arXiv subjects

Christoph Wolf

Publications and source records attributed to Christoph Wolf.

At least 19 recordsLinked to original sources

arXiv2026

Theory of Electron Spin Resonance Scanning Tunneling Microscopy: The First Decade

Electron spin resonance in scanning tunneling microscopy enabled the study of electronic transitions of magnetic impurities on surfaces at the atomic scale. This ESR-STM technique allows to spectroscopically probe and coherently manipulate spins using an all-electrical method without oscillating external magnetic driving fields. Here, we aim to review recent advancements in ESR-STM. We will discuss possible fundamental mechanisms by which the electric field drives spin resonance based on Heisenberg exchange, Kondo scattering, and Anderson impurity models. We validate theoretical predictions against experimental observations, to understand how electronic correlations, spin exchange, and many-body effects manifest in ESR-STM signals. After reviewing coherent spin control in the STM junction, we discuss potential applications of the ESR-STM method for coherent multi-spin control which enables multiple-qubit operations. Finally, we address recent developments in coupled electron-nuclear spin systems, including hyperfine-resolved ESR spectroscopy, and the driving and polarization of nuclear spins in ESR-STM.

cond-mat.mes-hall↗

arXiv2026

Probing the Weak-Driving Quantum Speed Limit via Drift-Aware Shooting Methods

A central goal of quantum optimal control is to achieve high-fidelity and low-energy control pulses. When quantum optimal control methods optimize every point of a pulse discretized over small time steps independently this can yield high fidelity control but also results in broadband and energy-hungry waveforms. We extend MAGICARP -- a shooting method inspired by Pontryagin's maximum principle on energy that generates an entire pulse from a small set of parameters, making it smooth and energy-efficient by construction -- from driftless systems to closed systems with the constant drift Hamiltonian of two exchange-coupled spins in an external magnetic field. The optimization proceeds in stages: the dressed states of the drift Hamiltonian structure the target, an initial shooting optimization is performed in the rotating-wave frame, and an exact laboratory-frame refinement follows. Benchmarked against Krotov and GRAPE at matched gate infidelity, MAGICARP consistently achieves the lowest energy and a conserved pulse area, concentrates its spectral weight on the gate-relevant transitions, and is the most robust to fluctuations in the exchange coupling; GRAPE independently converges to essentially the same pulse, while Krotov's method pays an order-of-magnitude energy premium. Moreover, a large statistical survey of unselected optimization runs resolves a weak-driving quantum speed limit for two exchange-coupled electron spins: low-amplitude realizations of the two-qubit quantum Fourier transform cease to exist below a critical gate time $T^*$ set by the drift's interaction rate, and the minimum control energy diverges on approach to this limit. The divergence obeys a simple two-parameter area-pole law, $E_2^{\mathrm{law}}(T)=A/T+B/(T-T^*)$, whose first term is the time-optimal area cost and whose second term is a pole at the speed limit.

quant-ph↗

arXiv2026

Quantifying water-driven geometric uncertainties in powder bed concrete printing using high-resolution 3D modeling

Dimensional accuracy in powder bed 3D printing of concrete is strongly influenced by binder distribution, and the resulting geometric deviations can be direction-dependent. This study examines how voxel-wise water dosage influences geometric fidelity and deviation anisotropy. Experiments show that small changes in water content can cause large, systematic deviations, including edge rounding and swelling. We quantify these effects using high-resolution stereophotogrammetry, aligning as-built scans with CAD models. We then compute deviation metrics such as point-wise distance errors and volumetric differences across multiple water-dosage settings, revealing repeatable, directionally biased deformation patterns that intensify with higher water content. Mechanical testing indicates that stiffness and strength change only marginally, with no clear trend in the tested range. This is explained by excess voxel water diffusing into surrounding powder, leaving the effective water-cement ratio largely unchanged. Finally, we demonstrate a design-compensation concept that pre-adjusts digital geometry to counter predictable deviations, improving accuracy without post-processing.

cs.CE↗

arXiv2026

An ab initio approach to energy alignment and charge-state prediction of adsorbates on ultrathin insulators

