Landau-Zener tunneling of a single Tb${}^{3+}$ magnetic moment allowing the electronic read-out of a nuclear spin

Landau-Zener tunneling of a single Tb $^{3 +}$ magnetic moment allowing the electronic read-out of a nuclear spin

M. Urdampilleta, S. Klyatskaya, M. Ruben, and W. Wernsdorfer

Phys. Rev. B 87, 195412 – Published 9 May 2013

Abstract

A multiterminal device based on a carbon nanotube quantum dot was used at very low temperature to probe a single electronic and nuclear spin embedded in a bis-(phthalocyaninato) terbium (III) complex (TbPc $_{2}$ ). A spin-valve signature with large conductance jumps was found when two molecules were strongly coupled to the nanotube. The application of a transverse field separated the magnetic signal of both molecules and enabled single-shot read-out of the terbium nuclear spin. The Landau-Zener (LZ) quantum tunneling probability was studied as a function of field sweep rate, establishing a good agreement with the LZ equation and yielding the tunnel splitting $Δ$ . It was found that $Δ$ increased linearly as a function of the transverse field. These studies are an essential prerequisite for the coherent manipulation of a single nuclear spin in TbPc $_{2}$ .

Received 30 October 2012

DOI:https://doi.org/10.1103/PhysRevB.87.195412

Authors & Affiliations

M. Urdampilleta¹, S. Klyatskaya², M. Ruben^2,3, and W. Wernsdorfer¹

¹Institut Néel, CNRS et Université Joseph Fourier, BP 166, F-38042 Grenoble Cedex 9, France
²Institute of Nanotechnology (INT), Karlsruhe Institute of Technology (KIT), 76344 Eggenstein-Leopoldshafen, Germany
³Institut de Physique et Chimie des Matériaux de Strasbourg (IPCMS), CNRS-Université de Strasbourg, 67034 Strasbourg, France

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Vol. 87, Iss. 19 — 15 May 2013

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Images

Figure 1
(a) Zeeman diagram of the ground state $J = 6$ . $| J = 6, J_{z} = \pm 6 〉$ is the low lying ground state doublet, which is separated by about 600 K from the first excited state $| J = 6, J_{z} = \pm 5 〉$ . The two mechanisms for moment reversal are quantum tunneling of magnetization (QTM) occurring at zero magnetic field and the direct transition (DT) occurring at finite magnetic field. (b) Structure of the TbPc $_{2}$ complex. The black, blue, white, and purple atoms correspond to C, N, H, and Tb, respectively. The magnetic easy axis and the hard plane are respectively orthogonal and parallel to the phthalocyanines. (c) Zoom on the avoided level crossing label by QTM in (a). $Δ$ is the tunnel splitting, and $P_{QTM}$ is the tunnel probability. (d) Zeeman diagram of the ground doublet $| J_{z} = \pm 6 〉$ split by the strong hyperfine interaction of Tb. The color code illustrates the different nuclear spin states and the circled intersections are avoided level crossings.Reuse & Permissions
Figure 2
Stability diagram of the device shown in the inset. The red lines are degeneracy points in the Coulomb blockade regime. Coupling between the leads and the quantum dot can be tuned by moving along one of these lines, by means of the back gate and side gate voltages ( $V_{bg}$ and $V_{sg}$ , respectively). Inset: scanning electron micrograph of the studied device. The green electrodes correspond to the source and drain, and the blue electrode corresponds to the side gate.Reuse & Permissions
Figure 3
(a) Magnetoconductance recorded at a sweep rate of 50 mTs $^{- 1}$ . The blue curve corresponds to the measurement made from $- 0.35$ T up to $+ 0.35$ T, and the red curve corresponds to the one made from $+ 0.35$ T down to $- 0.35$ T. Each of the sharp changes in conductance corresponds to the signature of a single TbPc $_{2}$ . The reversal, which takes place under a small magnetic field, is due to QTM, whereas that which takes place under a higher magnetic field is due to DT. (b) Magnetoconductance recorded at a sweep rate of 20 mTs $^{- 1}$ ; the color code is the same as for (a). The sharp conductance changes occur close to zero magnetic field and are the consequence of both molecules experiencing QTM.Reuse & Permissions
Figure 4
(a) Schematic of the relative orientation of the two molecules on the nanotube. We define the longitudinal field $H_{∥}$ and transverse field $H_{⊥}$ with respect to the molecule B which has its easy axis perpendicular to the nanotube axis [see Fig. 4a], and $θ$ the angle between the easy axis of B and A. (b) Anisotropy of the direct transition. The difference between the trace (from $- 1$ T to $+ 1$ T) and the retrace (from $+ 1$ T to $- 1$ T) is recorded as a function of angular orientation. The locus of the direct transition reversal is indicated by dashed lines. It is important to note that the reversal close to the $90^{\circ}$ orientation cannot occur because of the field limitations imposed by the magnetic field coils in the experimental setup.Reuse & Permissions
Figure 5
(a) Magnetoconductance curves recorded under a $0.35$ T transverse field, at a 100 mTs $^{- 1}$ sweep rate. The relative QTM position for molecules A and B are clearly split; the angle between their easy axes is then estimated around 15 $^{\circ}$ . (b) Histogram of the QTM position of molecule B, for 3500 consecutive traces recorded under the same conditions as those applied in (a). The position of these peaks corresponds to the avoided level crossing shown on the Zeeman diagram of the ground doublet $J_{z} = \pm 6$ split by the hyperfine coupling with the nuclear spin $I = 3 / 2$ .Reuse & Permissions
Figure 6
QTM probability as a function of the inverse of the sweep rate, for different transverse fields. The experimental data are fitted by exponential curves, in accordance with Eq. (3). The inset indicates the variation of tunnel splitting as a function of the transverse field; the red line is a guide for the eye.Reuse & Permissions

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