Search

We present the first microscopic model for chirality-induced spin selectivity effect in electron-transfer, in which the internal degrees of freedom of the chiral bridge are explicitly included. By exactly solving this model on short chiral chains we demonstrate that a sizable polarization on the acceptor arises from the interplay of coherent and incoherent dynamics, with strong electron-electron correlations yielding many-body states on the bridge as crucial ingredients. Moreover, we include the coherent and incoherent interactions with vibrational modes and show that they can play an important role in determining the long-time polarized state probed in experiments.

The implementation of a universal quantum processor still poses fundamental issues related to error mitigation and correction, which demand to investigate also platforms and computing schemes alternative to the main stream. A possibility is offered by employing multi-level logical units (qudits), naturally provided by molecular spins. Here we present the blueprint of a Molecular Spin Quantum Processor consisting of single Molecular Nanomagnets, acting as qudits, placed within superconducting resonators adapted to the size and interactions of these molecules to achieve a strong single spin to photon coupling. We show how to implement a universal set of gates in such a platform and to readout the final qudit state. Single-qudit unitaries (potentially embedding multiple qubits) are implemented by fast classical drives, while a novel scheme is introduced to obtain two-qubit gates via resonant photon exchange. The latter is compared to the dispersive approach, finding in general a significant improvement. The performance of the platform is assessed by realistic numerical simulations of gate sequences, such as Deutsch-Josza and quantum simulation algorithms. The very good results demonstrate the feasibility of the molecular route towards a universal quantum processor., Comment: 16 pages, 11 figures. Accepted in Physical Review Applied

The heterobimetallic metallacrown (MC), (TMA)$_2${Mn(OAc)$_2$[12-MC$_{Mn(III)Cu(II)N(shi)}$-4](CH$_3$OH)}$\cdot$2.90CH$_3$OH, 1, where TMA$^+$ is tetramethylammonium, $^-$OAc is acetate, and shi$^{3-}$ is salicylhydroximate, consists of a Mn$^{II}$ ion captured in the central cavity and alternating unambiguous and ordered manganese(III) and copper(II) sites about the MC ring, a first for the archetypal MC structure design. DC-magnetometry characterization and subsequent simulation with the Spin Hamiltonian $$H = -J_1(\mathbf{s}_1+\mathbf{s}_3)\cdot\mathbf{s}_5-J_2(\mathbf{s}_2+\mathbf{s}_4)\cdot\mathbf{s}_5-J_3\sum_{i=1}^{4}\mathbf{s}_i\cdot\mathbf{s}_{i+1} + d(s_{z,1}^2 + s_{z,3}^2) + \mu_B\sum_{j=1}^5 g_j\mathbf{s}_j\cdot\mathbf{B}$$ indicates an S = 5/2 ground state and a sizable axial zero-field splitting on Mn$^{III}$. AC-susceptibility measurements reveal that 1 displays slow magnetization relaxation akin to single-molecule magnet (SMM) behavior.

Nuclear spins are candidates to encode qubits or qudits due to their isolation from magnetic noise and potentially long coherence times. However, their weak coupling to external stimuli makes them hard to integrate into circuit-QED architectures, the leading technology for solid-state quantum processors. Here, we study the coupling of $^{173}$Yb(III) nuclear spin states in an [Yb(trensal)] molecule to superconducting cavities. Experiments have been performed on magnetically diluted single crystals placed on the inductors of lumped-element $LC$ superconducting resonators with characteristic frequencies spanning the range of nuclear and electronic spin transitions. We achieve a high cooperative coupling to all electronic and most nuclear [$^{173}$Yb(trensal)] spin transitions. This result is a big leap towards the implementation of qudit protocols with molecular spins using a hybrid architecture., Comment: 8 pages, 5 figures, 66 references, supplemental information (14 pages, 12 figures)

Understanding chiral induced spin-selectivity (CISS), resulting from charge transport through helical systems, has recently inspired many experimental and theoretical efforts, but is still object of intense debate. In order to assess the nature of CISS, we propose to focus on electron-transfer processes occurring at the single-molecule level. We design simple magnetic resonance experiments, exploiting a qubit as a highly sensitive and coherent magnetic sensor, to provide clear signatures of the acceptor polarization. Moreover, we show that information could even be obtained from time-resolved electron paramagnetic resonance experiments on a randomly-oriented solution of molecules. The proposed experiments will unveil the role of chiral linkers in electron-transfer and could also be exploited for quantum computing applications.