The rapid progress of electron spin resonance scanning tunneling microscopy experiments has enabled the manipulation of individual adsorbate spin states physisorbed on ultrathin oxide layers supported on metal substrates. Electron resonance requires unpaired spin density on the adsorbate, which can be achieved, for instance, through charge transfer from the supporting substrate. This requires the correct energy-level alignment between the energy levels of the adsorbate and the Fermi energy of the substrate. Experiments on molecules and single atoms adsorbed on metal-insulator systems have revealed complex phenomena, including electronic bandgap narrowing, charge transfer, Fermi-level pinning, and the re-ordering of adsorbate orbitals after charge transfer. Despite these advances, a predictive first-principles approach based on accurate methods such as quasiparticle GW, capable of capturing these effects without the prohibitive cost of full adsorbate/oxide/metal simulations, remains an open challenge. In this work, we present a theoretical approach to determine the energy-level alignment of adsorbates on oxide/metal substrates. Our method transparently exposes all physical processes and strikes a balance between computational cost and accuracy. Ionization potentials and electron affinities of the isolated adsorbates are obtained using GW calculations, electronic bandgap polarization is quantified through the quasiparticle renormalization caused by the substrate, Fermi-level pinning is evaluated within the integer charge transfer model, and work function shifts arising from Pauli pushback or from the adsorbate-metal dipole are determined from the local variations of the electrostatic potential. This computationally efficient framework paves the way for highthroughput screening of molecular qubits and organic electronic interfaces.

cond-mat.mes-hall↗

arXiv2026

On the interpretation of Hahn echo measurements in electron spin resonance scanning tunneling microscopy

Electron spin resonance scanning tunneling microscopy (ESR-STM) has become a powerful tool for probing spin dynamics and coherence of individual atoms and molecules on surfaces. In this work, we perform Rabi oscillation and Hahn echo pulse protocols on individual iron phthalocyanine (FePc) molecules on MgO/Ag(001) using ESR-STM. While Hahn echo protocols are widely used to extract spin coherence times, we show that in ESR-STM they are particularly susceptible to misinterpretation due to tunneling electrons generated by the applied radio-frequency (RF) voltage. The RF voltage not only drives the spin, but simultaneously probes and relaxes it, which consequently leads to an exponential decay that reflects spin relaxation rather than intrinsic phase coherence. We moreover show that varying both delay times in the refocusing pulse sequence is a reliable way to ensure a coherent nature of the echo signal. The extracted decay for the latter protocol suggests that T2 is approximately 30 ns and is thus closer to the decoherence time observed in Rabi oscillation measurements. This is significantly shorter than values reported in previous echo measurements. Our findings underscore the need for caution in interpreting T2 times from Hahn echo and Carr-Purcell protocols in ESR-STM and provide practical criteria for distinguishing true spin echoes from tunneling-induced relaxometry signals.

cond-mat.mes-hall↗

arXiv2025

Overcoming limitations on gate fidelity in noisy static exchange-coupled surface qubits

Recent experiments demonstrated that the spin state of individual atoms on surfaces can be quantum-coherently controlled through all-electric electron spin resonance. By constructing interacting arrays of atoms this results in an atomic-scale qubit platform. However, the static exchange coupling between qubits, limited lifetime and polarization of the initial state, impose significant limits on high-fidelity quantum control. We address this issue using open quantum systems simulation and quantum optimal control theory. We demonstrate the conditions under which high-fidelity operations ($\mathcal{F} \gtrsim 0.9$) are feasible in this qubit platform, and show how the Krotov method of quantum optimal control theory adapts to specific noise sources to outperform the conventional Rabi drivings. Finally, we re-examine the experimental setup used in the initial demonstration of this qubit platform and propose optimized experimental designs to maximize gate fidelity in this platform.

quant-ph↗

arXiv2025

Spin-State Engineering of Single Titanium Adsorbates on Ultrathin Magnesium Oxide

Single atomic adsorbates on ultrathin insulating films provide a promising route toward bottom-up quantum architectures based on atomically identical yet individually addressable spin qubits on solid surfaces. A key challenge in engineering quantum-coherent spin nanostructures lies in understanding and controlling the spin state of individual adsorbates. In this work, we investigate single titanium (Ti) atoms adsorbed on MgO/Ag(100) surfaces using a combined scanning tunneling microscopy and electron spin resonance. Our measurements reveal two distinct spin states, $S = 1/2$ and $S = 1$, depending on the local adsorption site and the thickness of the MgO film. Density functional theory calculations suggest a Ti$^+$ configuration for the Ti adsorbates with approximately 3 electrons in the 4$s$ and 3$d$ valence shells. Using a multi-orbital atomic multiplet calculations the site dependence of the spin can be rationalized as a charge redistribution between spin-polarizing and depolarizing orbitals. These findings underscore the potential of surface-supported single atoms as spin qubits with tunable spin and charge states, enabling atom-by-atom control in the realization of a versatile quantum platform on surfaces.

