Electric control of spin transitions at the atomic scale

The study addresses how to achieve efficient electric control of spin transitions at the atomic scale, an important goal for scalable, fast spintronics and quantum information processing. While ESR-STM enables atomic-scale spin spectroscopy with neV resolution, the DC bias voltage has not previously been exploited as a control knob for spin transitions. The authors hypothesize that the strong electric fields in the STM junction can modify the local environment of adsorbed spin systems (e.g., TiH on MgO), thereby tuning the g-factor and the effective magnetic field from the tip to control ESR transitions. Establishing such spin-electric coupling (SEC) at the single-atom/molecule level would provide a fast, electrically addressable degree of freedom for coherent control of single spins and coupled spin systems.

The paper situates its work within several decades of spintronics research, highlighting electric-field control concepts such as spin transistors, the spin Hall effect, dopants in silicon, and magnetic molecules. ESR-STM has extended ESR sensitivity to individual atoms/molecules with neV-scale energy resolution. Prior theoretical and experimental studies have explored SEC in molecular magnets (e.g., HoW10 with kHz/V shifts and SEC constants of ~11.4 Hz/(V/m)), and for TiH on MgO theory predicted modest electric-field-induced g-factor modulation on a specific adsorption site. However, bias voltage had not been used directly as a control parameter in ESR-STM experiments. The authors build on these works to demonstrate substantially larger bias-induced ESR shifts in a tunnel junction and extend SEC to interaction tuning in coupled dimers.

• Platform: ESR-STM measurements at base temperature ~310 mK with an external magnetic field perpendicular to the sample surface.
• Sample: TiH molecules adsorbed on a two-monolayer MgO film on Ag(100). TiH occupies bridge sites between two O atoms (TiH_OO) and, for comparison in supplementary data, O-top sites (TiH_O).
• Tip preparation: ESR-sensitive tips obtained by picking up 1–10 Fe atoms.
• Measurement conditions: Microwave frequencies from 60–100 GHz; primary data at f_rf = 61.545 GHz with U_rf ≈ 20 mV. Bias voltage swept while monitoring ESR peak positions versus external magnetic field at various current setpoints (e.g., I_sp = 100 pA, 250 pA; additional setpoints for systematic studies). Setpoint voltage typically U_sp = 100 mV unless stated. Homodyne detection used at zero bias.
• Data acquisition: Magnetic field/bias voltage sweeps recorded to map ESR resonance positions. Constant-voltage slices used to extract ESR peak positions. Horizontal rectification features from rf-induced tunneling nonlinearity identified and excluded from ESR analysis.
• Analysis framework: Linear Zeeman relation E_z = h f_res = g μ_B (B_ext + B_tip) with S = 1/2. Both g-factor and tip magnetic field B_tip modeled as functions of the electric field in the junction (i.e., bias voltage and tip–sample distance). Peak positions fitted across frequencies and setpoints to extract g(U_bias) and B_tip(U_bias). Estimated electric-field-induced displacement derived from observed shifts and a mechanical model of forces on the dipolar TiH (elastic Ti–MgO/Ti–H bonds vs electric force), yielding −11.5 fm/mV (~2.7 pm over 240 mV).
• Dimer studies: Two TiH_OO dimers with separations ~644 pm (J ≈ 1.1 GHz) and ~1.04 nm (J ≈ 0.67 GHz) investigated. ESR transitions modeled using a coupled-spin Hamiltonian with linear dependence of g-factors and B_tip on bias voltage; calculated ESR peak positions (white dashed lines) compared to experimental maps. Tip position controlled to probe site-specific SEC effects; tip–sample distance tuned to move an avoided crossing in bias to zero voltage.
• Instrumentation and preparation details: Unisoku USM-1300 STM with high-frequency cabling/antenna; DC bias on sample (current read at tip) except in supplementary oxygen-site measurements with reversed connections. U_rf calibrated via rf response of nonlinear tunneling spectroscopy. Ag(100) cleaned by Ar+ sputtering (5 kV) and annealing (820 K). MgO grown by Mg evaporation with O2 leak (10^-6 mbar) and substrate heating (520 K). Fe and Ti deposited by e-beam at low temperature (<16 K) to avoid clustering. Dimers found naturally or created by atom manipulation.

