurements have been performed on a spin 1/2 molecular complex, so called V$_{15}$. Despite the absence of a barrier, magnetic hysteresis is observed over a timescale of several seconds. A detailed analysis in terms of a dissipative two level model is given, in which fluctuations and splittings are of same energy. Spin-phonon coupling leads to long relaxation times and to a particular "butterfly" hysteresis loop., Comment: LaTeX/RevTeX, 3 figures.Approved for publication in PRL