cond-mat.mes-hall↗

arXiv2025

Spin-Electric Control of Individual Molecules on Surfaces

Individual magnetic molecules are promising building blocks for quantum technologies because of their chemical tunability, nanoscale dimensions, and ability to self-assemble into ordered arrays. However, harnessing their properties in quantum information processing requires precise local control of their spin properties. In this work, we present spin-electric coupling (SEC) for two molecular spin systems, iron phthalocyanine (FePc) and Fe-FePc complexes, adsorbed on a surface. We use electron spin resonance combined with scanning tunnelling microscopy (ESR-STM) to locally address them with the STM tip and electrically tune them using the applied bias voltage. These measurements reveal a pronounced nonlinear voltage dependence of the resonance frequency, linked to the energic onset of other molecular orbitals. We attribute this effect to a transport-mediated exchange field from the magnetic tip, providing a large, highly localized, and broadly applicable SEC mechanism. Finally, we demonstrate that the SEC enables all-electrical coherent spin control: In Rabi oscillation measurements of both single and coupled Fe-FePc complexes we show that the spin dynamics can be tuned, demonstrating a pathway towards electrically controlled quantum operation.

cond-mat.mes-hall↗

arXiv2025

Tailoring the Electronic Configurations of YPc$_2$ on Cu(111): Decoupling Strategies for Molecular Spin Qubits Platforms

Among the potential spin qubit candidates, yttrium phthalocyanine double-decker (YPc$_2$) features a diamagnetic metal ion core that stabilizes the molecular structure, while its magnetic properties arise primarily from an unpaired electron (S=1/2) delocalized over the two phthalocyanine (Pc) ligands. Understanding its properties in the proximity of metal electrodes is crucial to assess its potential use in molecular spin qubits architectures. Here, we investigated the morphology and electronic structure of this molecule adsorbed on Cu(111) surface using scanning tunneling microscopy (STM). On Cu(111), YPc$_2$ adsorbs flat, with isolated molecules showing a preferred orientation along the <111> crystal axes. Moreover, we observed two different types of self-assembly molecular packing when growing molecular patches. For YPc$_2$ in direct contact with Cu(111), STM revealed a widely separated highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO), suggesting the quenching of the unpaired spin. Conversely, when YPc$_2$ is separated from the metal substrate by a few-layer thick diamagnetic zinc phthalocyanine (ZnPc) layer, we found the HOMO to split into singly occupied and singly unoccupied molecular orbitals (SOMO/SUMO). We observed that more than 2 layers of ZnPc are needed to avoid intermixing between the two molecules and spin quenching in YPc2. Density functional theory (DFT) reveals the spin quenching is due to the hybridization between YPc$_2$ and Cu(111) states, confirming the importance of using suitable decoupling layers to preserve the unpaired molecular spin. Our results suggest the potential of YPc$_2$/ZnPc heterostructures as a stable and effective molecular spin qubit platform and validate the possibility of integrating this molecular spin qubit candidate in future quantum logic devices.

cond-mat.mes-hall↗

arXiv2025

Unraveling spin entanglement using quantum gates with scanning tunneling microscopy-driven electron spin resonance

Quantum entanglement is a fundamental resource for quantum information processing, and its controlled generation and detection remain key challenges in scalable quantum architectures. Here, we numerically demonstrate the deterministic generation of entangled spin states in a solid-state platform by implementing quantum gates via electron spin resonance combined with scanning tunneling microscopy (ESR-STM). Using two titanium atoms on a MgO/Ag(100) substrate as a model, we construct a two-qubit system whose dynamics are coherently manipulated through tailored microwave pulse sequences. We generate Bell states by implementing a Hadamard gate followed by a controlled-NOT gate, and evaluate its fidelity and concurrence using the quantum-master equation-based code TimeESR. Our results demonstrate that ESR-STM can create entangled states with significant fidelity. This study paves the way for the realization of atom-based quantum circuits and highlights ESR-STM as a powerful tool for probing and engineering entangled states on surfaces.

