Anisotropy induced Kondo splitting in a mechanically stretched molecular junction: A first-principles based study

Differences in Kondo Splitting of Surface Quantum Systems Induced by Two Distinct Magnetic Tips: A Joint Method of DFT and HEOM

The interactions between a magnetic tip and local spin impurities initiate unconventional Kondo phenomena, such as asymmetric suppression or even splitting of the Kondo peak. However, a lack of realistic theoretical models and comprehensive explanations for this phenomenon persists due to the complexity of the interactions. This research employs a joint method of density functional theory (DFT) and hierarchical equation of motion (HEOM) to simulate and contrast the modulation of the spin state and Kondo behavior in the Fe/Cu(100) system with two distinct magnetic tips. A cobalt tip, possessing a larger magnetic moment, incites greater atomic displacement of the iron atom, more notable alterations in electronic structure, and enhanced charge transfer with the environment compared with the control process utilizing a nickel tip. Furthermore, the Kondo resonance undergoes asymmetric splitting as a result of the ferromagnetic correlation between the iron atom and the magnetic tip. The Co tip's higher spin polarization results in a wider spacing between the splitting peaks. This investigation underscores the precision of the DFT + HEOM approach in predicting complex quantum phenomena and explaining the underlying physical principles. This provides valuable theoretical support for developing more sophisticated quantum regulation experiments.

Tweezer-like magnetic tip control of the local spin state in the FeOEP/Pb(111) adsorption system: a preliminary exploration based on first-principles calculations

The magnetic interactions between the spin-polarized scanning tunnelling microscopy (SP-STM) tip and the localized spin impurities lead to various forms of the Kondo effect. Although these intriguing phenomena enrich Kondo physics, detailed theoretical simulations and explanations are still lacking due to the rather complex formation mechanisms. Here, by combining density functional theory (DFT), complete active space self-consistent field (CASSCF) theory, and hierarchical equations of motion (HEOM) methods, we perform first-principles-based simulation to elaborate the regulation process of the magnetic Co-tip on the spin state and transport behaviour of FeOEP/Pb(111) system. Compared with the non-magnetic tip, the stronger interaction between the magnetic tip and FeOEP molecule results in a more drastic deformation of the molecular structure with more electron transfer from the local environment to Fe-3d orbitals. The magnetic anisotropy of FeOEP changes very drastically from positive values in the tunnelling region to negative values in the contact region. The ferromagnetic electron correlation between the magnetic tip and the molecule induces an asymmetric Kondo line-shape near the Fermi level. This work highlights that the DFT + CASSCF + HEOM approach can not only predict complex quantum phenomena and explain underlying physical mechanisms, but also facilitate the design of more fascinating quantum control experiments.

Hierarchical equations of motion approach for accurate characterization of spin excitations in quantum impurity systems

Recent technological advancement in scanning tunneling microscopes has enabled the measurement of spin-field and spin-spin interactions in single atomic or molecular junctions with an unprecedentedly high resolution. Theoretically, although the fermionic hierarchical equations of motion (HEOM) method has been widely applied to investigate the strongly correlated Kondo states in these junctions, the existence of low-energy spin excitations presents new challenges to numerical simulations. These include the quest for a more accurate and efficient decomposition for the non-Markovian memory of low-temperature environments and a more careful handling of errors caused by the truncation of the hierarchy. In this work, we propose several new algorithms, which significantly enhance the performance of the HEOM method, as exemplified by the calculations on systems involving various types of low-energy spin excitations. Being able to characterize both the Kondo effect and spin excitation accurately, the HEOM method offers a sophisticated and versatile theoretical tool, which is valuable for the understanding and even prediction of the fascinating quantum phenomena explored in cutting-edge experiments.

Unveiling the Decisive Factor for the Sharp Transition in the Scanning Tunneling Spectroscopy of a Single Nickelocene Molecule

Scanning tunneling microscopy (STM) has been utilized to realize the precise measurement and control of local spin states. Experiments have demonstrated that when a nickelocene (Nc) molecule is attached to the apex of an STM tip, the dI/dV spectra exhibit a sharp or a smooth transition when the tip is displaced toward the substrate. However, what leads to the two distinct types of transitions remains unclear, and more intriguingly, the physical origin of the abrupt change in the line shape of dI/dV spectra remains unclear. To clarify these intriguing issues, we perform first-principles-based simulations on the STM tip control process for the Cu tip/Nc/Cu(100) junction. In particular, we find that the suddenly enhanced hybridization between the d orbitals on the Ni ion and the metallic bands in the substrate leads to Kondo correlation overwhelming spin excitation, which is the main cause of the sharp transition in the dI/dV spectra observed experimentally.

