Electron spin resonance measured in the current-noise power spectrum of a DC-biased scanning tunneling microscope (ESR-STM) with nonmagnetic tip and substrate has been observed since 1989, but the microscopic mechanism that converts spin precession into current noise in this geometry remains unsettled. Horovitz and Golub (Phys. Rev. B 99, 241407(R) (2019)) proposed that the resonance arises from interference between parallel tunneling paths through two spin sites - a double quantum dot formed by the target surface spin and a second, unintentional spin, most plausibly located on the heavy-metal STM tip - and predicted, beyond the observed Larmor line at ν1=g1μBH\nu_1=g_1\mu_B H, additional resonances at the second Larmor frequency ν2=g2μBH\nu_2=g_2\mu_B H, at the difference frequency ∣ν1−ν2∣|\nu_1-\nu_2|, and at zero frequency, with peak heights comparable to the background shot noise. The open problem is to determine whether this two-spin mechanism underlies the observed noise resonances: observing or excluding the predicted field-dependent lines, identifying or excluding a second spin site on the tip, measuring the absolute peak noise power to test the predicted Fano factors, and completing the theory (coherence of the direct tunneling channel, exchange shifts of the Larmor frequencies, and the nonsecular linewidth term). Tunneling via two spins has been demonstrated for molecular dimers on a surface (2022) and a tungsten-oxide spin signal at a tip apex has been identified (2023), but the ν2\nu_2 and ∣ν1−ν2∣|\nu_1-\nu_2| resonances have not been observed, the absolute noise power has not been measured, and the coherence and nonsecular-linewidth questions remain untreated; no resolution of the mechanism question is known in the literature to date.

Background

Electron spin resonance in scanning tunneling microscopy (ESR-STM) comes in two variants. In the first, a DC-biased STM tip is placed over a localized spin center in a static magnetic field HH and the power spectrum of the tunnel-current fluctuations is measured; since 1989 this has yielded sharp resonances at the Larmor frequency ν=gμBH\nu = g\mu_B H (the precession frequency of a spin with g-factor gg; μB\mu_B is the Bohr magneton), with nonmagnetic tip and substrate, even at room temperature. In the second variant, an RF voltage applied to a tip carrying a permanently magnetized Fe atom enhances the DC current at resonance (Baumann et al. 2015; Willke et al. 2018); that mechanism - an oscillating exchange field from the magnetic tip - is well understood, and the source work emphasizes that it is fundamentally different from the noise mechanism considered here.

The mechanism of the first, DC-bias noise variant is the open issue. A single spin site tunnel-coupled to nonpolarized electrodes cannot produce a resonance: after a gauge rotation absorbing the spin-orbit tunneling phase, total SzS_z conservation forbids a single spin flip returning the tunneling electron to its original state. At least two interfering tunneling channels are needed. An earlier nanoscopic-interferometer model (direct tip-substrate tunneling in parallel with the spin-mediated path) produces a resonance but with a weak signal and without on-site Coulomb repulsion, which is expected to be strong at a localized spin site.

Horovitz and Golub (2019) proposed instead a double-quantum-dot (DQD) scenario: the current passes in parallel through two spin sites - the target surface spin plus a second, unintentional spin, most plausibly on the STM tip, whose heavy constituent metals provide significant spin-orbit coupling and are known to host dangling-bond surface states (unsatisfied surface chemical bonds that can each host a localized unpaired electron) that are candidate spin sites. Treating strong on-site Coulomb repulsion via a Schrieffer-Wolff transformation (a perturbative elimination of charge fluctuations that maps the localized electron onto effective exchange couplings J1J_1, J2J_2 between the lead fermions and the two spins), with an SU(2) spin-rotation matrix u^=eiσzφeiσyθ/2\hat{u} = e^{i\sigma_z\varphi}e^{i\sigma_y\theta/2} acting on one tunneling path to encode spin-orbit coupling, the solutions obtained with the Keldysh nonequilibrium Green's-function formalism and a Lindblad quantum master equation (two standard tools for open quantum systems driven out of equilibrium) predict current-noise resonances at ν1=g1μBH\nu_1 = g_1\mu_B H, at the second Larmor frequency ν2=g2μBH\nu_2 = g_2\mu_B H, at the difference frequency ∣ν1−ν2∣|\nu_1-\nu_2| (present even without spin-orbit coupling, and strongest for weak spin-orbit mixing), and at zero frequency. The linewidths are voltage-dominated,

