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Magnetic-field-modulated Kondo effect in a single-magnetic-ion molecule

Javier I. Romero, E. Vernek, G. B. Martins, and E. R. Mucciolo
Phys. Rev. B 90, 195417 – Published 13 November 2014
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  • INTRODUCTION
  • SIM MODEL AND BERRY-PHASE MODULATION OF…
  • BERRY-PHASE MODULATION OF ELECTRONIC…
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
    • References

    Abstract

    We study numerically the low-temperature electronic transport properties of a single-ion magnet with uniaxial and transverse spin anisotropies. We find clear signatures of a Kondo effect caused by the presence of a transverse (zero-field) anisotropy in the molecule. This Kondo effect has an SU(2) pseudospin character, associated with a doublet ground state of the isolated molecule, which results from the transverse anisotropy. Upon applying a transverse magnetic field to the single-ion magnet, we observe oscillations of the Kondo effect due to the presence of diabolical points (degeneracies) of the energy spectrum of the molecule caused by geometrical phase interference effects, similar to those observed in the quantum tunneling of multi-ion molecular nanomagnets. The field-induced lifting of the ground-state degeneracy competes with the interference modulation, resulting in some cases in a suppression of the Kondo peak.

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    • Received 14 April 2014
    • Revised 30 October 2014

    DOI:https://doi.org/10.1103/PhysRevB.90.195417

    ©2014 American Physical Society

    Authors & Affiliations

    Javier I. Romero1, E. Vernek2,3, G. B. Martins4, and E. R. Mucciolo1

    • 1Department of Physics, University of Central Florida, Orlando, Florida 32816-2385, USA
    • 2Instituto de Física, Universidade Federal de Uberlândia, Uberlândia, Minas Gerais 38400-902, Brazil
    • 3Instituto de Física de São Carlos, Universidade de São Paulo, São Carlos, São Paulo 13560-970, Brazil
    • 4Department of Physics, Oakland University, Rochester, Michigan 48309, USA

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    Issue

    Vol. 90, Iss. 19 — 15 November 2014

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    Images

    • Figure 1
      Figure 1

      (a) Schematic representation of the SIM with cotunneling processes that result in the pseudospin SU(2) Kondo effect: spin-down electron tunnels into predominantly |3/2〉 SIM ground state (left), resulting in a |−1〉+|1〉 virtual state (center). The subsequent tunneling out of a spin-up electron takes the SIM to a predominantly |−3/2〉 SIM ground state (degenerate with the initial |3/2〉 state). A coherent sequence of these processes screens the pseudospin doublet ground state. (b) An equivalent schematic representation in the pseudospin picture, where the gray rectangle indicates the tunneling barrier between SIM states with opposite Sz values.

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    • Figure 2
      Figure 2

      Energy eigenvalues Ei and splitting (Δ=E1−E0) for the bare molecule (not connected to the leads), where Ei is the ith eigenvalue. The interaction parameters (in units of D) are Vg=−0.25, U=0.5, JHund=5×10−2, B1=4.6×10−3, and B2=4.6×10−4. (a) Eigenvalues of the double occupied (or empty) Q=±1, S=1 charge-spin sector vs hx/D. (b) Eigenvalues of the neutral Q=0, S=3/2 charge-spin sector vs hx/D. (c) Energy splitting Δ for the Q=±1, S=1 [(black) circles] and Q=0, S=3/2 [(red) squares] charge-spin sectors.

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    • Figure 3
      Figure 3

      LDOS vs ω results for (a) hx/D=0, B2/D=0 [(black) squares] and B2/D=4.6×10−4 [(red) circles]. In (b), (c), and (d) 0.1≤hx/(10−3×D)≤3.5 and B2/D=4.6×10−4. The other interaction parameters are the same as in Fig. 2, and Γ=9×10−2D.

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    • Figure 4
      Figure 4

      Kondo temperature as a function of (a) the exchange coupling JHund (for B2/D=4.6×10−4) and (b) the transverse anisotropy parameter B2 (for JHund/D=5×10−2). Other parameter values are Vg/D=−0.25, U/D=0.5, B1/D=4.6×10−3, and hx=0. TK is obtained from the LDOS data as the full width at half maximum of the ω=0 peak.

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    • Figure 5
      Figure 5

      (a) Conductance through the molecule vs the transverse magnetic field hx. (b) Entropy contribution of the SIM vs temperature.

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