Erbium and thulium on MgO(100)/Ag(100) as candidates for single atom qubits

Lanthanide atoms on surfaces are an exceptional platform for atomic-scale magnetic information storage. However, their potential as qubits remains unexplored due to the limited number of experimental setups that can coherently drive the spins of single adatoms. Here we propose a combined experimental and theoretical method to estimate the performance of surface-adsorbed lanthanide atoms for quantum coherent operations. We investigate Er and Tm on MgO(100)/Ag(100) with x-ray absorption spectroscopy to address their magnetic and electronic properties and with scanning tunneling microscopy (STM) to identify their adsorption sites. With atomic multiplet calculations and density functional theory, we infer for both atoms a magnetic ground state that is suitable for quantum coherent operations. We investigate whether these systems lend themselves to electron spin resonance scanning tunneling microscopy (ESR-STM). By adapting the piezoelectric model of ESR-STM to the case of lanthanide atoms, we show that these systems should exhibit a detectable signal and that they have a higher Rabi rate compared to the systems studied up to date. In addition to their suitable electron spin properties, these elements possess a nontrivial nuclear spin that could be exploited to perform two-qubit operations on a single atom or to store quantum states in the nuclear spin.

Figure 1

Schematic of an XMCD experiment of lanthanide atoms ($\mathrm{Ln}=\mathrm{Er}$, Tm, yellow spheres) on MgO(100)/Ag(100) (Mg, blue sphere and O, red sphere). The lanthanide adatoms bind to the MgO surface on two possible adsorption sites, namely on oxygen and on bridge, as discussed in the text. The external magnetic field is always applied parallel to the direction of the x-rays while the whole sample is rotated by an angle ϑ. Right (RP) and left (LP) circularly polarized x-rays are represented by black and red circular arrows, respectively.

Figure 2

(a) Constant current STM image of individual Er atoms on MgO(100)/Ag(100). Red (green) circles indicate Er atoms on O (bridge) adsorption sites. Erbium coverage: 0.8% ML ($V_t=\text{–}200\mathrm{mV}$, $I_t=200\mathrm{pA}$, $T=5\mathrm{K}$). (b) Zoom into the region outlined by the dashed square in (a). A grid extracted from an atomically resolved STM image acquired on MgO is superimposed onto the image to identify the Er adsorption sites. (c) Constant current STM image showing individual Tm atoms with two apparent heights on MgO(100)/Ag(100) (square patches) and with one apparent height on the Ag(100) substrate. Magnesium oxide thicker than 2 ML appears as darker areas in the STM image. In the red (green) circle we indicate a Tm atom on the O (bridge) adsorption site. Thulium coverage: 0.2% ML ($V_t=200\mathrm{mV}$, $I_t=100\mathrm{pA}$, $T=10\mathrm{K}$).

Figure 3

(a) XAS and XMCD spectra at the $M_5$ edge of Er on MgO(100)/Ag(100) at normal (NI) and grazing incidence (GI). The experiments are reported as blue lines. Atomic multiplet calculations with $4f^{11}$ on O (red), $4f^{11}$ on bridge (dashed yellow) species yield the total fit (dotted black line). The fitting parameters with their confidence intervals are reported in Table 1. XAS and XMCD in grazing incidence are shifted up and down by 0.03 arb. units, respectively (MgO thickness: 3.9 ML, $B=6.7\mathrm{T}$, $T=2.5\mathrm{K}$). (b) XAS and XMCD at the $M_5$ edge of Tm on MgO(100)/Ag(100). Fits of the data using atomic multiplet calculations including two species ($4f^{13}$ on O, green; $4f^{12}$ on bridge, dashed yellow) are shown together with the total fit (dotted black line); the $4f^{12}$ on O and $4f^{13}$ on bridge spectra are omitted. The spectra in grazing incidence are shifted up and down by 0.015 arb. units, respectively (MgO thickness: 4.3 ML, $B=6.7\mathrm{T}$, $T=2.5\mathrm{K}$).

