Kondo screening regimes of a quantum dot with a single Mn ion

We study the Kondo and transport properties of a quantum dot with a single magnetic Mn ion connected to metallic leads. By employing a numerical renormalization group technique we show that depending on the value of ferromagnetic coupling strength between the local electronic spin and the magnetic moment of the Mn, two distinct Kondo regimes exist. In the weak-coupling limit, the system can be found in a completely screened Kondo state describing a local magnetic moment decoupled from the rest of the system. In contrast, in the strong-coupling regime the quantum dot spin and the local magnetic moment form a single large-spin entity partially Kondo screened. A crossover between these two regimes can be suitably tuned by varying the tunnel coupling between the quantum dot and the leads. The model investigated here is also suitable to study magnetic molecules adsorbed on a metallic surface. The rich phenomenology of these systems is reflected in the conductance across the system.

Figure 1

Schematic representation of a single-level quantum dot with a Mn ion. The large arrow ($\mathrm{M⃗}$) represents the spin of the Mn${}^{2+}$ while the small arrow ($\mathrm{s⃗}$) represents the spin of an electron in the dot. The matrix element $V$ allows for electrons to hop in and off the quantum dot.

Figure 2

Entropy (a), magnetic moment (b), and spin-spin correlation (c) as function of temperature for various values of $T_K/\left|J\right|$, keeping $J=-2.0\times {10}^{-5}$. In the dashed (green) curve we use $J=0$ and $T_K=2.41\times {10}^{-4}$ and serves as a reference (for which we have scaled the temperature by $2.0\times {10}^{-5}$ as in the other curves). (d) shows the spin-spin correlation as function of $J/T_K$ for various values of $T_K$.

Figure 3

Crossover temperature $T^{*}$ as function of $\left|J\right|/T_K$ showing the exponential dependence with $\left|J\right|/T_K$ as in Eq. (4). Symbols correspond to $T^{*}$ extracted from ${\mu }^2$ curves of Fig. 2a (see text), while the (red) solid line results from a linear regression for a linearized version of expression (4), which gives $\gamma =4.75$.

Figure 4

Spectral function vs $\omega$ near the Fermi level for various values of $T_K/\left|J\right|$ (fixing $J=-2\times {10}^{-5}$ and varying $T_k$) showing how the Kondo peak is affected due to changes in the coupling $J$. The line corresponds to $J=0$ and the same $T_K$ as in the dashed (black) line. The inset shows in a logarithmic scale the finite width of the sharp peak around the Fermi level.

Figure 5

Conductance as function of temperature for various values of $J$ and at a fixed $T_K=2.41\times {10}^{-4}$. The vertical dashed lines indicate the position of the various $\left|J\right|$ along the $x$ axis, showing a good coincidence with the spikes observed in the conductance.