Artificial magnetic molecules can contribute to progressing towards large scale quantum computation by: a) integrating multiple quantum resources and b) reducing the computational costs of some applications. Chemical design, guided by theoretical proposals, allows embedding nontrivial quantum functionalities in each molecular unit, which then acts as a microscopic quantum processor able to encode error protected logical qubits or to implement quantum simulations. Scaling up even further requires 'wiring-up' multiple molecules. We discuss how to achieve this goal by the coupling to on-chip superconducting resonators. The potential advantages of this hybrid approach and the challenges that still lay ahead are critically reviewed., Comment: 9 pages, 4 figures

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 ring to study the local spin densities on the Cr sites. Cr$_{8}$Cd can in fact be considered a model system of a finite AF open chain with an even number of spins. The NMR resonant frequencies are in good agreement with the theoretical local spin densities, by assuming a core polarization feld AC = -12.7 T/$\mu_B$. Moreover, these NMR results confirm the theoretically predicted non-collinear spin arrangement along the Cr$_{8}$Cd ring, which is typical of an even-open AF spin chain.

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-dimensional inelastic neutron scattering to portray how individual spins fluctuate around the magnetic ground state, thus fixing the exchange couplings of Mn$_{12}$ for the first time. Our results demonstrate the power of four-dimensional inelastic neutron scattering as an unrivaled tool to characterize magnetic clusters.

Measurements of proton Nuclear Magnetic Resonance (1H NMR) spectra and relaxation and of Muon Spin Relaxation ($\mu^{+}$SR) have been performed as a function of temperature and external magnetic field on two isostructural lanthanide complexes, Er(trensal) and Dy(trensal) featuring crystallographically imposed trigonal symmetry. Both the nuclear 1/T1 and muon $\lambda$ longitudinal relaxation rates, LRR, exhibit a peak for temperatures T lower than 30K, associated to the slowing down of the spin dynamics, and the width of the NMR absorption spectra starts to increase significantly at T ca. 50K, a temperature sizably higher than the one of the LRR peaks. The LRR peaks have a field and temperature dependence different from those previously reported for all Molecular Nanomagnets. They do not follow the Bloembergen-Purcell-Pound scaling of the amplitude and position in temperature and field and thus cannot be explained in terms of a single dominating correlation time $\tau$c determined by the spin slowing down at low temperature. Further, for T lower than 50K the spectral width does not follow the temperature behavior of the magnetic susceptibility chi. We suggest, using simple qualitative considerations, that the observed behavior is due to a combination of two different relaxation processes characterized by the correlation times $\tau$LT and $\tau$HT, dominating for T lower than 30K and T higher than 50K, respectively. Finally, the observed flattening of LRR for T lower than 5K is suggested to have a quantum origin.

We review a recent theoretical proposal for a universal quantum computing platform based on tunable nonlinear electromechanical nano-oscillators, in which qubits are encoded in the anharmonic vibrational modes of mechanical resonators coupled to a superconducting circuitry. The digital quantum simulation of spin-type model Hamiltonians, such as the Ising model in a transverse field, could be performed with very high fidelities on such a prospective platform. Here we challenge our proposed simulator with the actual IBM-Q quantum processor available on cloud. We show that such state-of-art implementation of a quantum computer, based on transmon qubits and superconducting technology, is able to perform digital quantum simulations. However, encoding the qubits in mechanical degrees of freedom would allow to outperform the current implementations in terms of fidelity and scalability of the quantum simulation., Comment: Proceedings of the 2018 Italian Quantum Information Science (IQIS18) conference, to appear in Proceedings MDPI

Magnetic molecules, modelled as finite-size spin systems, are test-beds for quantum phenomena and could constitute key elements in future spintronics devices, long-lasting nanoscale memories or noise-resilient quantum computing platforms. Inelastic neutron scattering is the technique of choice to probe them, characterizing molecular eigenstates on atomic scales. However, although large magnetic molecules can be controllably synthesized, simulating their dynamics and interpreting spectroscopic measurements is challenging because of the exponential scaling of the required resources on a classical computer. Here, we show that quantum computers have the potential to efficiently extract dynamical correlations and the associated magnetic neutron cross-section by simulating prototypical spin systems on a quantum hardware. We identify the main gate errors and show the potential scalability of our approach. The synergy between developments in neutron scattering and quantum processors will help design spin clusters for future applications.

