Quantum simulators are controllable systems that can be used to simulate other quantum systems. Here we focus on the dynamics of a chain of molecular qubits with interposed antiferromagnetic dimers. We theoretically show that its dynamics can be controlled by means of uniform magnetic pulses and used to mimic the evolution of other quantum systems, including fermionic ones. We propose two proof-of-principle experiments, based on the simulation of the Ising model in transverse field and of the quantum tunneling of the magnetization in a spin-1 system.
Molecular nanomagnets are zero-dimensional spin systems, that exhibit quantum mechanical behavior at low temperatures. Exploiting quantum-information theoretic measures, we quantify here the size of linear superpositions that can be generated within the ground multiplet of high- and low-spin nanomagnets. Amongst the former class of systems, we mainly focus on Mn12 and Fe8. General criteria for further increasing such sizes are also outlined, and illustrated in the case of spin rings. The actual character (micro or macroscopic) of linear superpositions in low-spin systems is inherently ill-defi…
The behavior of molecular nanomagnets in periodic magnetic field transverse to the easy axis direction is investigated. It is shown that at sufficiently strong field the tunneling time can be considerably reduced.
Antiferromagnetic spin rings represent prototypical realizations of highly correlated, low-dimensional systems. Here we theoretically show how the introduction of magnetic defects by controlled chemical substitutions results in a strong spatial modulation of spin-pair entanglement within each ring. Entanglement between local degrees of freedom (individual spins) and collective ones (total ring spins) are shown to coexist in exchange-coupled ring dimers, as can be deduced from general symmetry arguments. We verify the persistence of these features at finite temperatures, and discuss them in ter…
We present an accurate way to detect spin dynamics of a nutating molecular nanomagnet by inserting it in a tunnel Josephson junction and studying the current voltage (I-V) characteristic. The spin nutation of the molecular nanomagnet is generated by applying two circularly polarized magnetic fields. We demonstrate that modulation of the Josephson current by the nutation of the molecular nanomagnet's spin appears as a stepwise structure like Shapiro steps in the I-V characteristic of the junction. Width and heights of these Shapiro-like steps are determined by two parameters of the spin nutatio…
We study the spin nutation effects of the molecular nanomagnet on the Josephson current through a superconductor$|$molecular nanomagnet$|$superconductor tunnel junction. We explicitly demonstrate that due to the spin nutation of the molecular nanomagnet two oscillatory terms emerge in the $ac$ Josephson current in addition to the conventional $ac$ Josephson current. Some resonances occur in the junction due to the interactions of the transported quasiparticles with the bias voltage and molecular nanomagnet spin dynamics. The appearance of them indicate that the energy exchanged during these in…
We study the dynamics of molecular nanomagnets through a fully quantum mechanical model describing high-spin and high-anisotropy magnetic molecules subjected to a time-dependent magnetic field along the quantization axis, which continuously inverts the population of spin states. Crystals of molecular nanomagnets placed inside a resonant cavity interact with a quantized electromagnetic field. Relaxation of excited states takes place by means of spin-photon interaction, allowing stimulated emission of radiation and creating a maser effect.
Garlatti et al. [Appl. Phys. Lett. 103, 202410 (2013)] report theoretical simulations aimed at showing that the best molecular nanomagnets for magnetic refrigeration between T = 10 K and sub-Kelvin region are those made of strongly ferromagnetically-coupled magnetic ions. This Comment revises such conclusion based on results that, apparently, contrast with the established belief in this research field.