• Strong bias voltage dependence of ESR resonance in single TiH molecules: ESR peak shifts by many line widths across a 240 mV bias range; peaks at different biases are well separated.
• Mechanism: Electric field in the tunnel junction displaces the TiH molecule (~−11.5 fm/mV; total ~2.7 pm ≈ 1% of TiH–MgO distance), modifying the crystal field and g-factor, and altering the effective tip magnetic field B_tip felt by the spin.
• Extracted dependencies: Both g-factor and B_tip increase monotonically with bias voltage; changes are stronger at larger setpoint currents (smaller tip–sample distance), consistent with enhanced electric fields. Near zero bias, B_tip varies weakly with setpoint current while g-factor continues to increase with decreasing tip–sample distance.
• Quantitative shifts at I_sp = 250 pA: Effective frequency shifts vs bias of ~0.83 GHz/V (from g-factor change) and ~4.3 GHz/V (from B_tip change). SEC constants estimated (assuming ~5 Å gap) at ~0.4 Hz/(V/m) for g-factor and ~2.2 Hz/(V/m) for B_tip, compared to ~11.4 Hz/(V/m) reported for HoW10 nanomagnets.
• Tip field null point: At I_sp ≈ 250 pA near U_sp ≈ −140 mV, B_tip crosses zero, offering a "no tip influence" operating point to reduce tip-related systematic effects.
• Comparison to theory: Calculations for TiH on O-top site predicted ~0.2 GHz/V g-modulation; experiment observes roughly 4× larger g-related shift (even neglecting B_tip), likely due to site differences and additional bond or structural changes.
• Dimer control via SEC:
  • Strongly coupled dimer (644 pm, J ≈ 1.1 GHz): Three transitions (I–III) identified; bias tunes transitions, causing broadening and crossings. Transition III identified as a clock transition (requires unequal g-factors). Bias can align transitions II and III at the same external field.
  • Weaker dimer (1.04 nm, J ≈ 0.67 GHz): Singlet S approaches triplet |T0⟩, exhibiting an avoided crossing tunable with bias. Bias and tip–sample distance used to shift the avoided crossing position in bias without significantly changing the external field. Site-specific SEC inferred from differing bias sensitivities of transitions localized under or next to the tip.
• Coherence optimization: By increasing tip–sample distance, the avoided crossing is moved close to zero bias, minimizing tunneling current (dominant decoherence source) and maximizing coherence; homodyne detection reveals asymmetric ESR peaks at zero bias.

The results demonstrate that the STM junction bias voltage provides a powerful electric control parameter for atomic-scale spins by modulating both the g-factor and the tip magnetic field via electric-field-induced displacements and crystal field changes. This establishes spin-electric coupling in ESR-STM and shows that the resonance condition can be tuned by multiple line widths across modest voltage ranges. The interplay between tip–sample distance and bias complicates a clean separation of g-factor and tip-field contributions, highlighting that dipolar/exchange interactions and atomic, elastic, and electric forces all contribute. Nevertheless, the monotonic trends and stronger effects at higher currents support an electric-field-driven mechanism. Compared with bulk molecular systems, the frequency shifts per volt are orders of magnitude larger due to the extreme local fields in the tunneling junction, although the SEC constants per unit field can be smaller than optimized molecular nanomagnets. Importantly, in coupled dimers, SEC enables tuning of interaction-driven transitions, alignment of resonances, and control of avoided crossings, including moving them to zero bias to reduce decoherence. These capabilities directly address the goal of fast, scalable, and local electrical manipulation of spin states for quantum technologies.

This work establishes direct electrical control of atomic-scale spin transitions by exploiting the STM bias voltage in ESR-STM. The electric field in the junction tunes both the g-factor and the effective tip magnetic field, producing large, controllable ESR shifts and enabling precise manipulation of coupled-spin dimers, including clock-transition control and bias-positioning of avoided crossings near zero bias to enhance coherence. The approach adds bias voltage as a versatile degree of freedom alongside tip–sample distance for engineering complex spin Hamiltonians in situ. The findings pave the way for fast, coherent control schemes (e.g., qubit operations) and motivate exploration of SEC in other atoms/molecules, optimization of SEC strength, and investigations of electric-field effects on additional quantities such as magnetic anisotropy in higher-spin systems.

• The primary decoherence source is the tunneling current; minimizing current (e.g., at zero bias) is necessary to maximize coherence.
• Separation of g-factor and tip-field contributions is challenging due to intertwined dependencies on tip–sample distance and electric field.
• The study focuses on TiH on MgO (with bridge and O-top sites), so generality to other species/sites is inferred but not directly demonstrated.
• Linear dependence of g and B_tip on bias was assumed for modeling; deviations may occur outside the explored range.
• The TiH system was not optimized for maximal SEC; measured SEC constants per unit field are lower than those of optimized molecular nanomagnets.
• The procedure could not be tested on Fe atoms due to experimental limitations in the setup.