Verwey transition in single magnetite nanoparticles

Q. Yu, A. Mottaghizadeh, H. Wang, C. Ulysse, A. Zimmers, V. Rebuttini, N. Pinna, and H. Aubin

Phys. Rev. B 90, 075122 – Published 13 August 2014

Abstract

We present a tunnel spectroscopy study of the electronic spectrum of single magnetite ${Fe}_{3} O_{4}$ nanoparticles trapped between nanometer-spaced electrodes. The Verwey transition is clearly identified in the current-voltage characteristics where we find that the transition temperature is electric field dependent. The data show the presence of localized states at high energy, $ɛ \sim 0.6$ eV, which can be attributed to polaron states. At low energy, the density of states (DOS) is suppressed at the approach of the Verwey transition. Below the Verwey transition, a gap, $Δ \sim 300$ meV, is observed in the spectrum. In contrast, no gap is observed in the high temperature phase, implying that electronic transport in this phase is possibly due to polaron hopping with activated mobility.

Received 13 January 2014
Revised 13 June 2014

DOI:https://doi.org/10.1103/PhysRevB.90.075122

Authors & Affiliations

Q. Yu¹, A. Mottaghizadeh¹, H. Wang¹, C. Ulysse², A. Zimmers¹, V. Rebuttini³, N. Pinna³, and H. Aubin^1,*

¹Laboratoire de Physique et d'Etude des Matériaux, UMR 8213, ESPCI-ParisTech-CNRS-UPMC, 10 rue Vauquelin, 75231 Paris, France
²Laboratoire de Photonique et de Nanostructures, CNRS, 91460 Marcoussis, France
³Humboldt-Universität zu Berlin, Institut für Chemie, Brook-Taylor-Strasse 2, 12489 Berlin, Germany

^*Herve.Aubin@espci.fr

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Vol. 90, Iss. 7 — 15 August 2014

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Images

Figure 1
(a) TEM image of ${Fe}_{3} O_{4}$ nanoparticles. (b) Optical microscopy images of circuits. (c) High resolution SEM image, $\times 800 000$ , of a nanoparticle trapped between two electrodes.
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Figure 2
(a) $I V$ curves of a single nanoparticle junction. (b) $d V / d I$ as function of voltage. (c) $d V / d I$ as function of temperature at selected drain voltages. The dashed line shows the Verwey transition temperature $T_{V} \sim 120$ K. (d) Color plot of $d V / d I$ displaying the out-of-equilibrium phase diagram for the Verwey transition.
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Figure 3
(a) Fowler-Nordheim plot of the $I V$ curves shown Fig. 2. Three regimes can be distinguished, see text. (b) Transfer function for a tunnel barrier containing a polaron state at the energy $W_{P} \sim 0.6$ eV. The subpeaks are separated by the phonon energy $ℏ ω_{0} \sim 100$ meV. (c) Transfer function for a tunnel barrier containing a polaron state at the energy $W_{P} \sim 0.6$ eV and a gap $Δ = 300$ meV at the Fermi level. (d) Fowler-Nordheim plot of calculated $I V$ curves at temperatures between $T = 60$ and 300 K with no gap at the Fermi level. (e) Fowler-Nordheim plot of calculated $I V$ curves at temperatures between $T = 60$ and 300 K with a gap $Δ = 300$ meV at the Fermi level.
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Figure 4
Schematic of the junction with no applied bias (left) and applied bias (right). The different energy scales shown are the polaron binding energy $W_{P}$ , the fermi energy $E_{F}$ , the work function of the electrodes $Φ_{Electrode}$ , and the work function of the nanoparticle $Φ_{Nanoparticle}$ .
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Figure 5
(a) $d I / d V$ as function of temperature, from $T \sim 240$ to $\sim 75$ K. (b), (c), (e), and (f) The voltage scale has been replaced by the energy scale $ɛ = e V_{Drain} / 2$ . (b) Zooming shows that $d I / d V$ , at $V_{Drain} = 0$ , remains finite for $T > T_{V}$ , but decreases quickly to zero for $T < T_{V}$ . From these curves, the gap can be estimated to be about $Δ \sim 300$ meV in the insulating phase. (c) Normalized conductance $[d I / d V (T)] / [d I / d V (T = 240 K)]$ . The curves have been shifted for clarity. (d) Normalized conductance at $V_{Drain} = 0$ V as a function of temperature. (e) Arrhenius plot of the normalized conductance at $V_{Drain} = 0$ V. The full circles are the experimental data. The continuous line is a fit that provides the activation energy $E_{A} \sim 75$ meV. The dashed line represents the expected temperature dependence, at temperatures $T < T_{V}$ , of the zero bias conductance for the activation energy $E_{A} \sim 300$ meV. This last value for the activation energy is obtained from the energy spectra in (b). (f) Color plot of the normalized conductance shown in (c). It shows the opening of the gap $Δ \sim 300$ meV at the approach of the Verwey transition. (g) $d I / d V$ measured experimentally at $T \sim 75$ K (blue curve) and calculated (dark green curve) using the polaronic transfer function including a gap $Δ = 300$ meV. (h) $d I / d V$ measured experimentally at $T \sim 240$ K (orange curve) and calculated (dark green curve) using the polaronic transfer function including a gap $Δ = 75$ meV.
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