In a recent paper, cond-mat/0404041, J. Vanacken et al. reported experimental studies of crystals of Mn12-ac molecular nanomagnets in pulsed magnetic fields with sweep rates up to 4000 T/s. Steps in the magnetization curve were observed. The data were explained by collective dipolar relaxation. We give here an alternative explanation that is based on thermal avalanches triggered by defect molecules (faster relaxing species). These species are always present in Mn12-ac molecular nanomagnets. We propose a simple method to test this interpretation. Note that we do not question the possibility of …
In the molecular nanomagnet Fe$_{8}$ tunneling can occur from a metastable state to an excited state followed by a transition to the ground state. This transition is accompanied by an energy release of $115.6$GHz. We constructed an experimental setup to measure whether this energy is released in the form of thermal or electromagnetic energy. Contrary to a previous publication we find no evidence for release of electromagnetic radiation. Our results for transitions between the first and second excited states to the ground state are consistent with a release of only thermal energy. This energy r…
A viable qubit must have a long coherence time $T_2$. In molecular nanomagnets $T_2$ is often limited at low temperatures by the presence of dipole and hyperfine interactions, which are often mitigated through sample dilution, chemical engineering and isotope substitution in synthesis. Atomic-clock transitions offer another route to reducing decoherence from environmental fields by reducing the effective susceptibility of the working transition to field fluctuations. The Cr$_7$Mn molecular nanomagnet, a heterometallic ring, features a clock transition at zero field. Both continuous-wave and sp…
We present a flexible and effective ab-initio scheme to build many-body models for molecular nanomagnets, and to calculate magnetic exchange couplings and zero-field splittings. It is based on using localized Foster-Boys orbitals as one-electron basis. We apply this scheme to three paradigmatic systems, the antiferromagnetic rings Cr8 and Cr7Ni and the single molecule magnet Fe4. In all cases we identify the essential magnetic interactions and find excellent agreement with experiments.
A good qubit must have a coherence time long enough for gate operations to be performed. Avoided level crossings allow for clock transitions in which coherence is enhanced by the insensitivity of the transition to fluctuations in external fields. Because of this insensitivity, it is not obvious how to effectively couple qubits together while retaining clock-transition behavior. Here we present a scheme for using a heterodimer of two coupled molecular nanomagnets, each with a clock transition at zero magnetic field, in which all of the gate operations needed to implement one- and two-qubit gate…
One of the main roadblocks that still hampers the practical use of molecular nanomagnets is their cryogenic working temperature. In the pursuit of rational strategies to design new molecular nanomagnets with increasing blocking temperature, ab initio methodologies play an important role by guiding synthetic efforts at the lab stage. Nevertheless, when evaluating vibration-induced spin relaxation, these methodologies are still far from being computationally fast enough to provide a useful predictive framework. Herein, we present an inexpensive first-principles method devoted to evaluating vibra…
Answer to the comment of E. Chudnovsky concerning the following papers: (1) N.V. Prokof'ev, P.C.E. Stamp, Phys. Rev. Lett.80, 5794 (1998). (2) W. Wernsdorfer, T. Ohm, C. Sangregorio, R. Sessoli, D. Mailly, C. Paulsen, Phys. Rev. Lett. 82, 3903 (1999).
A Mn30 molecular cluster is established to be the largest single-molecule magnet (SMM) discovered to date. Magnetization versus field measurements show coercive fields of about 0.5 T at low temperatures. Magnetization decay experiments reveal an Arrhenius behavior and temperature-independent relaxation below 0.2 K diagnostic of quantum tunneling of magnetization through the anisotropy barrier.The quantum hole digging method is used to establish resonant quantum tunneling. These results demonstrate that large molecular nanomagnets,having a volume of 15 nm^3, with dimensions approaching the meso…
Time-dependent specific heat experiments on the molecular nanomagnet Fe8 and the isotopic enriched analogue 57Fe8 are presented. The inclusion of the 57Fe nuclear spins leads to a huge enhancement of the specific heat below 1 K, ascribed to a strong increase in the spin-lattice relaxation rate Gamma arising from incoherent, nuclear-spin-mediated magnetic quantum tunneling in the ground-doublet. Since Gamma is found comparable to the expected tunneling rate, the latter process has to be inelastic. A model for the coupling of the tunneling levels to the lattice is presented. Under transverse fie…
An unusually large magnetocaloric effect for the temperature region below 10 K is found for the Fe14 molecular nanomagnet. This is to large extent caused by its extremely large spin S ground-state combined with an excess of entropy arising from the presence of low-lying excited S states. We also show that the highly symmetric Fe14 cluster core, resulting in small cluster magnetic anisotropy, enables the occurrence of long-range antiferromagnetic order below T_N=1.87 K.