quant-ph↗

arXiv2025

Magnetic Resonance Imaging of Single Organic Radicals with Sub-Molecular Resolution

Interest in the magnetism of organic compounds is growing because of new organic magnets, spin-based electronics and the diverse properties of magnetic edge states in graphene nanoribbons. Electron spin resonance spectroscopy combined with the scanning tunneling microscopy has recently been developed as a powerful tool to address individual magnetic atoms and molecules at the atomic scale. Here we demonstrate electron spin resonance and magnetic resonance imaging of all-organic radical anions adsorbed on a protective thin insulating film grown on a metal support. We show that using the highly localized exchange field of the magnetic tip apex allows visualization of the delocalized spin density with sub-molecular resolution, enabling spin-density tomography that can distinguish similar molecular species. These results provide new opportunities for visualizing spin density and magnetic interactions at the atomic scale.

cond-mat.mes-hall↗

arXiv2025

Contrasting exchange-field and spin-transfer torque driving mechanisms in all-electric electron spin resonance

Understanding the coherent properties of electron spins driven by electric fields is crucial for their potential application in quantum-coherent nanoscience. In this work, we address two distinct driving mechanisms in electric-field driven electron-spin resonance as implemented in scanning tunneling spectroscopy. We study the origin of the driving field using a single orbital Anderson impurity, connected to polarized leads and biased by a voltage modulated on resonance with a spin transition. By mapping the quantum master equation into a system of equations for the impurity spin, we identify two distinct driving mechanisms. Below the charging thresholds of the impurity, electron spin resonance is dominated by a magnetically exchange-driven mechanism or field-like torque. Conversely, above the charging threshold spin-transfer torque caused by the spin-polarized current through the impurity drives the spin transition. Only the first mechanism enables coherent quantum spin control, while the second one leads to fast decoherence and spin accumulation towards a non-equilibrium steady-state. The electron spin resonance signals and spin dynamics vary significantly depending on which driving mechanism dominates, highlighting the potential for optimizing quantum-coherent control in electrically driven quantum systems.

cond-mat.mes-hall↗

arXiv2025

Probing Magnetism in Self-Assembled Organometallic Complexes using Kondo Spectroscopy

Control of individual spins at the atomic level holds great promise for miniaturized spintronics, quantum sensing, and quantum information processing. Both single atomic and molecular spin centers are prime candidates for these applications and are often individually addressed and manipulated using scanning tunneling microscopy (STM). In this work, we present a hybrid approach and demonstrate a robust method for self-assembly of magnetic organometallic complexes consisting of individual iron (Fe) atoms and molecules on a silver substrate using STM. We employ two types of molecules, bis(dibenzoylmethane) copper(II) [Cu(dbm)2] and iron phthalocyanine (FePc). We show that in both cases the Fe atoms preferentially attach underneath the benzene ring ligand of the molecules, effectively forming an organometallic half-sandwich arene complex, Fe(C6H6), that is akin to the properties of metallocenes. In both situations, a molecule can be combined with up to two Fe atoms. In addition, we observe a change in the magnetic properties of the attached Fe atoms in scanning tunneling spectroscopy, revealing a distinct Kondo signature at the Fe sites. We explain the latter using density functional theory calculations, and find that the bond formation between the Fe 3d-orbitals and the benzene {\pi}-molecular orbitals creates a favorable situation for Kondo screening of the d_xz- and d_yz-like orbitals. Thus, this work establishes a reliable design principle for forming hybrid organometallic complexes and simultaneous tuning of their atomic spin states.

cond-mat.mes-hall↗

arXiv2024

Controlling the Exchange Field of Surface Spin Impurities via DC Voltages

Recent advances in scanning tunneling microscopy have enabled quantum-coherent control of single surface spins via all-electric electron spin resonance (ESR). Such control requires magnetoelectric coupling, since spin resonance is a magnetic effect. We show that a magnetic tip induces a bias-dependent exchange field on a localized Anderson impurity via virtual particle exchange with the magnetic lead. This field differs from Heisenberg exchange and can be tuned, reversed, or suppressed by the bias voltage. Our model reproduces bias-controlled resonance shifts for S = 1/2 titanium atoms and Fe(II) phthalocyanine, enabling spin control via the exchange field and revealing the magnetoelectric mechanism behind all-electric ESR for spin-based quantum technologies.

