Mesoscopic quantum tunneling of the magnetization

Barbara, B.; Wernsdorfer, Wolfgang; Sampaio, Luiz C.; Park, J.G.; Paulsen, C.; Novak, Miguel A.; Ferré, R.; Mailly, D.; Sessoli, Roberta; Caneschi, Andréa; Hasselbach, K.; Benoı̂t, A.; Thomas, Luc

doi:10.1016/0304-8853(94)00585-0

Cited by 136 publications

(112 citation statements)

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“…Such complex multi-spin systems provide attractive targets for the study of quantum effects at the mesoscopic scale. In these molecules, the large energy barriers between collective spin states can be crossed by thermal activation or quantum tunnelling, depending on the temperature or an applied magnetic field [2][3][4] . There is the hope that these mesoscopic spin states can be harnessed for the realization of quantum bits-'qubits', the basic building blocks of a quantum computer-based on molecular magnets [5][6][7][8] .…”

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Quantum oscillations in a molecular magnet

Bertaina

Gambarelli

Mitra

et al. 2008

Nature

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354

320

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The term 'molecular magnet' generally refers to a molecular entity containing several magnetic ions whose coupled spins generate a collective spin, S (ref. 1). Such complex multi-spin systems provide attractive targets for the study of quantum effects at the mesoscopic scale. In these molecules, the large energy barriers between collective spin states can be crossed by thermal activation or quantum tunnelling, depending on the temperature or an applied magnetic field [2][3][4] . There is the hope that these mesoscopic spin states can be harnessed for the realization of quantum bits-'qubits', the basic building blocks of a quantum computer-based on molecular magnets [5][6][7][8] . But strong decoherence 9 must be overcome if the envisaged applications are to become practical. Here we report the observation and analysis of Rabi oscillations (quantum oscillations resulting from the coherent absorption and emission of photons driven by an electromagnetic wave 10 ) of a molecular magnet in a hybrid system, in which discrete and wellseparated magnetic V IV 15 clusters are embedded in a self-organized non-magnetic environment. Each cluster contains 15 antiferromagnetically coupled S 5 1/2 spins, leading to an S 5 1/2 collective ground state [11][12][13] . When this system is placed into a resonant cavity, the microwave field induces oscillatory transitions between the ground and excited collective spin states, indicative of longlived quantum coherence. The present observation of quantum oscillations suggests that low-dimension self-organized qubit networks having coherence times of the order of 100 ms (at liquid helium temperatures) are a realistic prospect.In the context of quantum computing, it was recently discussed how the decoherence of molecular magnet spin quantum bits could be suppressed, with reference to the discrete low spin clusters V 15 and Cr 7 Ni (ref. 7; see also refs 8 and 14). In both systems, their low spin states cause weak environmental coupling 7 , making them candidates for the realization of a long-lived quantum memory. Measurement of the spin relaxation time t 2 in Cr 7 Ni was subsequently reported and found to be interestingly large 15,16 ; however, the important Rabi quantum oscillations were not observed, probably because electronic and nuclear degrees of freedom were too strongly linked to each other. As these oscillations have until now only been observed in non-molecular spin systems (see, for example, refs 17-20), it has remained an open question whether quantum oscillations could in principle be realized in molecular magnets 7,8 . This question is now answered by our observation of quantum oscillations of the Rabi type in V 15 . The main reason for this success lies in the fact that the important pairwise decoherence mechanism 7,8 associated with dipolar interactions could be strongly reduced.Before discussing the observed quantum oscillations, we first briefly describe the magnetic/electronic structure of the V IV 15 species as determined experimentally. Following the synthesis of the ...

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confidence: 99%

Quantum oscillations in a molecular magnet

Bertaina

Gambarelli

Mitra

et al. 2008

Nature

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354

320

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“…At present, these steps are thought to result from the double well potential that separates spin states; magnetization reorientation transitions have optimal probability when the "spin up" and "spin down" levels of the different magnetic quantum numbers align with applied magnetic field [9][10][11][12][13][14][15]. High field EPR [16,17], neutron scattering [18], and submm [19] techniques have been used to measure the excitation energies between levels in these magnetic clusters.…”

Section: Introductionmentioning

confidence: 99%

Magnetic field effects on the far-infrared absorption inMn12-acetate

et al. 2001

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We report the far-infrared spectra of the molecular nanomagnet Mn12-acetate (Mn12) as a function of temperature (5-300 K) and magnetic field (0-17 T). The large number of observed vibrational modes is related to the low symmetry of the molecule, and they are grouped together in clusters. Analysis of the mode character based on molecular dynamics simulations and model compound studies shows that all vibrations are complex; motion from a majority of atoms in the molecule contribute to most modes. Three features involving intramolecular vibrations of the Mn12 molecule centered at 284, 306 and 409 cm −1 show changes with applied magnetic field. The structure near 284 cm −1 displays the largest deviation with field and is mainly intensity related. A comparison between the temperature dependent absorption difference spectra, the gradual low-temperature cluster framework distortion as assessed by neutron diffraction data, and field dependent absorption difference spectra suggests that this mode may involve Mn motion in the crown.

