Controlling the Exchange Field of Surface Spin Impurities via DC Voltages

TL;DR

We address how a DC bias in ESR-STM can tune the exchange field acting on a single surface spin, enabling all-electric control of spin resonance. We show that the resonance shift arises from a bias-dependent exchange field $\mathbf{B}_{\text{exch}}$ produced by virtual charge fluctuations in a single-orbital Anderson impurity coupled to a spin-polarized tip, with $g\mu_B \mathbf{B}_{\text{exch}} = \frac{1}{2\pi}\left[\gamma_T P_T \ln\left|\frac{eV_{DC}-\varepsilon- U}{eV_{DC}-\varepsilon}\right|\right] \hat{\mathbf{n}}_T$ and $h\,\delta f = h f_0 - g\mu_B B_{\text{ext}} = g\mu_B B_{\text{exch}}^{\parallel}$. The measured shifts for $S=1/2$ FePc and Ti on MgO/Ag(100) are reproduced, revealing the angular dependence $\delta f \propto B_{\text{exch}}^{\parallel}$ and the possibility to invert or suppress the effect by bias or tip polarization. A unified scaling across many datasets yields consistent impurity parameters ($\varepsilon$, $U$, $\gamma_T$) and confirms that the exchange field, not $g$-factor changes, drives the bias response. The work demonstrates magnetoelectric coupling as a robust mechanism for all-electric ESR in nanoscale devices and provides a practical framework for bias-tunable spin spectroscopy of surface impurities.

Abstract

Recent advances in scanning tunneling microscopy have enabled quantum-coherent control of single surface spins via all-electric electron spin resonance (ESR). Such control requires magnetoelectric coupling, since spin resonance is a magnetic effect. We show that a magnetic tip induces a bias-dependent exchange field on a localized Anderson impurity via virtual particle exchange with the magnetic lead. This field differs from Heisenberg exchange and can be tuned, reversed, or suppressed by the bias voltage. Our model reproduces bias-controlled resonance shifts for S = 1/2 titanium atoms and Fe(II) phthalocyanine, enabling spin control via the exchange field and revealing the magnetoelectric mechanism behind all-electric ESR for spin-based quantum technologies.

Figures (5)

• Figure 1: ESR frequency ($f_0$) shift of an individual FePc molecule and a Ti atom as a function of the DC bias. (a) STM image of the Fe, Ti atoms and the FePc molecule co-adsorbed on the MgO/Ag(100) surface. Scanning parameters: $V_\text{DC} = 200$ mV, $I_\text{set} = 20$ pA. (b) Schematic diagram of the ESR set-up at the tunneling junction, integrated into a plate capacitor model. $\vec{P}_\mathrm{T}$ represents the spin-polarization of the tip, forming an angle $\theta$ with the out-of-plane direction. (c) Experimentally measured magnetic moments of FePc at different $V_\text{DC}$. The red solid lines give the weighted average values of magnetic moments. (d) Corresponding resonance frequencies $f_0$ of FePc. The red dashed line indicates resonance frequencies calculated from DFT. (e) and (f) show the same data for Ti. The tip height was fixed with respect to the tunneling parameters of $V_\text{DC} = 100$ mV, $I_\text{set} = 20$ pA for FePc and $I_\text{set} = 35$ pA for Ti. ESR conditions: $V_\text{RF} = 20$ mV for FePc and $V_\text{RF} = 30$ mV for Ti, $B_z = 560$ mT, $T = 1.8$ K.
• Figure 2: Energy diagram and d$I$/d$V$ spectrum for SAIM. (a) Energy-level diagram illustrating the key transport parameters governing the exchange field. The spin impurity splits into two states, $\downarrow$ (ground state) and $\uparrow$ (excited state), separated by the Zeeman energy. Filled and empty arrows denote singly occupied electron states and hole states, respectively. The applied DC bias is $eV_\text{DC}=\mu_S-\mu_T$. (b) Simulated density of states (DOS, left) and experimental d$I$/d$V$ spectrum (right) of a FePc molecule on MgO.
• Figure 3: Resonance frequency shift of a Ti atom measured by bistable tip. (a) Experimentally measured (squares) and simulated (solid lines) frequency shift at varied $V_\text{DC}$ with a bistable tip showing two opposite signs of the spin-polarization (tip up, positive, and tip down, negative). In both (a) and (b), the red dashed line represent the bare resonance frequency set by external magnetic field and $g$-factor. The blue curves in (b) shows the resonance frequencies calculated using Eqs. \ref{['eq:hdeltaf']} and \ref{['eq:exchB']} with two opposing signs of the polarization (solid and dashed lines). (c) Experimentally measured (diamonds and circles), simulated (blue and green solid lines) and bare (red and orange dashed lines) frequencies vs $V_\text{DC}$ with the external magnetic field along the out-of-plane ($B_z$) and in-plane ($B_x$) direction, respectively. Inset: geometry of the exchange field indicating the homodyne angle $\theta$ and the parallel (perpendicular) projections $B_{\text{exch}}^{\parallel}$ ($B_{\text{exch}}^{\perp}$) onto the spin $\vec{S}$. (d) Parameters used for the simulations in (a) and (c). ESR experimental parameters: (a) $V_\text{RF} = 28$ mV, (b) $V_\text{RF} = 30$ mV. The tip height at different $V_\text{DC}$ was fixed by referring to the tunneling condition of (a) $V_\text{DC} = 100$ mV, $I_\text{set} = 20$ pA, (c) $V_\text{DC} = 100$ mV, $I_\text{set} = 40$ pA.
• Figure 4: Comparing the frequency shift of FePc and Ti measured with the same tip. (a) and (b) depict the experimental (circles and triangles) and simulated (solid lines) resonance frequencies as a function of $V_\text{DC}$ with the same tip for a FePc molecule and a Ti atom, respectively. The experimental values are extracted from Figs. \ref{['fig:1']} and \ref{['fig:2']}. (c) Parameters used in the transport simulations for FePc and Ti in (a) and (b), respectively. Since the tip used here differs from that in Fig. \ref{['fig:3']}, a different angle $\theta$ is chosen, approximately one third of $\theta_x$, which provides a reasonable fit of the ESR signal in terms of both linewidth and asymmetry.
• Figure 5: Unified rescaled behavior of the resonance frequency shift of Ti described by the exchange-field model. (a) Datasets from Fig. \ref{['fig:3']}, Fig. \ref{['fig:4']}, and additional ones (see Supplementary Material SM3) are combined and rescaled to obtain a unified fit using a single set of adjustable parameters: $F = \gamma_\mathrm{T} P_\mathrm{T} \cos\theta$, $U$, and $\varepsilon$. The dataset acquired with a bistable tip of positive polarization is inverted. The grey shaded area indicates the overall uncertainty of the united fit. (b) Scaling factors $r$ used to align the datasets in (a) and the corresponding fit parameters with uncertainties indicated by the shaded area.