Ferromagnetic Proximity Effect in a Ferromagnet–Quantum-Dot–Superconductor Device

The ferromagnetic proximity effect is studied in InAs nanowire based quantum dots strongly coupled to a ferromagnetic ($F$) and a superconducting ($S$) lead. The influence of the $F$ lead is detected through the splitting of the spin-$1/2$ Kondo resonance. We show that the $F$ lead induces a local exchange field on the quantum dot, which has varying amplitude and sign depending on the charge states. The interplay of the $F$ and $S$ correlations generates an exchange field related subgap feature.

Figure 1

(a) A scanning electron microscopy picture of a device. The right lead is a $\mathrm{Ti}/\mathrm{Al}$ bilayer superconductor, while the left longer one is a $\mathrm{Ni}/\mathrm{Co}/\mathrm{Pd}$ trilayer ferromagnet. The $B$ field is applied parallel to easy axis of the $F$ lead. (b) Schematic view of the $F\mathrm{\text{−}}\mathrm{QDot}\mathrm{\text{−}}S$ system. The spin degeneracy on the QD is lifted by an exchange splitting induced by the ferromagnetic proximity effect. (c) Because of the spin polarized charge fluctuations, the spin ground state of the QD is opposite when the occupation of the highest orbital level fluctuates between 1 and 0 (${ϵ}_d\approx 0$) or 1 and 2 (${ϵ}_d\approx -U$).

Figure 2

(a) Differential conductance as a function of $V_{\mathrm{BG}}$ and $V_{\mathrm{sd}}$ of a $F\mathrm{\text{−}}\mathrm{QD}\mathrm{\text{−}}S$ device at $B=0\mathrm{T}$. $B_{\mathrm{ex}}$ modifies the Kondo resonances (odd numbered states) differently. The $S$ lead induces peaks in the conductance at $V_{\mathrm{sd}}=\pm \Delta$. $B$ dependence of different charge states: (b) with no signature of $B_{\mathrm{ex}}$ [state 7 in Fig. 2a], (c) with $B_{\mathrm{ex}}<0$, which is compensated by external $B$ [state 3 in Fig. 2a], (d) with $B_{\mathrm{ex}}>0$, which is enhanced by $B$. Panel (d) is measured in a charge state at $V_{\mathrm{BG}}=2.31\mathrm{V}$.

Figure 3

Measurements on state 1. (a) Differential conductance as a function of $V_{\mathrm{BG}}$ and $B$ measured at $V_{\mathrm{sd}}=0\mathrm{mV}$. The two horizontal ridges (dotted lines) are the charge state boundaries. The high conductance ridge is the restored Kondo resonance, where $B=-B_{\mathrm{ex}}(V_{\mathrm{BG}})$. This ridge separates the regions where spin-$\uparrow$ or spin-$\downarrow$ is the ground state. The white line is a plot based on Eq. (1) using the parameters obtained from the fits shown in (c). The white arrow shows the sweeping direction of $B$. The black arrow points out the position where the magnetization of the $F$ lead changes sign. (b) Color scale plots at different magnetic fields. The dashed line highlights the position of the tilted Kondo resonance at $B=0.2\mathrm{T}$. (c) The evolution of the Kondo resonance is presented for different $B$ fields by symbols. The lines are fits using Eq. (1).

Figure 4

(a) $G(B,V_{\mathrm{sd}})$ measurement: A subgap feature appears (horizontal dashed lines) at the energy scale of the exchange field. The feature is suppressed above the critical field of the superconductor. (b) $G(V_{\mathrm{BG}},V_{\mathrm{sd}})$ at $B=0\mathrm{mT}$ showing the relation of the new subgap structure to $B_{\mathrm{ex}}$. Inside the superconducting gap additional resonance lines appear in even charge states (see dotted lines). These resonances change their position with gate voltage and merge into the exchange split Kondo resonance lines at the border of the odd charge state. The line graphs show $G(V_{\mathrm{sd}})$ cuts in the middle of the three charge states.