Spin-Flip Inelastic Electron Tunneling Spectroscopy

• Spin-flip inelastic electron tunneling spectroscopy is a technique that probes localized magnetic excitations through inelastic electron tunneling using STM setups.
• It utilizes effective spin Hamiltonians, cotunneling processes, and non-equilibrium Green’s functions to quantitatively analyze spin transitions at the atomic scale.
• The method enables mapping of magnetic interactions and collective modes in systems like adatoms, molecular magnets, and spintronic devices with atomic spatial resolution.

Spin-flip inelastic electron tunneling spectroscopy (SF-IETS) is a technique that exploits the interplay between electronic transport and local spin excitations, providing direct access to the energy scales and selection rules governing magnetic excitations in nanoscale systems. By measuring the inelastic contributions to the tunneling current—typically as steps or peaks in the differential conductance (dI/dV) or its derivatives—SF-IETS enables quantitative spectroscopy of single-atom spins, molecular magnets, and extended magnetic systems with atomic spatial resolution.

1. Fundamental Mechanisms of Spin-Flip Inelastic Tunneling

In SF-IETS, a scanning tunneling microscope (STM) or related tunnel junction is used to drive electrons from a metallic tip to a substrate via a tunnel barrier containing a localized magnetic entity (adatom, chain, or molecule). When the energy of the tunneling electron exceeds the threshold for a local spin excitation, an inelastic tunneling process becomes possible, in which the electron exchanges energy and angular momentum with the magnetic object—effecting a transition (spin-flip) between spin eigenstates. This process is modeled using spin Hamiltonians for the local moment, such as

$$\mathcal{H} = -g\mu_B \vec{B} \cdot \vec{S} + D S_z^2 + E(S_x^2 - S_y^2)$$

where $D$ and $E$ quantify uniaxial and transverse magnetic anisotropies, $g$ is the gyromagnetic factor, and $\vec{B}$ is the external field. The onset of inelastic channels, visible as step-like increases in dI/dV at bias voltages corresponding to spin excitation energies, is governed by the coupling between the tunneling electron and the local spin, frequently described by exchange or cotunneling processes (1102.3788, 1103.3676).

The excitation event is often described within the sudden approximation, where an intermediate total spin state $|J, M_J\rangle$ (with $J = S \pm 1/2$) forms transiently during tunneling. The relative intensity of spin-flip transitions is encoded in matrix elements involving spin projection operators, with mixing parameters $c$ and $\phi$ quantifying the relative contributions and phase between $J = S+1/2$ and $J = S-1/2$ channels.

2. Theoretical and Modeling Approaches

The principal theoretical frameworks underlying SF-IETS include:

• Sudden Approximation and Effective Spin Hamiltonians: The tunneling event is modeled as a sudden perturbation, with inelastic transitions calculated using eigenstates of the effective spin Hamiltonian and Clebsch-Gordan algebra. The relative probability for inelastic tunneling is given by

$I_\text{inel} = 1 - \frac{X_\text{el}}{Z}$

where $X_\text{el}$ and $Z$ denote, respectively, the elastic and total transition probability sums over relevant quantum numbers (1102.3788).

• Cotunneling and Anderson/Kondo Models: In systems deep in Coulomb blockade (e.g., adatoms and molecules on surfaces), electrons tunnel via second-order (cotunneling) processes. The virtual occupation of charge states provides a microscopic mechanism for spin-flip excitations and connects in the appropriate limit to the effective Kondo exchange Hamiltonian (1103.3676).
• Non-equilibrium Green’s Function Formalism: For atomic chains and more complex structures, the s-d model and NEGF methods are used. Here, the self-energy due to spin-flip scattering is introduced perturbatively (Born approximation), capturing the opening of inelastic channels and yielding the full I–V and dI/dV spectra (1103.2652). Selection rules and transition intensities follow from the spin matrix elements $|\langle m | S^i | n \rangle|^2$ weighted by occupancy.
• First-Principles Methods: Advanced ab initio approaches, such as combining Korringa-Kohn-Rostoker (KKR) Green’s function, time-dependent density functional theory (TDDFT), and many-body perturbation theory, enable evaluation of the electron self-energy due to coupling with spin excitations, predicting complex spectral features including line-shape asymmetries and satellite peaks beyond the simple step structure (Schweflinghaus et al., 2014).
• Many-Body Treatments and Temperature Effects: Extensions using non-crossing approximation (NCA) and self-consistent ladder approximation (SCLA) permit quantitative inclusion of Kondo-like correlations, yielding additional peaks near excitation thresholds, gap renormalization, and detailed temperature evolution distinct from simple one-electron models (1112.6288).

3. Experimental Control and Dependencies

The amplitude and nature of the inelastic signal in SF-IETS depend on both intrinsic and extrinsic parameters:

• Intrinsic: Spin quantum number $S$, magnetic anisotropy parameters $D$ and $E$, and the detailed excitation spectrum of the local moment dictate the energy thresholds, selection rules, and allowed transitions.
• Extrinsic: Experimental conditions such as tip–sample distance and resultant tunnel junction resistance ($R$) critically affect the observed inelastic signal. Increased distance leads to enhanced "by-tunneling" (electrons circumventing the magnetic site), decreasing the inelastic contribution $I_\text{inel}$ as fewer electrons interact with the spin-active region (1102.3788). Bulk doping and accompanying band bending modulate the two-dimensional electron system (2DES) and can influence the effective energy alignment but typically have a smaller effect on $I_\text{inel}$ than geometric tunneling parameters.