The discovery of magnetic bistability in Mn$_{12}$ more than 20 years ago marked the birth of molecular magnetism, an extremely fertile interdisciplinary field and a powerful route to create tailored magnetic nanostructures. However, the difficulty to determine interactions in complex polycentric molecules often prevents their understanding. Mn$_{12}$ is an outstanding example of this difficulty: although it is the forefather and most studied of all molecular nanomagnets, an unambiguous determination of even the leading magnetic exchange interactions is still lacking. Here we exploit four-dime…
Three decades of research in molecular nanomagnets have raised their magnetic memories from liquid helium to liquid nitrogen temperature thanks to a wise choice of the magnetic ion and coordination environment. Still, serendipity and chemical intuition played a main role. In order to establish a powerful framework for statistically driven chemical design, we collected chemical and physical data for lanthanide-based nanomagnets, catalogued over 1400 published experiments, developed an interactive dashboard (SIMDAVIS) to visualise the dataset, and applied inferential statistical analysis. Our an…
The magnetization of the prototypical molecular magnet Mn12-acetate exhibits a series of sharp steps at low temperatures due to quantum tunneling at specific resonant values of magnetic field applied along the easy c-axis. An abrupt reversal of the magnetic moment of such a crystal can also occur as an avalanche, where the spin reversal proceeds along a "deflagration" front that travels through the sample at subsonic speed. In this article we review experimental results that have been obtained for the ignition temperature and the speed of propagation of magnetic avalanches in molecular nanomag…
The Landau Zener method allows to measure very small tunnel splittings Δin molecular clusters Fe_8. The observed oscillations of Δas a function of the magnetic field applied along the hard anisotropy axis are explained in terms of topological quantum interference of two tunnel paths of opposite windings. Studies of the temperature dependence of the Landau Zener transition rate P gives access to the topological quantum interference between exited spin levels. The influence of nuclear spins is demonstrated by comparing P of the standard Fe_8 sample with two isotopically substituted samples. The …
The nuclear spin-lattice relaxation rate 1/T_1_ is calculated for magnetic ring clusters by fully diagonalizing their microscopic spin Hamiltonians. Whether the nearest-neighbor exchange interaction J is ferromagnetic or antiferromagnetic, 1/T_1_ versus temperature T in ring nanomagnets may be peaked at around k_B_T=|J| provided the lifetime broadening of discrete energy levels is in proportion to T^3^. Experimental findings for ferromagnetic and antiferromagnetic Cu^II^ rings are reproduced with crucial contributions of magnetic anisotropies as well as acoustic phonons.
Electrical control of spins at the nanoscale offers significant architectural advantages in spintronics, because electric fields can be confined over shorter length scales than magnetic fields. Thus, recent demonstrations of electric-field (E-field) sensitivities in molecular spin materials are tantalising, raising the viability of the quantum analogues of macroscopic magneto-electric devices.However, the E-field sensitivities reported so far are rather weak, prompting the question of how to design molecules with stronger spin-electric couplings. Here we show that one path is to identify an en…
We show that the dynamic magnetic susceptibility and the superparamagnetic blocking temperature of an Fe8 single molecule magnet oscillate as a function of the magnetic field Hx applied along its hard magnetic axis. These oscillations are associated with quantum interferences, tuned by Hx, between different spin tunneling paths linking two excited magnetic states. The oscillation period is determined by the quantum mixing between the ground S=10 and excited multiplets. These experiments enable us to quantify such mixing. We find that the weight of excited multiplets in the magnetic ground stat…
We study the phase transition of the escape rate of exchange-coupled dimer of single-molecule magnets which are coupled either ferromagnetic ally or antiferromagnetically in a staggered magnetic field and an easy $z$-axis anisotropy. The Hamiltonian for this system has been used to study molecular dimer nanomagnets [Mn$_4$]$_2$. We generalize the method of mapping a single-molecule magnetic spin problem onto a quantum-mechanical particle to dimeric molecular nanomagnets. The problem is mapped to a single particle quantum-mechanical Hamiltonian in terms of the relative coordinate and a coordina…
A new mechanism is proposed for the magnetization reversal of molecular nanomagnets such as \Fe8. In this process the spin tunnels from the lowest state near one easy direction to the first excited state near the opposite easy direction, and subsequently decays to the second easy direction with the emission of a phonon, or it first emits a phonon and then tunnels to the final state. This mechanism is the simplest imaginable one that allows magnetization relaxation in the presence of a longitudinal magnetic field that is so large that the nuclear spin environment cannot absorb the energy requir…
The paper reports a computational study of the quantum entanglement in V12 cluster molecular magnet. The low-temperature properties of the system are modelled with anisotropic quantum Heisenberg model on a tetramer of spins $S=1/2$ in the external magnetic field. The two-spin entanglement is quantified using the concurrence, whereas the fidelity serves as a measure of four-spin entanglement. The analytic and numerical results are derived and discussed, emphasizing the importance of real-space and spin-space interaction anisotropy and the role of quantum level crossings in the entanglement desc…
The strong influence of nuclear spins on resonant quantum tunneling in the molecular cluster Fe_8 is demonstrated for the first time by comparing the relaxation rate of the standard Fe_8 sample with two isotopic modified samples: (i) 56_Fe is replaced by 57_Fe, and (ii) a fraction of 1_H is replaced by 2_H. 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 import…