Γ=16πeVN(0)2(J12+J22)(ωres=ν1,ν2,0),\Gamma = 16\pi e V N(0)^2 (J_1^2+J_2^2) \quad (\omega_{\rm res}=\nu_1,\nu_2,0), Γ(∣ν1−ν2∣)=16πeVN(0)2(J12+J22−J1J2cos⁡θ2cos⁡φ),\Gamma(|\nu_1-\nu_2|) = 16\pi e V N(0)^2 (J_1^2+J_2^2 - J_1 J_2 \cos\tfrac{\theta}{2}\cos\varphi),

where VV is the bias and N(0)N(0) the density of states; the J1J2J_1J_2 term in the second formula is nonsecular (it couples non-degenerate spin transitions) and its consequences were left unexplored. Here the Fano factor - the ratio of the resonance peak height to the background shot-noise level, shot noise being the white noise of spectral density ≈eI\approx eI generated by the discreteness of the tunneling charge - is predicted to be of order unity, with explicit formulas such as F(0)F(0) and F(∣ν1−ν2∣)F(|\nu_1-\nu_2|) in the source. The model assumes (i) that the direct tip-substrate tunneling current, expected to dominate the total current, is incoherent with the spin-mediated currents - if coherent, it would induce a large shift of the resonance frequencies - and (ii) that direct exchange coupling between the two spins is negligible (argued for the tip-surface geometry, since that exchange is much weaker than J1J_1 or J2J_2). Because the existing spectra are acquired via modulation of the magnetic field, the absolute peak noise power has never been directly measured, so the Fano-factor predictions are untested. The predicted additional lines, in particular ∣ν1−ν2∣|\nu_1-\nu_2|, can fall well below the frequency window accessible to the impedance-matched detection circuits (about 580-780 MHz in the relevant experimental setup), which is part of why they have not been reported.

Problem Statement

Determine whether the two-spin (double-quantum-dot) interference mechanism proposed by Horovitz and Golub is the physical origin of the spin-resonance lines observed in the current-noise power spectrum of a DC-biased STM junction with nonmagnetic tip and substrate. The question is answerable by confirmation or by refutation, and the requested results jointly serve this single objective: item 1 is the decisive line-detection test, items 2 and 3 are supporting measurements that make that test interpretable, and item 4 is a theory completion that can redirect the experimental test rather than resolve the question by itself.

  1. Detect, or exclude with stated sensitivity, the predicted additional resonance lines in the current-noise power spectrum - at the second Larmor frequency ν2=g2μBH\nu_2=g_2\mu_B H, at the difference frequency ∣ν1−ν2∣|\nu_1-\nu_2| (expected to be the strongest line when spin-orbit mixing is weak), and at zero frequency - each tracking the applied magnetic field HH with the corresponding slope, in experiments on systems where a single spin site is otherwise imaged and characterized.
  2. Identify, or exclude, the second spin site that the mechanism requires - most plausibly a spin on the STM tip (for example a tungsten-oxide or dangling-bond center on a heavy-metal tip) - for instance through tip-exchange, tip-material, or tip-treatment controls.
  3. Measure the absolute peak noise power and the background shot-noise level directly, so that the predicted Fano factors (the resonance-peak-to-shot-noise ratios of order unity, including the explicit predictions for the ν1\nu_1, ν2\nu_2, ∣ν1−ν2∣|\nu_1-\nu_2|, and zero-frequency lines) can be quantitatively compared with experiment for the first time.
  4. Complete the theoretical account of the mechanism: the consequences of coherence between the direct tip-substrate tunneling current and the spin-mediated currents (predicted to induce a large shift of the resonance frequencies), the effect of direct exchange coupling between the two spins on the Larmor frequencies and resonance positions in the tip-surface geometry, and the role of the nonsecular J1J2J_1J_2 term in the linewidth of the ∣ν1−ν2∣|\nu_1-\nu_2| resonance.

Observation of the predicted additional magnetic-field-dependent frequencies in the current-noise power spectrum would constitute the clearest support for the mechanism, as stated in the source (which also notes that the presence of the unintentional second spin can be tested by monitoring these predictions); a controlled exclusion of the predicted lines at the predicted sensitivity, or a demonstration that an alternative mechanism accounts for the observed spectra, would refute it; a theoretical analysis that substantially modifies these predictions (for example through the coherence or exchange effects of item 4) would redirect the experimental test.

References

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