Unravelling the robustness of magnetic anisotropy of a nickelocene molecule in different environments: a first-principles-based study

Recent scanning tunneling spectroscopy with single metallocene molecule-functionalized tips have proved to be a powerful tool to probe and control individual spins and spin-spin exchange interactions due to the robustness of the magnetic properties of the metallocene molecule in different surroundings. However, accurate prediction of such robustness at a first-principles-based level by the conventional density functional theory (DFT) has remained challenging. In this paper, we have performed a detailed investigation of the evolution of electronic and magnetic properties of a nickelocene molecule (NiCp₂) in different environments, i.e., free-standing, adsorbed on Cu(100) and as a functionalized tip apex. Using an embedding method, which combines DFT and the complete active space self-consistent field (CASSCF) method recently developed, we demonstrate that the nickelocene molecule almost preserves its spin and magnetic anisotropy upon adsorption on Cu(100), and also in the position of the tip apex. In particular, the cyclic π* orbital of the Cp rings could hybridize with the singly occupied d_π orbitals of the Ni center of the molecule, protecting these orbitals from external states. Hence the molecular spin maintains S = 1, the same as in the free-standing case, and its magnetic anisotropy is also robust with energies of 3.56, 3.34, and 3.51 meV in free-standing, adsorbed on Cu(100), and functionalized tip apex states, respectively, in good agreement with previous theoretical and experimental results. This work thus provides a first-principles-based understanding of the relevant experiments. Such agreement between theoretical simulations and experimental measurements highlights the potential usefulness of the method for investigating the local electronic and spin states of organometallic molecule-surface composite systems.

Origin of Asymmetric Splitting of Kondo Peak in Spin-Polarized Scanning Tunneling Spectroscopy: Insights from First-Principles-Based Simulations

The spin-polarized scanning tunneling microscope (SP-STM) has served as a versatile tool for probing and manipulating the spintronic properties of atomic and molecular devices with high precision. The interplay between the local spin state and its surrounding magnetic environment significantly affects the transport behavior of the device. Particularly, in the contact regime, the strong hybridization between the SP-STM tip and the magnetic atom or molecule could give rise to unconventional Kondo resonance signatures in the differential conductance (dI/dV) spectra. This poses challenges for the simulation of a realistic tip control process. By combining the density functional theory and the hierarchical equations of motion methods, we achieve first-principles-based simulation of the control of a Ni-tip/Co/Cu(100) junction in both the tunneling and contact regimes. The calculated dI/dV spectra reproduce faithfully the experimental data. A cotunneling mechanism is proposed to elucidate the physical origin of the observed unconventional Kondo signatures.

Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)

An open quantum system refers to a system that is further coupled to a bath system consisting of surrounding radiation fields, atoms, molecules, or proteins. The bath system is typically modeled by an infinite number of harmonic oscillators. This system-bath model can describe the time-irreversible dynamics through which the system evolves toward a thermal equilibrium state at finite temperature. In nuclear magnetic resonance and atomic spectroscopy, dynamics can be studied easily by using simple quantum master equations under the assumption that the system-bath interaction is weak (perturbative approximation) and the bath fluctuations are very fast (Markovian approximation). However, such approximations cannot be applied in chemical physics and biochemical physics problems, where environmental materials are complex and strongly coupled with environments. The hierarchical equations of motion (HEOM) can describe the numerically "exact" dynamics of a reduced system under nonperturbative and non-Markovian system-bath interactions, which has been verified on the basis of exact analytical solutions (non-Markovian tests) with any desired numerical accuracy. The HEOM theory has been used to treat systems of practical interest, in particular, to account for various linear and nonlinear spectra in molecular and solid state materials, to evaluate charge and exciton transfer rates in biological systems, to simulate resonant tunneling and quantum ratchet processes in nanodevices, and to explore quantum entanglement states in quantum information theories. This article presents an overview of the HEOM theory, focusing on its theoretical background and applications, to help further the development of the study of open quantum dynamics.

