Kondo Effect in the Presence of Magnetic Impurities

We measure transport through gold grain quantum dots fabricated using electromigration, with magnetic impurities in the leads. A Kondo interaction is observed between dot and leads, but the presence of magnetic impurities results in a gate-dependent zero-bias conductance peak that is split due to a RKKY interaction between the spin of the dot and the static spins of the impurities. A magnetic field restores the single Kondo peak in the case of an antiferromagnetic RKKY interaction. This system provides a new platform to study Kondo and RKKY interactions in metals at the level of a single spin.

Figure 1

Kondo effect in a gold grain quantum dot without magnetic impurities. (a) Atomic force microscopy picture of the device. A thin (12 nm) Au wire, connected to thick leads, lies on top of an oxidized Al gate (width $1\mu \mathrm{m}$). Inset: After electromigration, a small gap ($\lesssim 1\mathrm{nm}$, too small to resolve) is created containing small grains. (Scale bar corresponds to 100 nm.) (b) Differential conductance as a function of bias ($V_b$) and gate voltage ($V_g$). At $V_g\sim -0.2\mathrm{V}$, four diamond edges (peaks in $G=dI/d{V}_b$) come together in a charge degeneracy point. At the left hand side of the degeneracy point a conductance enhancement around $V_b=0\mathrm{V}$ is observed due to the Kondo effect. The dashed (diamond edges) and dotted (Kondo effect) lines are drawn as guides to the eye. Color scale ranges from $2\mu \mathrm{S}$ (black, dark blue online) to $22\mu \mathrm{S}$ (dark gray, dark red online). $T=2.3\mathrm{K}$. (c) The height of the Kondo peak (at $V_g=-2\mathrm{V}$) decreases as a function of temperature. (d) Fit (red curve online) of the peak height to the expected temperature dependence suggests $T_K\approx 60\mathrm{K}$.

Figure 2

SZBP of a gold grain quantum dot in the presence of magnetic impurities. (a) Top: Schematic of the device. Bottom: Sketch of the expected dependence of the zero-bias conductance $G(0)$ on the scaled RKKY coupling strength ($I/T_k$), at temperatures higher than the triplet Kondo temperature $T_{K-t}$ [26]. $G(0)$ is suppressed both for strong FM and AFM interactions. (b) Differential conductance $G$ as a function of bias ($V_b$) and gate voltage ($V_g$). The split zero-bias anomaly vanishes when an extra electron is added to the quantum dot ($V_g=-1\mathrm{V}$). Dashed lines (diamond edges) are a guide to the eye. Color scale from $28\mu \mathrm{S}$ (black, dark blue online) to $55\mu \mathrm{S}$ (dark gray, dark red online). $T=2.3\mathrm{K}$. (c) Line plots from (a), showing suppression of zero-bias dip near charge degeneracy. (d) $G\equiv dI/d{V}_b$ versus bias for several gate voltages from a different device. Here the Kondo peak can be nearly restored with the gate. The depth of the zero-bias suppression is strongly gate dependent, but the peak separation remains constant.

Figure 3

Temperature dependence of the split zero-bias peak [same device as in Fig. 2b]. (a) $G\equiv dI/d{V}_b$ as a function of bias for different temperatures. (b) Nonmonotonic temperature dependence of the conductance at $V_b=0\mathrm{V}$. Data points are measurements; the line is a guide to the eye.

Figure 4

Magnetic-field dependence of the split zero-bias anomaly. (a) For AFM interaction, the singlet-triplet transition energy (vertical arrow) decreases, then increases with B field. For FM interaction, the triplet-singlet energy always increases with field. (b), (c) Line plots are taken at different values of the external magnetic field, increasing from $B=0\mathrm{T}$ (bottom line) to $B=9\mathrm{T}$ (top line) in steps of 0.9 T. Data taken at $T=250\mathrm{mK}$ (b) Restoration of the Kondo effect at finite field, typical for AFM interaction between two spins. Line plots offset by $1.5\times {10}^{-3}(2e^2/h)$, for clarity. (c) For a FM interaction the peak separation increases linearly with $|B|$. The peak separation at $B=0\mathrm{T}$ is determined by extrapolating from peak positions to zero field (inset) and yields $1.4\pm 0.3\mathrm{meV}$. Line plots offset by $1\times {10}^{-2}(2e^2/h)$.