Spin dynamics of molecular nanomagnets unravelled at atomic scale by four-dimensional inelastic neutron scattering

Journal name:
Nature Physics
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Molecular nanomagnets are among the first examples of finite-size spin systems and have been test beds for addressing several phenomena in quantum dynamics. In fact, for short-enough timescales the spin wavefunctions evolve coherently according to an appropriate spin Hamiltonian, which can be engineered to meet specific requirements. Unfortunately, so far it has been impossible to determine these spin dynamics directly. Here we show that recently developed instrumentation yields the four-dimensional inelastic-neutron scattering function in vast portions of reciprocal space and enables the spin dynamics to be determined directly. We use the Cr8 antiferromagnetic ring as a benchmark to demonstrate the potential of this approach which allows us, for example, to examine how quantum fluctuations propagate along the ring or to test the degree of validity of the Néel-vector-tunnelling framework.

At a glance


  1. Magnetic energy spectrum of Cr8 and zero-temperature INS transitions.
    Figure 1: Magnetic energy spectrum of Cr8 and zero-temperature INS transitions.

    a, Low-lying energy multiplets as a function of their total spin for the isotropic exchange Hamiltonian of Cr8 (equation (1) with D=0). The arrows indicate the three transitions seen by INS at zero temperature. All other transitions have negligible cross-section. The blue and red symbols indicate L- and E-band states, respectively; grey symbols indicate states not belonging to these bands. The inset shows the core of Cr8 (C80Cr8F8D144O32; green, Cr; yellow, F; red, O; dark grey, C; D omitted). b, Measured low-T INS spectra for a powder Cr8 sample, with an incident neutron wavelength λ=3.1Å. The labels indicate the three peaks corresponding to the transitions reported in a. The p=1 transition is partially hidden by the elastic signal. The inset reports higher-resolution measurements with λ=5Å showing the p=1 transition split by magnetic anisotropy.

  2. Constant-energy plots of the neutron scattering intensity for the p[thinsp]=[thinsp]1excitation.
    Figure 2: Constant-energy plots of the neutron scattering intensity for the p=1excitation.

    Cuts are shown in the QxQy, QzQy and QzQx planes, where the primed reference frame is defined in Supplementary Fig. S1. The measurement was carried out with a 5Å incident neutron wavelength, and a sample temperature of 1.5K.

  3. Constant-energy plots of the neutron scattering intensity for all of the possible magnetic excitations in Cr8 at 1.5[thinsp]K.
    Figure 3: Constant-energy plots of the neutron scattering intensity for all of the possible magnetic excitations in Cr8 at 1.5K.

    The maps show the dependency of intensity on two wave-vector components QxQy lying in the ring’s xy plane, integrated over the full Qz range. a, Data from transition p=1, measured with a 5.0Å incident neutron wavelength. b,c, Data from transitions p=2 (b) and p=3 (c), measured with a 3.1Å incident neutron wavelength. df, Fits to equation (2) for excitations 1 (d), 2 (e) and 3 (f). One-dimensional cuts along specific directions in the QxQy plane are shown in Supplementary Fig. S2.

  4. Propagation of a local disturbance deduced from the present INS spectra and in a NVT regime.
    Figure 4: Propagation of a local disturbance deduced from the present INS spectra and in a NVT regime.

    The frames show the time evolution of left fencesz(i)right fence in an eight-spin ring after a delta-pulse perturbation −bsz(1)δ(t) applied on the red (d=1) spin. Note that as the ground state is a singlet, left fencesz(i)right fence=0 just before t=0 (frame not shown). a, Dynamics deduced from equations (4) and (5) using the present experimental Fourier coefficients (Tables 1 and 2) and frequencies. The delay between two frames is 1.85×10−13s, that is, 1/32 of the longest oscillation period 2πplanck/Δ, with Δ=0.7meV. b, Results for a hypothetical ring in a NVT regime, that is, D/J=−0.2 corresponding to a tunnel action . The delay between two frames is 1/32 of the tunnelling oscillation period 2πplanck/Δ, with Δ being the tunnelling gap.


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Author information


  1. Institut Laue-Langevin, BP 156, 6 rue Jules Horowitz, 38042 Grenoble Cedex 9, France

    • Michael L. Baker,
    • Jacques Ollivier &
    • Hannu Mutka
  2. School of Chemistry and Photon Institute, The University of Manchester, Manchester M13 9PL, UK

    • Michael L. Baker,
    • Grigore A. Timco,
    • Eric J. L. McInnes &
    • Richard E. P. Winpenny
  3. ISIS facility, Rutherford Appleton Laboratory, Didcot OX11 0QX, UK

    • Tatiana Guidi
  4. Dipartimento di Fisica e Scienze della Terra, Università di Parma, I-43124 Parma, Italy

    • Stefano Carretta,
    • Giuseppe Amoretti &
    • Paolo Santini
  5. Department of Chemistry and Biochemistry, University of Bern, 3000 Bern, Switzerland

    • Hans U. Güdel


M.L.B., T.G., S.C., J.O., H.M., H.U.G. and G.A. performed the experiment on a crystal synthesized by G.A.T. after discussion with E.J.L.M. and R.E.P.W. Data treatment was carried out by M.L.B., T.G., J.O. and H.M., and data simulations and fits were performed by M.L.B., T.G. and S.C.; S.C., G.A. and P.S. developed the idea to use four-dimensional INS measurements for a direct extraction of dynamical correlation functions of molecular nanomagnets. S.C., G.A. and P.S. also performed theoretical calculations and wrote the manuscript with input from all co-authors.

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