We present a microscopic description of molecular magnets by the multi-orbital Hubbard model, which includes the correlated hopping term, i.e. the dependence of electron hopping amplitude between orbitals on the degree of their occupancy. In the limit of large Coulomb on-site interaction, we derived the spin Hamiltonian using the perturbation theory. The magnetic coupling constant between two ions we determined in two different ways: a)from the expression obtained in the perturbation calculus and b)from the analysis of distances between the lowest levels of the energy spectrum obtained by the …
Ramsey et al. [Nature Phys. 4, 277-281 (2008)] report the observation of quantum interference associated with tunnelling trajectories between states of different total spin length in a dimeric molecular nanomagnet. They argue that the interference is a consequence of the unique characteristics of a molecular Mn12 wheel, which behaves as a molecular dimer with weak ferromagnetic exchange coupling. We show here that the data published by Ramsey et al. are not consistent and unfortunately mostly wrong. We show further that the Landau-Zener (LZ) formula, which links the tunnel probability with the…
We present here an exact version of our response (dated April 27) to Wernsdorfer's correspondence submitted to Nature Physics on March 31, 2008. After consultation with a referee, Nature Physics chose not publish any part of this exchange. We would therefore like to point out that our original study has now been considered favorably by four separate referees chosen by Nature Physics. Unfortunately, Wernsdorfer subsequently posted two further variations of his correspondence on this archive (arXiv:0804.1246v1 and arXiv:0804.1246v2). We note that aspects of the most recent posting (dated after s…
Molecular Nanomagnets have attracted the attention of the scientific community since the rich physics behind their magnetic behaviour make them ideal test-beds for fundamental concepts in quantum mechanics. Sophisticated experiments and targeted research activities have also unveiled their potential for several technological applications. Inelastic neutron scattering is a powerful and widely used technique to investigate the properties of these systems. The new generation of spectrometers, equipped with arrays of position-sensitive detectors, enable to efficiently measure the neutron cross-sec…
We present details about an experimental method based on the Landau Zener model which allows to measure very small tunnel splittings $Δ$ in molecular clusters Fe8. The measurements are performed with an array of micro-SQUIDs. The observed oscillations of Delta as a function of the magnetic field applied along the hard anisotropy axis are explained in terms of topological quantum interference of two tunnel paths of opposite windings. Transitions between M = -S and (S - n), with n even or odd, revealed a parity (symmetry) effect which is analogous to the suppression of tunneling predicted for ha…
The time evolution of the magnetization of a magnetic molecular crystal is obtained in an external time-dependent magnetic field, with sweep rates in the kT/s range. We present the 'exact numerical' solution of the time dependent Schrödinger equation, and show that the steps in the hysteresis curve can be described as a sequence of two-level transitions between adiabatic states. The multilevel nature of the problem causes the transition probabilities to deviate significantly from the predictions of the Landau-Zener-Stückelberg model. These calculations allow the introduction of an efficient ap…
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…
An accurate experimental characterization of finite antiferromagnetic (AF) spin chains is crucial for controlling and manipulating their magnetic properties and quantum states for potential applications in spintronics or quantum computation. In particular, finite AF chains are expected to show a different magnetic behaviour depending on their length and topology. Molecular AF rings are able to combine the quantum-magnetic behaviour of AF chains with a very remarkable tunability of their topological and geometrical properties. In this work we measure the $^{53}$Cr-NMR spectra of the Cr$_{8}$Cd …
In recent years, studies on cyclic molecular nanomagnets have captivated the attention of researchers. These magnets are finite in size and contain very large spins. They are interesting because they possess macroscopic quantum tunneling of Néel vectors. For antiferromagnetic molecular nanomagnets with finite number of even-numbered coupled spins, tunneling involves two classical localized Néel ground states separated by a magnetic energy barrier. The question is: can such phenomena be observed in nano magnets with odd number of magnetic ions? The answer is not directly obvious because cyclic …
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 (E…
Single molecule magnets straddle the classical and quantum mechanical worlds, displaying many fascinating phenomena. They may have important technological applications in information storage and quantum computation. We review the physical properties of two prototypical molecular nanomagnets, Mn_12-acetate and Fe_8: each behaves as a rigid, spin-10 object, and exhibits tunneling between up and down directions. As temperature is lowered, the spin reversal process evolves from thermal activation to pure quantum tunneling. At low temperatures, magnetic avalanches occur in which the magnetization o…
We address the characterization of molecular nanomagnets at the quantum level and analyze the performance of local measurements in estimating the physical parameters in their spin Hamiltonians. To this aim, we compute key quantities in quantum estimation theory, such as the classical and the quantum Fisher information, in the prototypical case of an heterometallic antiferromagnetic ring. We show that local measurements, performed only on a portion of the molecule, allow a precise estimate of the parameters related to both magnetic defects and avoided level crossings.
