Unraveling the Nature of Spin Coupling in a Metal-Free Diradical: Theoretical Distinction of Ferromagnetic and Antiferromagnetic Interactions.

Metal-free diradicals based on polycyclic aromatic hydrocarbons are promising candidates for organic spintronics due to their stable magnetism and tunable spin coupling. However, distinguishing and elucidating the origins of ferromagnetic and antiferromagnetic interactions in these systems remain challenging. Here, we investigate the 2-OS diradical molecule sandwiched between gold electrodes using a combined density functional theory and hierarchical equations of motion approach. We find that the dihedral angle between the radical moieties controls the nature and strength of the intramolecular spin coupling, transitioning smoothly from antiferromagnetic to ferromagnetic as the angle increases. Distinct features in the inelastic electron tunneling spectra are identified that can discern the two coupling regimes, including spin excitation steps whose energies directly reveal the exchange coupling constant. Mechanical stretching of the junction is predicted to modulate the spectral line shapes by adjusting the hybridization of the molecular radicals with the electrodes. Our work elucidates the electronic origin of tunable spin interactions in 2-OS and provides spectroscopic fingerprints for characterizing magnetism in metal-free diradicals.

Unconventional Surface Doping Effect on the Spin State of an Adsorbed Magnetic Molecule.

Magnetic molecules adsorbed on two-dimensional (2D) substrates have attracted broad attention because of their potential applications in quantum device applications. Experimental observations have demonstrated substantial alteration in the spin excitation energy of iron phthalocyanine (FePc) molecules when adsorbed on nitrogen-doped graphene substrates. However, the underlying mechanism responsible for this notable change remains unclear. To shed light on this, we employ an embedding method and ab initio quantum chemistry calculations to investigate the effects of surface doping on molecular properties. Our study unveils an unconventional chemical bonding at the interface between the FePc molecule and the N-doped graphene. This bonding interaction, stronger than non-covalent interactions, significantly modifies the magnetic anisotropy energy of the adsorbed molecule, consistent with experimental observations. These findings provide valuable insights into the electronic and magnetic properties of molecules on 2D substrates, offering a promising pathway for precise manipulation of molecular spin states.

Square Root Statistics of Density Matrices and Their Applications.

To estimate the degree of quantum entanglement of random pure states, it is crucial to understand the statistical behavior of entanglement indicators such as the von Neumann entropy, quantum purity, and entanglement capacity. These entanglement metrics are functions of the spectrum of density matrices, and their statistical behavior over different generic state ensembles have been intensively studied in the literature. As an alternative metric, in this work, we study the sum of the square root spectrum of density matrices, which is relevant to negativity and fidelity in quantum information processing. In particular, we derive the finite-size mean and variance formulas of the sum of the square root spectrum over the Bures-Hall ensemble, extending known results obtained recently over the Hilbert-Schmidt ensemble.

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.

On the practical truncation tier of fermionic hierarchical equations of motion.

The fermionic hierarchical equations of motion (HEOM) approach has found wide application in the exploration of open quantum systems, and extensive efforts have been committed to improving its efficiency and accuracy in practical calculations. In this work, by scrutinizing the stationary-state and dynamic properties of Kondo-correlated quantum impurity systems, we show that the strength of Kondo correlation induced by the system-environment entanglement primarily determines the converged hierarchical truncation tier of the HEOM method. This complements the rule of thumb regarding the positive correlation between the height of hierarchy and system-environment coupling strength. These insights will provide useful guidelines for developing a more sophisticated fermionic HEOM method for the investigation of many-body open quantum systems.

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.

Magnet-Free Time-Resolved Magnetic Circular Dichroism with Pulsed Vector Beams.

Magnetic circular dichroism (MCD) is a widely used spectroscopic technique which reveals valuable information about molecular geometry and electronic structure. However, the weak signal and the necessary strong magnets impose major limitations on its application. We propose a novel protocol to overcome these limitations by using pulsed vector beams (VBs), which consist of nanosecond gigahertz pump and femtosecond UV-vis probe pulses. By virtue of the strong longitudinal electromagnetic fields, the MCD signal detected by using the pulsed VBs is greatly enhanced compared to conventional MCD performed with plane waves. Furthermore, varying the pump-probe time delay allows monitoring the ultrafast variation of molecular properties.

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.

Enhancing Circular Dichroism Signals with Vector Beams.

Circular dichroism (CD) is broadly employed for distinguishing molecular chiralities. However, its practical application is often limited by the weak magnitude of chiral signal. We propose to use azimuthally and radially polarized vector beams to probe CD spectra. By taking advantage of the strong longitudinal components of the vector beams, the transmitted light can be detected in the radial direction. The resulting CD signal is several orders of magnitude stronger than conventional CD signal with plane waves. Quantitative analysis and numerical simulations show that the enhancement factor is independent of molecular properties and can be increased by decreasing the path length of the sample cuvette and the interaction cross section between the light beam and molecular sample. The proposed novel CD spectroscopy is feasible with the current optical technology.

Probing Molecular Chirality by Orbital-Angular-Momentum-Carrying X-ray Pulses.

A twisted X-ray beam with orbital angular momentum is employed in a theoretical study to probe molecular chirality. A nonlocal response description of the matter-field coupling is adopted to account for the field short wavelength and the structured spatial profile. We use the minimal-coupling Hamiltonian, which implicitly takes into account the multipole contributions to all orders. The combined interactions of the spin and orbital angular momentum of the X-ray beam give rise to circular-helical dichroism signals, which are stronger than ordinary circular dichroism signals, and may serve as a useful tool for the study of molecular chirality in the X-ray regime.

Monitoring Spontaneous Charge-Density Fluctuations by Single-Molecule Diffraction of Quantum Light.

Homodyne X-ray diffraction signals produced by classical light and classical detectors are given by the modulus square of the charge density in momentum space |σ(q)|2, missing its phase, which is required in order to invert the signal to real space. We show that quantum detection of the radiation field yields a linear diffraction pattern that reveals σ(q) itself, including the phase. We further show that repeated diffraction measurements with variable delays constitute a novel multidimensional measure of spontaneous charge-density fluctuations. Classical diffraction, in contrast, only reveals a subclass of even-order correlation functions. Simulations of two-dimensional signals obtained by two diffraction events are presented for the amino acid cysteine.

Imaging electron-density fluctuations by multidimensional X-ray photon-coincidence diffraction.

The ultrafast spontaneous electron-density fluctuation dynamics in molecules is studied theoretically by off-resonant multiple X-ray diffraction events. The time- and wavevector-resolved photon-coincidence signals give an image of electron-density fluctuations expressed through the four-point correlation function of the charge density in momentum space. A Fourier transform of the signal provides a real-space image of the multipoint charge-density correlation functions, which reveal snapshots of the evolving electron density in between the diffraction events. The proposed technique is illustrated by ab initio simulations of the momentum- and real-space inelastic scattering signals from a linear cyanotetracetylene molecule.