Symmetry breaking, either via asymmetric coupling or additional interaction channels (e.g., hyperfine coupling), can enable otherwise forbidden inelastic transitions, as exemplified by the Mn dimer case where symmetry-suppressed signals are enhanced through nuclear spin coupling or tip asymmetry (Delgado et al., 2022).

4. Advanced Applications: Collective Modes and Spatially Resolved Spectroscopy

For extended systems, such as atomic chains or engineered nanographene ribbons, SF-IETS enables the real-space mapping and momentum-resolved characterization of collective spin excitations:

• Collective Excitations: In atomic chains, the spatially resolved second derivative of the tunneling current can be Fourier transformed to reconstruct magnon and triplon dispersion relations when the excitations form standing waves. This method, termed Scanning Tunneling Energy Dispersion Spectroscopy (STEDS), retrieves energy–momentum relations in systems without translational symmetry (Henriques et al., 19 Feb 2025). The approach is effective when excitations can be approximated as standing waves (e.g., ferromagnets, dimerized antiferromagnets) but not for spinon continua in homogeneous antiferromagnetic chains where excitations are inherently fractionalized.
• Detection of Spin Density of States: For large or complex systems where no discrete steps are visible in dI/dV, the local spin density of states can be extracted via the double differential conductance $d^2I/dV^2$. This facilitates probing of both gapless and gapped modes, including collective magnon modes and localized edge states, even in the presence of broad continua (Rist et al., 23 Jul 2025).
• Spatial Oscillations and Friedel Patterns: Spin-inelastic Friedel oscillations, resulting from spatially modulated inelastic scattering at magnetic impurities, manifest as oscillations in $d^2I/dV^2$ with wavevectors determined by excitation energies. These have been predicted and imaged using STM, offering a spatial probe of the energy spectrum of local spin transitions (1108.3217).

5. Material Platforms and Functional Integration

SF-IETS has been applied across a wide range of systems, including:

• Transition metal adatoms and molecules: Mn, Fe, Co, Ni centers on various substrates provide model systems for single-spin physics, Kondo effects, and the impact of anisotropy (Schweflinghaus et al., 2014, Ormaza et al., 2016).
• Molecular junctions and functionalized tips: Attaching molecules such as nickelocene to STM tips creates spin-active probes, enhancing sensitivity and enabling double excitation processes, resulting in significant amplification of inelastic signals (Ormaza et al., 2016).
• Spintronic Tunnel Junctions: Inelastic spectroscopy is crucial in assessing spin-filter junctions, where spin-flip scattering during tunneling limits the spin injection efficiency. Suppression of inelastic (especially magnon-mediated) processes via Fermi surface matching between electrodes improves device performance, directly verified using IETS (1207.5372).
• Topological quantum materials: In topological insulators (TIs) and quantum spin liquids (QSLs), the interplay between spin-momentum locked surface states and spin excitations leads to unique conductance features. In TIs, strong helical edge currents can suppress inelastic spin-flip signatures at low current densities, with conductance steps reappearing only upon significant spin pumping (1209.1579, 1209.2055). In QSLs, spin-flip scattering at fractionalized excitations generates gapped conductance features absent in conventional systems (König et al., 2020).

6. Signal Analysis, Limitations, and Practical Considerations

Key implementation details involve:

• Separation of Elastic and Inelastic Contributions: The relative weights of elastic and inelastic tunneling must be accurately disentangled, often using sudden approximation models and signal decomposition techniques. The inelastic contribution $I_\text{inel} = 1 - (X_\text{el}/Z)$ links directly to spectroscopic features (1102.3788).
• Temperature Effects: Finite temperature induces thermal broadening, smearing spectral features. Many-body peaks near excitation thresholds are robust up to temperatures much larger than the Kondo scale, while step positions shift due to many-body renormalizations (1112.6288).
• Role of Device Geometry and Junction Engineering: Control over tip position, distance, and the possibility of by-tunneling is vital for quantitative spectroscopy. As symmetry effects can suppress or enhance signal magnitude, device design and junction asymmetry (intentional or accidental) may critically affect experimental observables (Delgado et al., 2022).
• Direct Extraction of Spin Density of States: For large systems, the calculation and measurement of $d^2I/dV^2$ enables mapping of the spin LDOS, even when dI/dV does not show well-defined steps (Rist et al., 23 Jul 2025).

7. Impact, Extensions, and Future Directions

SF-IETS constitutes a crucial probe for magnetic excitations at the atomic scale. Its sensitivity to selection rules, collective excitations, and device geometry allows in-depth characterization of quantum magnets, molecular spins, magnetic junctions, and topological phases. The integration with first-principles calculations, many-body physics, and nonequilibrium approaches has extended interpretive reach to systems exhibiting Kondo correlations, quantum phase transitions, and fractionalization.

Notably, SF-IETS has enabled:

• Measurement of magnon and triplon dispersions in finite systems via local probes and Fourier analysis (Henriques et al., 19 Feb 2025).
• Identification of zero-frequency edge modes and in-gap excitations through specialized analysis of differential conductance (Rist et al., 23 Jul 2025).
• Optimization of spintronic devices by quantifying the impact of inelastic spin-flip scattering on spin transport and injection (1207.5372).
• Probing of spin-flip resonances and broad continuum excitations in quantum spin liquids and topological insulators, distinguishing fractionalized from magnonic excitations via tunneling spectroscopy (1209.1579, König et al., 2020).

The continued evolution of SF-IETS—combining spatial mapping, double-differential spectroscopy, and integration with quantum transport models—supports both fundamental studies of spin and correlation phenomena and the engineering of next-generation quantum materials and devices.