Electric-Field-Driven Spin Resonance by On-Surface Exchange Coupling to a Single-Atom Magnet

Abstract

Coherent control of individual atomic and molecular spins on surfaces has recently been demonstrated by using electron spin resonance (ESR) in a scanning tunneling microscope (STM). Here, a combined experimental and modeling study of the ESR of a single hydrogenated Ti atom that is exchange-coupled to a Fe adatom positioned 0.6-0.8 nm away by means of atom manipulation is presented. Continuous wave and pulsed ESR of the Ti spin show a Rabi rate with two contributions, one from the tip and the other from the Fe, whose spin interactions with Ti are modulated by the radio-frequency electric field. The Fe contribution is comparable to the tip, as revealed by its dominance when the tip is retracted, and tunable using a vector magnetic field. The new ESR scheme allows on-surface individual spins to be addressed and coherently controlled without the need for magnetic interaction with a tip. This study establishes a feasible implementation of spin-based multi-qubit systems on surfaces.

Keywords: Rabi rate; atom manipulation; electron spin resonance; scanning tunneling microscopy; single spin qubit; single-atom magnet.

Figure 1

Electron spin resonance in Ti‐Fe pairs. a) Schematic showing a Ti spin (S = 1/2) coupled with Fe on MgO in electron spin resonance. J _Ti,Fe and J _Ti,tip are Ti‐Fe and Ti‐tip spin‐spin interactions, which drive the ESR of the Ti spin when coupled with the RF voltage V _RF applied to the tunnel junction. b–d) STM images of Ti atoms with Fe positioned at distances of 1.9, 0.72, and 0.59 nm away from Ti, respectively (V _DC = 50 mV, setpoint tunnel current I _tun = 10 pA). e) Continuous wave ESR spectra measured on Ti atoms in b) (black), c) (red), and d) (blue) at B _ext = 0.9 T with the polar angle θ _ext = 82^o (V _DC = 50 mV, V _RF = 20 mV, I _tun = 15 pA, T = 1.2 K). The frequency f _c indicates the center of the two peaks in each curve.

Figure 2

Influence of Fe on the Rabi rate. a,b) Rabi oscillations using pulsed ESR on Ti atoms shown in Figure 1b–d at junction conductance of a) 0.5 and b) 0.15 nS, V _RF = 100 mV. The oscillation period of each curve is marked by the vertical bar. The curves are successively shifted vertically by 40 fA for clarity. c) Rabi rate Ω extracted from Rabi oscillation measurements of isolated Ti (gray circles), Ti‐Fe of 0.72 nm (red crosses), and Ti‐Fe of 0.59 nm (blue triangles) (I _tun = 10 pA, V _RF = 100 mV, T = 1.2 K, B _ext = 0.9 T, θ _ext = 82^o). The dotted circles denote the data points corresponding to the curves in (a,b) with the same color codes. Two insets illustrate the magnetic interactions, J _Ti,Fe and J _Ti,tip, for small (left) and large (right) tunnel conductance regimes, respectively. Solid curves are fits using the model described in Text S1, Supporting Information, resulting in zero conductance Rabi rates Ω₀/2π of 27 ± 2 and 14 ± 2MHz for the pairs of 0.59 and 0.72 nm, respectively.

Figure 3

Crossover from tip‐driven to Fe‐driven ESR. a) CW‐ESR spectra measured on the Ti‐Fe of 0.72 nm at frequency ranges across the peaks $f_{\Uparrow }$ (red) and $f_{\Downarrow }$ (blue) for a varying tunnel conductance (I _tun = 15 pA, V _RF = 20 mV, T = 1.2 K, B _ext = 0.9 T, θ _ext = 82^o). The solid curves are asymmetric Lorentzian fits. The curves are successively shifted vertically by 0.3 pA for clarity. b) Peak height I _ESR versus tunnel conductance extracted from CW‐ESR spectra in (a). Fits according to the discussion in the main text are overlaid (solid curves; see Section 3). Extrapolation of the fit curves to zero conductance gives intercepts I _sat = 0.226 pA ($f_{\Uparrow }$) and 0.142 pA ($f_{\Downarrow }$). The three insets illustrate the vectorial relationships between the ESR driving fields contributed from the Fe (red or blue) and the tip (light green). c) Vectorial relationship of driving fields from Fe ( B _1,Fe) and tip ( B _1,tip). B ₀ is the total static field at the Ti position, composed of external ( B _ext), tip‐induced field ( B _tip), and Fe‐induced ( B _Fe) fields. B _1,Fe⊥ and B _1,tip⊥ denote projections of B _1,Fe and B _1,tip, respectively, to a plane perpendicular to the total static field B ₀. d) A schematic of the Bloch sphere in a condition that B _1,Fe⊥ and B _1,tip⊥ are antiparallel (ϕ = 180^o) and showing resultant Rabi rotations of the Bloch vector of the Ti spin (brown thick arrow). The net driving field B _1⊥ changes its direction depending on the magnitude of the tip‐induced driving field B _1,tip⊥, leading to corresponding change in the Rabi rotation.

Figure 4

Angle dependence of ESR frequencies on the applied magnetic field. a) ESR resonance peak frequencies and b) splitting Δf in CW‐ESR spectra measured from Ti‐Fe pairs of 0.72 nm (red) and 0.59 nm (blue) at a varying polar angle (θ _ext) of B _ext. Solid curves are fits using the model described in Equations (1) and (2). Red solid (dashed) curves correspond to the up (down) state of the tip spin. (V _DC = 200 mV, I _tun = 10 pA, V _RF = 30 mV for the 0.59 nm pair; V _DC = 30 mV, I _tun = 20 pA, V _RF = 30 mV for the 0.72 nm pair; T = 0.4 K, B _ext = 0.6 T). c,d) Schemes of the net magnetic field B _net at the Ti position, composed of the external field B _ext and Fe‐induced field B _Fe in the plane of B _ext vector with c) an arbitrary and d) 90^o field angle θ _ext. α and α ₀ denote the angles added by the Fe‐induced field. Here, the field induced by the tip magnetic field B _tip is omitted to focus on the discussion only on the effect of B _Fe.

Figure 5

ESR of Ti using two Fe atoms. a) A Fe‐Ti‐Fe spin complex with Ti‐Fe separations of 0.72 nm. b) Continuous wave ESR spectra measured on Ti of the complex in (a) (purple) and a Ti‐Fe pair of 0.72 nm (red) (V _DC = 50 mV, I _tun = 15 pA, V _RF = 100 mV, T = 1.2 K, B _ext = 0.9 T, θ _ext = 82^o). c) Rabi rates obtained from pulsed ESR of the complex (purple triangles) and Ti‐Fe pair of 0.72 nm (red crosses), and an isolated Ti (gray open circles) at a varying tunnel conductance. The insets schematically depict the Ti‐Fe interactions for three groups of Rabi rates (V _RF = 100 mV, T = 1.2 K, B _ext = 0.9 T, θ _ext = 82^o).