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“…the magnetization decreases (time dependent) and quantum relaxation tends to diminish hysteresis. Between steps, the two ladders are shifted and tunnelling is impossible; the magnetization remains constant (in field and time) leading to hysteretic plateaus [4,5]. Such a staircase hysteresis loop (which figures out semiclassical quantization of the magnetization at the macroscopic scale) is completely different from a classical hysteresis loop characterized by a single step at the anisotropy field H A = 2DS/gm B (approx.…”

Section: Mesoscopic Tunnelling Of Large Spinsmentioning

confidence: 97%

“…The Hilbert space dimension D H = (2S + 1) N (for a same magnetic species) is generally too large to enable exact diagonalization, unless approximations are made to reduce it. In the case of Mn 12 -ac containing 4 Mn 3+ and 8 Mn 2+ spins, D H = (2 × 3/2 + 1) 4 (2 × 2 + 1) 8 = 10 8 can be lowered to D H = 10 4 if spin pairs with the largest couplings J Max are 'locked', i.e. form a single spin equal to the algebraic sum of the two.…”

Section: Mesoscopic Tunnelling Of Large Spinsmentioning

confidence: 99%

“…In magnetism, this subject started in the early 1970s and first consisted in observing whether the reversal of the magnetization of a macroscopic magnet, thermally activated at high temperature, could take place by quantum tunnelling at low temperature. After a relatively long 'middle ground' owing to the lack of systems with identical nanoparticles [3], the phenomenon of macroscopic quantum tunnelling in magnetism and its cross over towards the thermally activated regime at higher temperature was demonstrated with the nearly non-interacting S = 10 spins of the Mn 12 -ac singlemolecule magnet (SMM) 1 [4,5] and later with the nearly non-interacting angular moments J ∼ 10 of rare earth (RE) ions diluted in an insulator [6,7].…”

Section: Introductionmentioning

confidence: 99%

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Mesoscopic systems: classical irreversibility and quantum coherence

Barbara

2012

Phil. Trans. R. Soc. A.

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Mesoscopic physics is a sub-discipline of condensed-matter physics that focuses on the properties of solids in a size range intermediate between bulk matter and individual atoms. In particular, it is characteristic of a domain where a certain number of interacting objects can easily be tuned between classical and quantum regimes, thus enabling studies at the border of the two. In magnetism, such a tuning was first realized with large-spin magnetic molecules called single-molecule magnets (SMMs) with archetype Mn 12 -ac. In general, the mesoscopic scale can be relatively large (e.g. micrometre-sized superconducting circuits), but, in magnetism, it is much smaller and can reach the atomic scale with rare earth (RE) ions. In all cases, it is shown how quantum relaxation can drastically reduce classical irreversibility. Taking the example of mesoscopic spin systems, the origin of irreversibility is discussed on the basis of the Landau-Zener model. A classical counterpart of this model is described enabling, in particular, intuitive understanding of most aspects of quantum spin dynamics. The spin dynamics of mesoscopic spin systems (SMM or RE systems) becomes coherent if they are well isolated. The study of the damping of their Rabi oscillations gives access to most relevant decoherence mechanisms by different environmental baths, including the electromagnetic bath of microwave excitation. This type of decoherence, clearly seen with spin systems, is easily recovered in quantum simulations. It is also observed with other types of qubits such as a single spin in a quantum dot or a superconducting loop, despite the presence of other competitive decoherence mechanisms. As in the molecular magnet V 15 , the leading decoherence terms of superconducting qubits seem to be associated with a non-Markovian channel in which short-living entanglements with distributions of twolevel systems (nuclear spins, impurity spins and/or charges) leading to 1/f noise induce t 1 -like relaxation of S z with dissipation to the bath of two-level systems with which they interact most. Finally, let us mention that these experiments on quantum oscillations are, most of the time, performed in the classical regime of Rabi oscillations, suggesting that decoherence mechanisms might also be treated classically.

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Mesoscopic quantum tunneling of the magnetization

Cited by 136 publications

References 30 publications

Quantum oscillations in a molecular magnet

Quantum oscillations in a molecular magnet

Magnetic field effects on the far-infrared absorption inMn12-acetate

Mesoscopic systems: classical irreversibility and quantum coherence

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