Digital quantum simulators are among the most appealing applications of a quantum computer. Here we propose a universal, scalable, and integrated quantum computing platform based on tunable nonlinear electromechanical nano-oscillators. It is shown that very high operational fidelities for single and two qubits gates can be achieved in a minimal architecture, where qubits are encoded in the anharmonic vibrational modes of mechanical nanoresonators, whose effective coupling is mediated by virtual fluctuations of an intermediate superconducting artificial atom. An effective scheme to induce large single-phonon nonlinearities in nano-electromechanical devices is explicitly discussed, thus opening the route to experimental investigation in this direction. Finally, we explicitly show the very high fidelities that can be reached for the digital quantum simulation of model Hamiltonians, by using realistic experimental parameters in state-of-the art devices, and considering the transverse field Ising model as a paradigmatic example., Comment: 14 pages, 8 figures

We report the results of inelastic neutron scattering experiments performed with triple-axis spectrometers to investigate the low-temperature collective dynamics in the ordered phase of uranium dioxide. The results are in excellent agreement with the predictions of mean-field RPA calculations emphasizing the importance of multipolar superexchange interactions. By comparing neutron scattering intensities in different polarization channels and at equivalent points in different Brillouin zones, we show the mixed magneto-vibrational-quadrupolar character of the observed excitations. The high energy resolution afforded by the cold triple-axis spectrometer allowed us to study in detail the magnon-phonon interaction giving rise to avoided crossings along the $[00\xi]$ reciprocal space direction.

Entanglement between individual spins can be detected by using thermodynamics quantities as entanglement witnesses. This applies to collective spins also, provided that their internal degrees of freedom are frozen, as in the limit of weakly-coupled nanomagnets. Here, we extend such approach to the detection of entanglement between subsystems of a spin cluster, beyond such weak-coupling limit. The resulting inequalities are violated in spin clusters with different geometries, thus allowing the detection of zero- and finite-temperature entanglement. Under relevant and experimentally verifiable conditions, all the required expectation values can be traced back to correlation functions of individual spins, that are now made selectively available by four-dimensional inelastic neutron scattering.

We introduce a scheme to perform quantum-information processing that is based on a hybrid spin-photon qubit encoding. The proposed qubits consist of spin-ensembles coherently coupled to microwave photons in coplanar waveguide resonators. The quantum gates are performed solely by shifting the resonance frequencies of the resonators on a ns timescale. An additional cavity containing a Cooper-pair box is exploited as an auxiliary degree of freedom to implement two-qubit gates. The generality of the scheme allows its potential implementation with a wide class of spin systems.

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., Comment: 5 pages, 3 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.

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., Comment: Phys. Rev. Lett., in press

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

We address the cause of the unusual muon spin relaxation (muSR) results on molecular nanomagnets (MNMs). Through measurements on protonated and deuterated samples of the MNMs Cr7Mn (S=1) and Cr8 (S=0), we show that the muon spin for $S \neq 0$ MNMs is relaxed via dynamic fluctuations of the electronic spins. A freezing out of dynamic processes occurs on cooling and at low temperatures the muon spins are relaxed by the electronic spins which themselves are dephased by incoherent nuclear field fluctuations.We observe a transition to a state of static magnetic order of the MNM electronic spins in Cr7Mn below 2 K., Comment: 4 pages, 3 figures

We study the magnetization and the spin dynamics of the Cr$_7$Ni ring-shaped magnetic cluster. Measurements of the magnetization at high pulsed fields and low temperature are compared to calculations and show that the spin Hamiltonian approach provides a good description of Cr$_7$Ni magnetic molecule. In addition, the phonon-induced relaxation dynamics of molecular observables has been investigated. By assuming the spin-phonon coupling to take place through the modulation of the local crystal fields, it is possible to evaluate the decay of fluctuations of two generic molecular observables. The nuclear spin-lattice relaxation rate $1/T_1$ directly probes such fluctuations, and allows to determine the magnetoelastic coupling strength., Comment: 3 pages, 2 figures, submitted as a contributed article for the Jems conference in Dublin (September 14-19 2008)

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

We investigate the role of topology and distortions in the quantum dynamics of magnetic molecules, using a cyclic spin system as reference. We consider three variants of antiferromagnetic molecular ring, i.e. Cr$_8$, Cr$_7$Zn and Cr$_7$Ni, characterized by low lying states with different total spin $S$. We theoretically and experimentally study the low-temperature behavior of the magnetic torque as a function of the applied magnetic field. Near level crossings, this observable selectively probes quantum fluctuations of the total spin (''$S$ mixing") induced by lowering of the ideal ring symmetry. We show that while a typical distortion of a model molecular structure is very ineffective in opening new $S$-mixing channels, the spin topology is a major ingredient to control the degree of $S$ mixing. This conclusion is further substantiated by low-temperature heat capacity measurements., Comment: 5 pages, 4 figures

