MOLECULAR NANO-MAGNETS
People
Alberto Ghirri
Filippo Troiani
Valerio Bellini
Marco Affronte @ Modena
Molecular spin clusters are nanomagnets whose low temperature magnetic properties are determined by molecular quantum states. For most of them the relevant degree of freedom is the electronic spin of the transition metal ions that form the core of the molecule. When the exchange coupling among metal ions of the same core is the leading interaction, a total spin (superspin) can be defined for the molecule while an energy barrier arises from the magnetic anisotropy.
| Quantum effects at macroscopic scale |
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S. Carretta, P. Santini, G. Amoretti, M. Affronte, A. Ghirri, I. Sheikin, S. Piligkos, G. Timco, and R. E. P. Winpenny, "Topology and spin dynamics in magnetic molecules", Phys. Rev. B 72, 060403(R) (2005). |
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| Observation of Long Range Ordering in lattice of high spin systems |
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M. Affronte, J.C. Lasjaunias, W. Wernstorfer, R. Sessoli, D. Gatteschi, S.L. Health, A. Fort, and A. Rettori, “Magnetic Ordering in a High-Spin Fe19 Magnetic Nanomagnet”, Phys. Rev. B 66, 064408 (2002). |
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| Magnetocaloric effect |
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M. Affronte, A. Ghirri, S. Carretta, G. Amoretti, S. Piligkos, G.A. Timko, and R.E.P. Winpenny, “Engineering Molecular Rings for Magnetocaloric effect”, Appl. Phys. Lett. 84, 3468 (2004).
M. Evangelisti, A. Candini, A. Ghirri, M. Affronte, E. K. Brechin, and E. J. L. McInnes, “Spin-enhanced magnetocaloric effect in molecular nanomagnets”, Appl. Phys. Lett. 87, 072504 (2005). |
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| This CNR team is member of the European Institute of Molecular Magnetism |
FROM QUANTUM EFFECTS TO QUANTUM COMPUTATION WITH MOLECUAR NANOMAGNETS.
Intro. Molecular nanomagnets (MNs) represent a variety of spin clusters, where the physical properties are widely tunable by chemical synthesis and the electron spins are protected degrees of freedom. They thus represent an attractive playground for investigating quantum phenomena – such as entanglement and coherence – and implementing quantum computation.
Project. Our group coordinated the EU FP7 FET Open project MolSpinQIP
Highlights
Quantum computation and quantum simulation. We have developed schemes for implementing quantum computation and simulation, based on the use of low-spin MNs as spin-cluster qubits. Heterometallic wheels with antiferromagnetic coupling between neighbouring spins represent effective two-level systems, with specific excited levels that can be exploited within the manipulation in order to controllably switch the coupling between the qubits. Schemes based on global (i.e. spatially homogeneous) magnetic field pulses have also been developed. The possibility of exploiting auxiliary levels within the MN for effectively switching the qubit-qubit coupling can also be exploited for simulating a large class of quantum systems with translational invariance.
Spin-electric coupling. Given the spatial and temporal resolutions required for coherently and selectively manipulating molecular qubits, electric fields might be preferable to magnetic ones. We have thus identified a class of molecules (namely antiferromagnetic spin triangles with Dzyaloshinskii-Moriya interaction) where pulsed electric fields can induce transitions between states of opposite spin chirality. We have identified the symmetry properties that make such spin-electric coupling possible, described the underlying physical mechanism in terms of an Hubbard model, and pointed out possible fingerprints in different experimental techniques.
Quantum entanglement. We have provided the first demonstration of equilibrium-state entanglement between nanomagnets. This has required an engineering of the coupling between two molecular spin cluster qubits at the chemical level, and a detailed characterization of the system and of its Hamiltonian. The intermolecular entanglement has been experimentally proven by using the magnetic susceptibility as an entanglement witness, and quantified by the calculation of concurrence within an effective two-qubit picture, based on the underlying microscopic model.
Hyperfine-induced decoherence. At low temperatures, the electron spin coherence of MNs is mainly limited by the coupling to nuclear spins. In order to simulate this effect, we have developed a microscopic model, that allows to estimate the contributions of the different elements, as well as the effect of chemical substitutions. Decoherence of entanglement (Bell states) between spin-cluster qubits has also been investigated in existing ring dimers. Decoherence of singlet-triplet superpositions in the same system differs both quantitatively (longer timescales) and qualitatively (relevant nuclei and physical processes) from that of the Bell states.
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Fig 1. (a) Spin (Cu3) triangle exposed to an electric field created by, e.g., an STM-tip. The exchange couplings, represented by the thickness of Cu-Cu bonds, are equal (light triangle). A finite E affects the (super-) exchange coupling in a directional way (dark triangle). (b),(c) Low-energy S =1/2 states of Cu in a magnetic field B, with Dzyaloshinskii-Moriya interaction. Red and blue lines represent the states with chirality Cz=±1. If B is along z (b), the transitions induced by E (thin arrows) flip chirality, while conserving Sz; for tilted B (c), these transitions also result in a change of spin orientation (thick arrows).
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Fig 2. (a) Temperature dependence of the measured (triangles) and simulated (solid lines) dc susceptibility components for the ring dimer. Χ⊥ (red) is the component perpendicular to the largest surface of the crystal. Χ|| refers to the directions parallel to the crystal plane; rotation of magnetic field within this plane does not evidence changes in the magnetic response. The average (Χ⊥/g⊥² + 2Χ||/ g||²)T/3 identify the temperature range where the two rings are entangled (shaded area).
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Publications
Molecular Spins for Quantum Information Technologies
F. Troiani and M. Affronte
Chemical Society Reviews 40, 3119-3129 (2011).
Proposal for Quantum Gates in Permanently Coupled Antiferromagnetic Spin Rings without Need of Local Fields
F. Troiani, M. Affronte, S. Carretta, P. Santini, and G. Amoretti
Phys. Rev. Lett. 94, 190501 (2005).
Molecular nanomagnets as quantum simulators
P. Santini, S. Carretta, F. Troiani, and G. Amoretti
Phys. Rev. Lett. 107, 230502 (2011).
Spin-Electric Coupling in Molecular Magnets
M. Trif, F. Troiani, D. Stepanenko, and D. Loss
Phys Rev Lett 101, 217201 (2008).
Spin electric effects in molecular antiferromagnets
M. Trif, F. Troiani, D. Stepanenko, and D. Loss
Phys. Rev. B 82, 045429 (2010).
Entanglement in Supramolecular Spin Systems of Two Weakly Coupled Antiferromagnetic Rings (Purple-Cr7Ni)
A. Candini, G. Lorusso, F. Troiani, A. Ghirri, S. Carretta, P. Santini, G. Amoretti, C. Muryn, F. Tuna, G. Timco, E. J. L. McInnes, R. E. P. Winpenny, W. Wernsdorfer, and M. Affronte
Phys Rev Lett 104, 037203 (2010).
Engineering the coupling between molecular spin qubits by coordination chemistry
G. A. Timco, S. Carretta, F. Troiani, F. Tuna, R. J. Pritchard, C. A. Muryn, E. J. L. McInnes, A. Ghirri, A. Candini, P. Santini, G. Amoretti, M. Affronte, and R. E. P. Winpenny
Nature Nanotech 4, 173 (2009).
Decoherence induced by hyperfine interactions with nuclear spins in antiferromagnetic molecular rings
F. Troiani, V. Bellini, and M. Affronte
Phys. Rev. B 77, 054428 (2008).
Decoherence of intermolecular entanglement in exchange-coupled nanomagnets
A. Szallas and F. Troiani
Phys. Rev. B 82, 224409 (2010).