Andreev transport through single-molecule magnets

F. Pawlicki and I. Weymann

Phys. Rev. B 98, 085411 – Published 7 August 2018

Abstract

The Andreev transport through a large-spin magnetic molecule, such as a single molecular magnet, attached to superconducting and ferromagnetic leads is studied theoretically by means of the real-time diagrammatic technique. It is shown that due to the proximity effect, molecular Andreev bound states form in the system, with energies depending on the intrinsic parameters of the molecule. We study the spin-resolved Andreev current, conductance, and tunnel magnetoresistance in both the linear and nonlinear response regimes and find regions of negative differential conductance, as well as either enhanced or negative tunnel magnetoresistance. The mechanisms leading to those effects are thoroughly discussed. It is also shown that the tunnel magnetoresistance can provide information about particular spin multiplets responsible for the Andreev reflection processes.

Received 26 March 2018

DOI:https://doi.org/10.1103/PhysRevB.98.085411

Physics Subject Headings (PhySH)

Andreev reflection Proximity effect Quantum transport Spintronics

Molecular junctions Molecular magnets

Perturbation theory

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

F. Pawlicki^* and I. Weymann^†

Faculty of Physics, Adam Mickiewicz University, ul. Umultowska 85, 61-614 Poznań, Poland

^*filemon.pawlicki@gmail.com
^†weymann@amu.edu.pl

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Issue

Vol. 98, Iss. 8 — 15 August 2018

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Images

Figure 1
Schematic of the system under consideration. The magnetic molecule is attached to an $s$ -wave superconductor with coupling strength $Γ_{S}$ and to ferromagnetic leads with spin-dependent couplings, $Γ_{L}^{σ}$ and $Γ_{R}^{σ}$ , respectively. Transport occurs due to tunneling through the lowest unoccupied molecular orbital (LUMO) of the molecule, which is exchange-coupled (with exchange interaction $J$ ) to the magnetic core spin $S$ of the molecule. The magnetizations of the ferromagnetic leads can be either parallel or antiparallel. The case of infinite superconducting gap $Δ \to \infty$ is considered. The chemical potential of the superconductor is set to zero.
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Figure 2
The Andreev current (first row) and the associated Andreev differential conductance (second row) as a function of the bias voltage $e V$ and the LUMO level detuning $δ = 2 ɛ + U$ in the case of (a), (b) $J = 0$ , (c), (d) ferromagnetic exchange coupling ( $J > 0$ ) between the LUMO level and the molecule's core spin, and (e), (f) the antiferromagnetic exchange interaction ( $J < 0$ ). The leads are assumed to be nonmagnetic, $p = 0$ . The dashed (dotted) lines indicate the energies of Andreev bound states, $E$ ( $E_{exc}$ ), derived analytically; see the main text for details. The parameters are $T = 0.03$ , $Γ_{S} = 0.4$ , $Γ = 0.01$ , $| J | = 0.2$ , $D = 0.05$ in units of $U \equiv 1$ , while the spin of the molecule is $S = 2$ . The current is plotted in units of $I_{0} = e Γ / ℏ$ .
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Figure 3
The Andreev differential conductance in (a) the parallel and (b) antiparallel magnetic configuration as well as (c) the tunnel magnetoresistance plotted as a function of bias voltage $e V$ and the molecule's level detuning $δ$ in the case of ferromagnetic exchange interaction with $J / U = 0.2$ . The parameters are the same as in Fig. 2 with $p = 0.5$ . The dashed and dotted lines indicate the positions of the corresponding Andreev bound states derived in Sec. 2b and given by Eqs. (13) and (14).
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Figure 4
The bias voltage dependence of (a), (d) the Andreev current, (b), (e) the differential conductance in the parallel and antiparallel configuration, as well as (c), (f) the tunnel magnetoresistance calculated for ferromagnetic exchange interaction. The left column corresponds to $δ = 0$ , while the right column shows the results for $δ / U = 2$ . The inset in (d) presents the expectation values of the spin-resolved LUMO occupation for the parallel configuration and for bias voltages where the negative differential conductance develops. The other parameters are the same as in Fig. 3.
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Figure 5
The Andreev differential conductance in (a) the parallel and (b) antiparallel magnetic configuration and (c) the TMR calculated as a function of $e V$ and $δ$ in the case of antiferromagnetic exchange interaction. The parameters are the same as in Fig. 3 with $J / U = - 0.2$ . The dashed and dotted lines indicate the positions of the corresponding Andreev bound states derived in Sec. 2b and given by Eqs. (17) and (18).
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Figure 6
(a), (d) The Andreev current, (b), (e) differential conductance, and (c), (f) TMR plotted as a function of bias voltage for $δ = 0$ (left column) and $δ / U = 2$ (right column). The inset in (d) shows the spin-resolved LUMO occupations for the parallel magnetic configuration and for bias voltages where the negative differential conductance develops. The parameters are the same as in Fig. 5.
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