Inelastic neutron scattering has been applied to the study of the spin dynamics of Cr-based antiferromagnetic octanuclear rings where a finite total spin of the ground state is obtained by substituting one Cr(III) ion (s = 3/2) with Zn (s = 0), Mn (s = 5/2) or Ni (s = 1) di-cations. Energy and intensity measurements for several intra-multiplet and inter-multiplet magnetic excitations allow us to determine the spin wavefunctions of the investigated clusters. Effects due to the mixing of different spin multiplets have been considered. Such effects proved to be important to correctly reproduce the energy and intensity of magnetic excitations in the neutron spectra. On the contrary to what is observed for the parent homonuclear Cr8 ring, the symmetry of the first excited spin states is such that anticrossing conditions with the ground state can be realized in the presence of an external magnetic field. Heterometallic Cr7M wheels are therefore good candidates for macroscopic observations of quantum effects., Comment: 9 pages, 11 figures, submitted to Phys. Rev. B, corrected typos and added references, one sentence changed

We propose a scheme for the implementation of quantum gates which is based on the qubit encoding in antiferromagnetic molecular rings. We show that a proper engineering of the intercluster link would result in an effective coupling that vanishes as far as the system is kept in the computational space, while it is turned on by a selective excitation of specific auxiliary states. These are also shown to allow the performing of single- and two-qubit gates without an individual addressing of the rings by means of local magnetic fields., Comment: To appear in Physical Review Letters

The fundamental magnetic interactions of Pr$_{2}$Fe$_{17}$ are studied by inelastic neutron scattering and anisotropy field measurements. Data analysis confirms the presence of three magnetically inequivalent sites, and reveals an exceptionally large value of the exchange field. The unexpected importance of $J$-mixing effects in the description of the ground-state properties of Pr$_{2}$Fe$_{17}$ is evidenced, and possible applications of related compounds are envisaged., Comment: 4 RevTeX pages, 4 EPS figures. Accepted for publication by Appl. Phys. Lett. (will be found at http://apl.aip.org)

We investigate the time autocorrelation of the molecular magnetization $M(t)$ for three classes of magnetic molecules (antiferromagnetic rings, grids and nanomagnets), in contact with the phonon heat bath. For all three classes, we find that the exponential decay of the fluctuations of $M(t)$, associated with the irreversible exchange of energy with the heat bath, is characterized by a single characteristic time $\tau (T,B)$ for not too high temperature $T$ and field $B$. This is reflected in a nearly single-lorentzian shape of the spectral density of the fluctuations. We show that such fluctuations are effectively probed by NMR, and that our theory explains the recent phenomenological observation by Baek et al. (PRB70, 134434) that the Larmor-frequency dependence of $1/T_1$ data in a large number of AFM rings fits to a single-lorentzian form., Comment: Published as Phys. Rev. Letters 94, 077203 (2005) in slightly reduced form

The substitution of one metal ion in a Cr-based molecular ring with dominant antiferromagnetic couplings allows to engineer its level structure and ground-state degeneracy. Here we characterize a Cr7Ni molecular ring by means of low-temperature specific-heat and torque-magnetometry measurements, thus determining the microscopic parameters of the corresponding spin Hamiltonian. The energy spectrum and the suppression of the leakage-inducing S-mixing render the Cr7Ni molecule a suitable candidate for the qubit implementation, as further substantiated by our quantum-gate simulations., Comment: To appear in Physical Review Letters

The role of $S$-mixing in the quantum tunneling of the magnetization in nanomagnets has been investigated. We show that the effect on the tunneling frequency is huge and that the discrepancy (more than 3 orders of magnitude in the tunneling frequency) between spectroscopic and relaxation measurements in Fe$_8$ can be resolved if $S$-mixing is taken into account., Comment: REVTEX, 10 pages, 3 jpg figures, to appear in PRL

The magnetic grid molecule Mn(II)-[3 x 3] has been studied by high-field torque magnetometry at 3He temperatures. At fields above 5 T, the torque vs. field curves exhibit an unprecedented oscillatory behavior. A model is proposed which describes these magneto oscillations well., Comment: REVTEX 4, 4 pages, 3 figures, to appear in PRL

Combining recent and new inelastic neutron scattering data for the molecular cyclic cluster Cr8 produces a deep understanding of the low lying excitations in bipartite antiferromagnetic Heisenberg rings. The existence of the L-band, the lowest rotational band, and the E-band, essentially spin wave excitations, is confirmed spectroscopically. The different significance of these excitations and their physical nature is clearly established by high-energy and Q-dependence data., Comment: 4 pages, 4 figures, RevTex4, to appear in PRL

Molecular nanomagnets, besides promising to open new frontiers in technology, have attracted huge interest in the scientific community because they can exhibit the phenomenon known as quantum tunnelling of the magnetization, i.e. coherent fluctuations of the direction of the total spin vector. In this paper we study a different quantum phenomenon involving fluctuations of the magnitude of the total spin vector. These fluctuations are related to the mixing between states with different spin quantum number, and imply new macroscopic effects, which we theoretically investigated in the Mn-[3x3] grid., Comment: 10 pages latex, 6 figures