Electric-dipole-induced spin resonance in a lateral double quantum dot incorporating two single-domain nanomagnets

F. Forster, M. Mühlbacher, D. Schuh, W. Wegscheider, and S. Ludwig

Phys. Rev. B 91, 195417 – Published 14 May 2015

Abstract

On-chip magnets can be used to implement relatively large local magnetic field gradients in nanoelectronic circuits. Such field gradients provide possibilities for all-electrical control of electron spin qubits where important coupling constants depend crucially on the detailed field distribution. We present a double quantum dot (QD) hybrid device laterally defined in a GaAs/AlGaAs heterostructure which incorporates two single-domain nanomagnets. They have appreciably different coercive fields which allows us to realize four distinct configurations of the local inhomogeneous field distribution. We perform dc transport spectroscopy in the Pauli-spin blockade regime as well as electric-dipole-induced spin resonance (EDSR) measurements to explore our hybrid nanodevice. Characterizing the two nanomagnets we find excellent agreement with numerical simulations. By comparing the EDSR measurements with a second double QD incorporating just one nanomagnet we reveal an important advantage of having one magnet per QD: It facilitates strong field gradients in each QD and allows us to control the electron spins individually for instance in an EDSR experiment. With just one single-domain nanomagnet and common QD geometries EDSR can likely be performed only in one QD.

Received 6 March 2015
Revised 13 April 2015

DOI:https://doi.org/10.1103/PhysRevB.91.195417

Authors & Affiliations

F. Forster¹, M. Mühlbacher¹, D. Schuh², W. Wegscheider^2,3, and S. Ludwig^1,*

¹Center for NanoScience & Fakultät für Physik, LMU-Munich, 80539 München, Germany
²Fakultät für Physik, Universität Regensburg, 93040 Regensburg, Germany
³Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland

^*Present address: Paul-Drude-Institut für Festkörperelektronik, Hausvogteiplatz 5–7, 10117 Berlin, Germany; ludwig@pdi-berlin.de

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Vol. 91, Iss. 19 — 15 May 2015

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Images

Figure 1
Sample layout: (a) Scanning electron microscope image of the wafer surface. The GaAs surface is dark gray, gold gates are shown in yellow, magnetic cobalt gates in blue. Both magnets are $≃ 2 μ m$ long and $≃ 60$ nm high, the left one (L) is $≃ 100$ nm and the right one (R) $≃ 230$ nm wide. Red filled circles indicate possible QD positions in the two-dimensional electron system 85 nm beneath the surface; actual positions depend on gate voltages and disorder potential. The voltages applied to gates R and $\sim$ are radio frequency modulated for EDSR measurements. (b) Magnetic force microscopy measurement of the magnets before the gold gates were processed; height profile in the upper panel and out-of-plane magnetization in the lower panel indicating single-domain magnetization of both magnets.
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Figure 2
(a) Sketch showing the relevant two-electron levels of the double QD in Pauli-spin blockade and the lead chemical potentials ( $μ_{R} - μ_{L} = 1$ meV). All horizontal lines depict chemical potentials, vertical lines indicate tunnel barriers, blue areas correspond to occupied states of the degenerate Fermi liquid in the leads. (b) Corresponding charge stability diagram at $B_{ext} = 0$ , presenting the current through the double QD. The numbers of electrons charging the left, right dot in stable areas of the stability diagram are indicated in parentheses. For our EDSR measurements the system was pulsed between the two red dots; details in main text. (c) Current at $ε ≃ 100 μ eV$ as function of $B_{ext}$ , which was swept at a rate of 30 mT/min. Arrows indicate the sweep directions. (d) Numerically calculated eigenenergies of the $(1, 1)$ states of the system Hamiltonian (1) as a function of $B_{ext}$ . $| ψ_{1, 4} 〉$ are almost identical to $T_{\pm}$ and $| ψ_{2, 3} 〉$ are superpositions of $T_{0}$ and $S_{11}$ . For the used parameters, $ε = 100 μ eV$ and $t_{c} = 4 μ eV$ , the (2,0) state has a much lower energy. Vertical steps at $B_{ext} ≃ 50, 80$ mT indicate discontinuities of $B_{nm}$ caused by the numerically included switching of the nanomagnets. (e) Overlap of the $(1, 1)$ eigenstates shown in (d) with the $S_{20}$ state (which would be zero for the $T_{11}$ states in a homogeneous field): all four states in the inset. The main panel is a magnified view of the gray area. It contains the two states with the smallest overlap, the current limiting bottleneck states (almost $T_{\pm}$ ). (f) Sketch of the four current resonances belonging to the four different magnets' configurations. The red and blue line resemble the switching behavior of the actual current in (c) (arrows indicate sweep directions).
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Figure 3
(a) EDSR measurement scheme, from left to right: initialization in Pauli-spin blockade $\to$ separation of the QD states from the leads (Coulomb blockade) $\to$ EDSR manipulation by rf-modulation of gate voltage $\to$ read-out ( $I > 0$ for EDSR resonance) and re-initialization. (b) Current $I (B_{ext}, f)$ through the DQD (bottom panel) and position of current maxima at EDSR resonance (top panel) while driving with the pulse sequence shown in (a). (c) Same as (b) but high resolution measurement near the coercive field of the left magnet $B_{c}^{L} \sim 80$ mT, where the resonance line forms a step.
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Figure 4
Coexistence of two EDSR resonances: (a) $I (B_{ext}, f)$ through the DQD as in Figs. 3 and 3 but for a different gate voltage configuration (configuration II). (b) Position of the current maxima at EDSR resonances in (a). Lines indicate fits with Eq. (2). (c) Typical current trace at constant $B_{ext}$ along dashed line in (a).
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Figure 5
OOMMF simulations of $B_{nm}$ [24]. Magnetic field component $B_{nm} |_{z}$ along $B_{ext}$ ( $z$ axis) for (a) parallel and (b) antiparallel magnetization of the two nanomagnets. $B_{nm} |_{z}$ is relevant for the EDSR resonance condition, Eq. (2). (c) and (d) Absolute value of the gradient of the perpendicular component $B_{nm}^{⊥}$ within the plane of the 2DES; $B_{nm} = B_{nm} |_{z} + B_{nm}^{⊥}$ . The EDSR signal strength scales with $| \nabla_{x, z} B_{nm}^{⊥} |$ . Colored circles in (a)–(d): Approximate QD center positions for the two different gate voltage tunings. Arrows indicate nanomagnets polarization directions.
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Figure 6
Double quantum dot with one instead of two single-domain nanomagnets reproduced from Ref. [27]. (a) Scanning electron microscope image; color coding analog to Fig. 1. (b) OOMMF simulations of the perpendicular field gradient along $B_{ext}$ aligned with the $z$ axis. This is also the main direction of the rf electron displacement. The lower panel is a horizontal cross section of the color plot at $x = 100$ nm. (c) $I (B_{ext}, f)$ through the DQD as in Figs. 3 and 4 showing a single EDSR resonance at a modulation amplitude of $≃ 15$ mV. (d) Multiple EDSR resonances at about twice the modulation power.
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