Electronic and magnetic properties of CoPc and FePc molecules on graphene: the substrate, defect, and hydrogen adsorption effects

Transition metal phthalocyanines (TMPcs) are particularly appealing for spintronic processing and data storage devices due to their structural simplicity and functional flexibility. To realize effective control of the spins in TMPc-based systems, it is necessary to quantify how the structural and chemical environment of the molecule affects its spin center. Herein we perform a detailed investigation of the electronic and spintronic properties of vertically stacked heterostructures formed by CoPc or FePc adsorbed on a monolayer of graphene under the influences of the gold substrate, vacancies in graphene, and extra atomic hydrogen coordination on the TMPc. By using density functional theory (DFT), we reveal that both the TMPc molecules prefer the carbon-top position on graphene, and the existence of the Au substrate enhances the stability of the adsorption, while this enhanced adsorption will not modify the molecular magnetism, keeping it the same value as in the free standing case. Moreover, with the aid of a combination of DFT and ab initio wavefunction-based calculations, our results indicate that the magnetic anisotropy of the FePc-graphene complex can be actively tuned by the Au substrate. Our calculations also show that defects in graphene including single and double vacancies can modify the magnetism of these heterostructures. In particular, the spin state of FePc can be tuned from S = 1 to S = 2 with such defect engineering. Further spin state tunability can be achieved from a hydrogenation process, with the coordination of one extra hydrogen on the Co-top site for CoPc and the pyridinic N site for FePc, respectively, tuning their spin states from S = 1/2 to S = 0 and from S = 1 to S = 2. These findings may prove to be instrumental for rational design of future molecular spintronics devices integrated with two-dimensional materials.

Simulation of inelastic spin flip excitations and Kondo effect in STM spectroscopy of magnetic molecules on metal substrates

Single-ion magnetic anisotropy in molecular magnets leads to spin flip excitations that can be measured by inelastic scanning tunneling microscope (STM) spectroscopy. Here I present a semi ab initio scheme to compute the spectral features associated with inelastic spin flip excitations and Kondo effect of single molecular magnets. To this end density functional theory calculations of the molecule on the substrate are combined with more sophisticated many-body techniques for solving the Anderson impurity problem of the spin-carrying orbitals of the magnetic molecule coupled to the rest of the system, containing a phenomenological magnetic anisotropy term. For calculating the STM spectra an exact expression for the [Formula: see text] in the ideal STM limit, when the coupling to the STM tip becomes negligibly small, is derived. In this limit the [Formula: see text] is simply related to the spectral function of the molecule-substrate system. For the case of an Fe porphyrin molecule on the Au(1 1 1) substrate, the calculated STM spectra are in good agreement with recently measured STM spectra, showing the typical step features at finite bias associated with spin flip excitation of a spin-1 quantum magnet. For the case of Kondo effect in Mn porphyrin on Au(1 1 1), the agreement with the experimental spectra is not as good due to the neglect of quantum interference in the tunneling.

On the exact truncation tier of fermionic hierarchical equations of motion

The hierarchical equations of motion (HEOM) theory is in principle exact for describing the dissipative dynamics of quantum systems linearly coupled to Gaussian environments. In practice, the hierarchy needs to be truncated at a finite tier. We demonstrate that, for general systems described by the fermionic HEOM, the (n+L̃)th-tier truncation with L̃=2N_σN_ν yields the exact density operators up to the nth tier. Here, N_σ = 2 for fermionic systems and N_ν is the system degrees of freedom. For noninteracting systems, L̃ is further reduced by half. Such an exact termination pattern originates from the Pauli exclusion principle for fermions, and it holds true regardless of the system-environment coupling strength, the number of coupling reservoirs, or the specific scheme employed to unravel the environment memory contents. The relatively small L̃ emphasizes the nonperturbative nature of the HEOM theory. We also propose a simplified HEOM approach to further reduce the memory cost for practical calculations.

Precise Control of Local Spin States in an Adsorbed Magnetic Molecule with an STM Tip: Theoretical Insights from First-Principles-Based Simulation

The precise tuning of local spin states in adsorbed organometallic molecules by a mechanically controlled scanning tunneling microscope (STM) tip has become a focus of recent experiments. However, the underlying mechanisms remain somewhat unclear. We investigate theoretically the STM tip control of local spin states in a single iron(II) porphyrin molecule adsorbed on the Pb(111) substrate. A combined density functional theory and hierarchical equations of motion approach is employed to simulate the tip tuning process in conjunction with the complete active space self-consistent field method for accurate computation of magnetic anisotropy. Our first-principles-based simulation accurately reproduces the tuning of magnetic anisotropy realized in experiment. Moreover, we elucidate the evolution of geometric and electronic structures of the composite junction and disclose the delicate competition between the Kondo resonance and local spin excitation. The understanding and insight provided by the first-principles-based simulation may help to realize more fascinating quantum state manipulations.

Manipulation of spin and magnetic anisotropy in bilayer magnetic molecular junctions

The Kondo effect and magnetic anisotropy in bilayer TMPc/TMPc/Pb(111) junctions can be actively tuned by changing the intermediate decoupling layer.