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Landau-Zener Transition in a Continuously Measured Single-Molecule Spin Transistor

F. Troiani, C. Godfrin, S. Thiele, F. Balestro, W. Wernsdorfer, S. Klyatskaya, M. Ruben, and M. Affronte
Phys. Rev. Lett. 118, 257701 – Published 23 June 2017
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  • Introduction.—
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    Abstract

    We monitor the Landau-Zener dynamics of a single-ion magnet inserted into a spin-transistor geometry. For increasing field-sweep rates, the spin reversal probability shows increasing deviations from that of a closed system. In the low-conductance limit, such deviations are shown to result from a dephasing process. In particular, the observed behaviors are successfully simulated by means of an adiabatic master equation, with time averaged dephasing (Lindblad) operators. The time average is tentatively interpreted in terms of the finite time resolution of the continuous measurement.

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    • Received 11 January 2017

    DOI:https://doi.org/10.1103/PhysRevLett.118.257701

    © 2017 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Molecular magnetismQuantum coherence & coherence measuresQuantum measurementsSpintronicsTransport phenomena
    1. Physical Systems
    Molecular junctions
    General PhysicsCondensed Matter, Materials & Applied Physics

    Authors & Affiliations

    F. Troiani1, C. Godfrin2, S. Thiele2, F. Balestro2, W. Wernsdorfer2,3, S. Klyatskaya3, M. Ruben3, and M. Affronte1,4

    • 1Centro S3, Istituto Nanoscienze-CNR, via G. Campi 213/A, I-41125 Modena, Italy
    • 2Institut L. Néel, CNRS, Av des Martyrs 25, F-38000 Grenoble, France
    • 3Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), D-76344 Eggenstein Leopoldshafen, Germany
    • 4Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, via G. Campi 213/a, I-41125 Modena, Italy

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    Issue

    Vol. 118, Iss. 25 — 23 June 2017

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    Images

    • Figure 1
      Figure 1

      (a) Artistic view of the molecular spin transistor with the TbPc2 molecule embedded between the gold electrodes. (b) Schematics of the molecular system: one of the phthalocyanine ligands acts as a read-out quantum dot, where the spins of the localized electrons are exchange coupled to the total angular momentum (J=6) of the Tb3+ ion, whose MJ=±6 states define an effective two-level system. (c) The system is prepared in the initial ground state |↑⟩, evolves under the effect of a magnetic field Bz that depends linearly on time, and ends up in the final ground state |↓⟩ with probability Pgs. (d) If the system is prepared in the initial excited state, the spin reversal leads to the final excited state with probability Pes.

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    • Figure 2
      Figure 2

      (a) Measured values of the spin-reversal probabilities Pgs (black squares) and Pes (red), obtained after preparing the spin in the initial ground and exited states, respectively (the solid lines are drawn as a guide for the eye). This set of probabilities has been obtained with a conductance of g=0.245  μS. (b) Difference between Pgs and Pes as a function of the conductance, for different values of the field-sweep rate (dB/dt). The solid lines correspond to linear fits of the experimental results (symbols).

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    • Figure 3
      Figure 3

      (a) Computed spin-reversal probability Pc as a function of the inverse field-sweep rate, for different values of the averaging time τav, normalized to τΔ. For a given Δ, the quantity reported in the horizontal axis can also be identified with the time that the spin takes to go through the anticrossing, being τac/τΔ=(Δ2/ℏgJμB)(dB/dt)−1. For all the solid curves, the dephasing time is τd=τΔ, while the dotted curve corresponds to the coherent case (τd=∞). (b) Dependence of Pc on the inverse sweeping rate for a fixed averaging time, τav=20τΔ, and for different values of the dephasing time τd.

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    • Figure 4
      Figure 4

      Simulated values of the spin-reversal probability as a function of the inverse sweeping rate, for different values of the dephasing time τd and of the averaging time τav=20τd. The reported values of the inverse sweeping rate and of the dephasing time correspond to a zero-field gap Δ≃3.4  μK or, equivalently, to a time scale τΔ≃2.25  μs.

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