Efforts to miniaturize information storage to the single-atom level have primarily focused on manipulating the spin of magnetic atoms adsorbed on surfaces. This is because the orbital angular momentum (L) is often quenched due to the anisotropic crystal field and spin-orbit coupling, leaving spin (S) as the main controllable parameter. Even when some orbital moment remains, the spin-orbit interaction typically leads to superpositions of orbital and spin states, hindering independent control. The stability and lifetime of an atom's magnetization are directly affected by orbital quenching, necessitating a large single-site magnetic anisotropy for practical applications. This anisotropy arises from the interplay between the crystal field and spin-orbit coupling; a strong axial crystal field can help preserve the orbital moment and enhance anisotropy. 3d transition metals are attractive due to their abundance and ease of deposition and local probing. Previous studies on Fe and Co atoms on MgO/Ag(100) surfaces demonstrated nearly axial crystal fields and partially preserved orbital moments, resulting in large zero-field splittings. However, in these cases, the spin and orbital states were mixed, preventing independent excitations. This research aims to create a single-atom system exhibiting both a large magnetic anisotropy energy (MAE) and a fully unquenched orbital angular momentum along the uniaxial direction, allowing independent control over the spin and orbital degrees of freedom.

Prior research on single-atom magnets has largely focused on manipulating the spin due to the common quenching of the orbital angular momentum. Studies on Fe and Co atoms on MgO/Ag(100) surfaces demonstrated large zero-field splittings due to partially preserved orbital moments, but the spin and orbital states remained coupled, preventing independent control. This work builds upon these studies by aiming for a system with both large MAE and a fully unquenched orbital moment, enabling independent manipulation of spin and orbital degrees of freedom. The researchers cite several papers demonstrating previous work on single-atom magnetism, spin coupling, and magnetic anisotropy, highlighting the context of their work within the existing literature.

The experiment used a low-temperature, high-magnetic-field scanning tunneling microscope (STM). A monolayer of Cu₂N was grown on a Cu₃Au(100) surface, and individual Fe atoms were deposited. Inelastic electron tunneling spectroscopy (IETS) measurements were performed using standard lock-in techniques at 330 mK with a variable out-of-plane magnetic field. Multiplet calculations employed an anisotropic spin-orbit Hamiltonian, incorporating Stevens operators, spin-orbit coupling, and the Zeeman energy. The calculations used parameters obtained from fitting to energy spectra derived from multiorbital electronic Hamiltonians. The point-charge model (PCM) and a more accurate Wannier Hamiltonian approach, considering charge transfer and surface polarization, were both used. Transport calculations under the co-tunneling regime assumed electron-hole symmetry. The parameters for the anisotropic spin-orbit Hamiltonian were obtained by fitting the energy spectrum to results from multiorbital electronic Hamiltonian calculations at zero magnetic field. The authors also describe the parameters for the surface and tip hybridization constants, and the direct tunneling term used in the calculations.

The researchers successfully created a single-atom system with a large MAE (~18 meV) and a fully unquenched uniaxial orbital moment by positioning a Fe atom atop the nitrogen site of the Cu₂N/Cu₃Au(100) surface. IETS measurements revealed independent spin and orbital excitations. A spin excitation (ΔSz = ±1, ΔLz = 0) was observed with threshold voltages of 17.9 ± 0.7 meV and 19.4 ± 0.7 meV at 4T, corresponding to spin-only transitions between specific states. A higher-energy excitation (73.9 ± 0.8 meV) was identified as an orbital excitation (ΔLz = 4), representing a full, independent rotation of the unquenched orbital moment without altering the spin state. This orbital transition was explained by a co-tunneling mechanism mediated through a negatively charged virtual state. The magnetic field dependence of these excitations confirmed their assignment as independent spin and orbital transitions, with Zeeman shifts of 0.23 ± 0.04 meV/T and 0.31 ± 0.05 meV/T for spin and orbital transitions, respectively. The experimental results show remarkable agreement with theoretical transport calculations based on the PCM and the spin-orbit model, further corroborating the independent control of spin and orbital degrees of freedom. The conductance dependence of the inelastic electron transport was investigated, revealing nonlinearities due to longer relaxation times from state 1) than the average tunneling time. These non-equilibrium features decrease in strength with increasing current, attributed to the local field from the exchange interaction between the Fe atom and the tip. Simulations confirmed this behaviour.

The results demonstrate the ability to independently control the spin and orbital degrees of freedom in a single-atom system, opening up new possibilities for information processing at the atomic scale. The observation of a full reversal of the orbital moment via a single-electron tunneling event highlights the potential for manipulating both spin and orbital states independently for applications in quantum computing and spintronics. The good agreement between experimental data and theoretical calculations supports the validity of the proposed co-tunneling mechanism for the orbital excitation. The ability to independently manipulate both the spin and orbital angular momentum adds a new dimension to single-atom magnetism, potentially paving the way for designing extended lattices where interactions occur via both spin and orbital angular momenta.

This research successfully demonstrated independent control over the spin and orbital degrees of freedom of a single Fe atom by using a specific surface configuration (Fe atom on a nitrogen site of the Cu₂N lattice). The observed complete reversal of the orbital moment via a single-electron tunneling event, without affecting the spin, is a significant advance in single-atom magnetism. The findings open new avenues for exploring quantum phenomena and developing novel spintronic devices based on independent manipulation of both spin and orbital angular momentum. Future work could focus on extending this approach to create extended lattices that interact through both spin and orbital angular momentum, further expanding the possibilities for single-atom-based information processing.

While the study demonstrated remarkable agreement between experimental and theoretical results, some limitations should be noted. The experiments were conducted on individual atoms, and the results might not directly translate to extended lattices. Slight variations in measured threshold voltages were observed, possibly due to the tip field or variations in the local environment, influencing the accuracy of some measurements. The co-tunneling model used for the orbital excitation is a simplified representation of a complex phenomenon, and the validity of the assumption of electron-hole symmetry might be limited depending on experimental conditions.