We have studied numerically the quantum-classical crossover in the escape-rate for an uniaxial spin system with an arbitrarily directed field. Using the simple quantum transition-state theory, we have obtained the boundary separating the first- and the second-order crossover and the escape-rate in the presence of the transverse and longitudinal field. The results apply to the molecular nanomagnet, ${\rm Mn_{12}}$.
Numerical modelling of coherent spin relaxation in nanomagnets, formed by magnetic molecules of high spins, is accomplished. Such a coherent spin dynamics can be realized in the presence of a resonant electric circuit coupled to the magnet. Computer simulations for a system of a large number of interacting spins is an efficient tool for studying the microscopic properties of such systems. Coherent spin relaxation is an ultrafast process, with the relaxation time that can be an order shorter than the transverse spin dephasing time. The influence of different system parameters on the relaxation …
We propose an analog quantum simulator for the Holstein molecular-crystal model based on a superconducting circuit QED system in the dispersive regime. By varying the driving field on the superconducting resonators, one can readily access both the adiabatic and anti-adiabatic regimes of this model. Strong e-ph coupling required for small-polaron formation can also be reached. We show that small-polaron state of arbitrary quasimomentum can be generated by applying a microwave pulse to the resonators. We also show that significant squeezing in the resonator modes can be achieved in the polaron-c…
The notion of artifical atom relies on the capability to change the number of carriers one by one in semiconductor quantum dots, and the resulting changes in their electronic structure. Organic molecules with transition metal atoms that have a net magnetic moment and display hysteretic behaviour are known as single molecule magnets (SMM). The fabrication of CdTe quantum dots chemically doped with a controlled number of Mn atoms and with a number of carriers controlled either electrically or optically paves the way towards a new concept in nanomagnetism: the artificial single molecule magnet. H…
We propose a quantum inverse iteration algorithm which can be used to estimate the ground state properties of a programmable quantum device. The method relies on the inverse power iteration technique, where the sequential application of the Hamiltonian inverse to an initial state prepares an approximate groundstate. To apply the inverse Hamiltonian operation, we write it as a sum of unitary evolution operators using the Fourier approximation approach. This allows to reformulate the protocol as separate measurements for the overlap of initial and propagated wavefunction. The algorithm thus cruc…
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…
We show that molecular spin qudits provide an ideal platform to simulate the quantum dynamics of photon fields strongly interacting with matter. The basic unit of the proposed molecular quantum simulator can be realized by a simple dimer of a spin 1/2 and a spin $S$ transition metal ion, solely controlled by microwave pulses. The spin $S$ ion is exploited to encode the photon field in a flexible architecture, which enables the digital simulation of a wide range of spin-boson models much more efficiently than by using a multi-qubit register. The effectiveness of our proposal is demonstrated by …
We show that the low-temperature physics of molecular nanomagnets, contrary to the prevailing one-molecule picture, must be determined by the long-range magnetic ordering due to many-body dipolar interactions. The calculations here performed, using Ewald's summation, suggest a ferromagnetic ground state with a Curie temperature of about 130 mK. The energy of this state is quite close to those of an antiferromagnetic state and to a glass of frozen spin chains. The latter may be realized at finite temperature due to its high entropy.
Molecular nanomagnets show clear signatures of coherent behavior and have a wide variety of effective low-energy spin Hamiltonians suitable for encoding qubits and implementing spin-based quantum information processing. At the nanoscale, the preferred mechanism for control of quantum systems is through application of electric fields, which are strong, can be locally applied, and rapidly switched. In this work, we provide the theoretical tools for the search for single molecule magnets suitable for electric control. By group-theoretical symmetry analysis we find that the spin-electric coupling …