Figure 4

Energy level diagrams of Er (a) and Tm (b) adsorbed on the O sites of MgO(100)/Ag(100) showing the lowest atomic multiplet. The out-of-plane external magnetic field (6.7 T) splits the lowest doublet ($|1\rangle$ and $|2\rangle$) by the Zeeman energy $\mathrm{\Delta }E$ shown in the zoomed region. The second excited state is separated from the ground state by the zero-field splitting.

Figure 5

Predicted Zeeman energy splitting calculated with atomic multiplet calculations for Er (a) and Tm (b) as a function of ${\mathit{B}}_{\mathrm{ext}}$ at $0^{\circ }$ (blue line), ${45}^{\circ }$ (red line), and ${90}^{\circ }$ (yellow line). Predicted Zeeman splitting for Er (c) and Tm (d) as a function of the external magnetic field angle at 500 mT (blue solid line) and 1000 mT (red solid line) in comparison with an isotropic spin ½ system (dashed lines).

Figure 6

Predicted angle δ between ${\mathit{B}}_{\mathrm{ext}}$ and the atom $\mathit{J}$ as a function of the magnetic field angle for Er (a) and Tm (b). A schematic of the magnetic field alignment (red arrow) and the atom $\mathit{J}$ (black arrow) is reported alongside the graph.

Figure 7

Predicted Rabi rate as a function of the external magnetic field angle for Er (a) and Tm (b) at a driving rf voltage of 250 mV.

Figure 8

XAS and XMCD spectra in NI and GI simulated with atomic multiplet calculations of the Er species used in the fit in Fig. 3 and Table 1.

Figure 9

XAS and XMCD spectra in NI and GI simulated with atomic multiplet calculations of the Tm species used in the fit in Fig. 3 and Table 1.

Figure 10

(a) XAS and XMCD spectra at the $M_5$ edge of Er on MgO(100)/Ag(100) at normal (NI) and grazing incidence (GI). The experiments are reported as blue lines. Atomic multiplet calculations with $4f^{11}$ on O (red); $4f^{11}$ on bridge (dashed yellow), and $4f^{11}$ dimer (dotted purple) species yield the total fit (dotted black line). The fitting parameters with their confidence intervals are reported in Table 6. XAS and XMCD in grazing incidence are shifted up and down by 0.03 arb. units, respectively (MgO thickness: 3.9 ML, $B=6.7\mathrm{T}$, $T=2.5\mathrm{K}$). (b) XAS and XMCD at the $M_5$ edge of Tm on MgO(100)/Ag(100). Fits of the data using atomic multiplet calculations including three species ($4f^{13}$ on O, green; $4f^{12}$ on bridge, dashed yellow; and $4f^{12}$ dimers, dotted purple) are shown together with the total fit (dotted black line). The spectra in grazing incidence are shifted up and down by 0.015 arb. Units, respectively (MgO thickness: 4.3 ML, $B=6.7\mathrm{T}$, $T=2.5\mathrm{K}$). We model dimers for both elements assuming an isotropic behavior to take into account the expected distribution of their angular orientations on the surface.

Figure 11

Schematic of an ESR-STM experiment on a lanthanide atom ($\mathrm{Ln}=\mathrm{Er}$, Tm) based on the model used in the main text. The magnetic tip magnetization ($M_{\mathrm{tip}}$) follows ${\mathit{B}}_{\mathrm{ext}}$ while the high magnetic anisotropy of the lanthanide atom on the O adsorption site of MgO(100)/Ag(100) aligns the atom $\mathit{J}$ in plane. In the general case (b) of an external magnetic field angle ϑ different from $0^{\circ }$ (a) or ${90}^{\circ }$ (c), an angle α is present between the tip and the atom $\mathit{J}$.

Figure 12

Calculated ESR-STM signal for Er (a) and Tm (b). In the top panel, the signal is reported as a function of the external magnetic field intensity and angle. The dashed gray line represents the region with constant Zeeman splitting of 20 GHz. In the bottom panel, the signal at constant Zeeman splitting of 20 GHz is reported as a function of the external magnetic field angle for Er (c) and Tm (d).