cond-mat.mes-hall↗

arXiv2024

Quantum Spin-Engineering in On-Surface Molecular Ferrimagnets

The design and control of atomic-scale spin structures constitute major challenges for spin-based quantum technology platforms, including quantum dots, color centers, and molecular spins. Here, we showcase a strategy for designing the quantum properties of molecular spin qubits by combining tip-assisted on-surface assembly with electron spin resonance scanning tunneling microscopy (ESR-STM): We fabricate magnetic dimer complexes that consist of an iron phthalocyanine (FePc) molecule and an organometallic half-sandwich complex formed by the FePc ligand and an attached iron atom, Fe(C6H6). The total complex forms a mixed-spin (1/2,1) quantum ferrimagnet with a well-separated correlated ground state doublet, which we utilize for coherent control. As a result of the correlation, the quantum ferrimagnet shows an improved spin lifetime (>1.5 ${\mu}$s) as it is partially protected against inelastic electron scattering. Lastly, the ferrimagnet units also enable intermolecular coupling, that can be used to realize both ferromagnetic or antiferromagnetic structures. Thus, quantum ferrimagnets provide a versatile platform to improve coherent control in general and to study complex magnetic interactions.

cond-mat.mes-hall↗

arXiv2024

Efficient driving of a spin-qubit using single-atom magnets

The realization of electron-spin resonance at the single-atom level using scanning tunneling microscopy has opened new avenues for coherent quantum sensing and quantum state manipulation at the ultimate size limit. This allows to build many-body Hamiltonians and the study of their complex physical behavior. Recently, a novel qubit platform has emerged from this field, raising questions about the driving mechanism from single-atom magnets. In this work, we demonstrate how single-atom magnets can be used to drive a nearby single spin qubit efficiently. We show that the modulation of exchange coupling is the primary driving force, which successfully reproduces Rabi rates in the tens of MHz range, consistent with experimental data, while also addressing critical aspects related to the optimization of experimental parameters.

cond-mat.mes-hall↗

arXiv2024

Formation of Oriented Bilayer Motif -- Vanadyl Phthalocyanine on Ag(100)

The adsorption and self-assembly of vanadyl phthalocyanine molecules on Ag(100) has been investigated using a combination of scanning tunneling microscopy and density functional theory. At sub-monolayer coverage, we observe two distinct adsorption configurations of isolated molecules, corresponding to the central O atom pointing toward (O-down) or away (O-up) from the substrate. Upon adsorption in the O-up orientation, the otherwise achiral molecules take on a windmill-like chiral appearance due to their interaction with the substrate. At monolayer coverage, we observe a self-assembled square lattice with a mixture of O-up and O-down molecules. At higher coverage we find a strong preference for bilayer formation with O-up and O-down molecules in alternating layers, suggesting stabilization by dipolar interactions. Close inspection of the multi-layer surface reveals grain boundaries separating domains of opposite organizational chirality, and long-range ordering.

cond-mat.mtrl-sci↗

arXiv2024

Interpreting X-ray absorption spectra of Vanadyl Phthalocyanines Spin Qubit Candidates using a Machine Learning-Assisted Approach

The magnetic dilution of Vanadyl phthalocyanine (VOPc) within the isostructural diamagnetic Titanyl phthalocyanine (TiOPc) affords promising molecular spin qubit platforms for solid-state quantum computing. The development of quantitative methods for determining how the interactions with a supporting substrate impact the electronic structure of the system are fundamental to determine their potential integration in physical devices. In this work we propose a combined approach based on X-ray absorption spectroscopy (XAS), atomic multiplet calculations, and density functional theory (DFT) to investigate the 3d orbital level structure of VOPc on TiOPc/Ag(100). We characterize VOPc in different molecular environments realized by changing the thickness of TiOPc interlayer and adsorption configuration on Ag(100). Depending on the molecular film structure, we find characteristic XAS features that we analyze using atomic multiplet calculations. We use a Bayesian optimization algorithm to accelerate the parameter search process in the multiplet calculations and identify the ground state properties, such as the 3d orbital occupancy and splitting, as well as intra-atomic interactions. Our analysis indicates that VOPc retains its spin S = 1/2 character in all configurations. Conversely, the energy separation and sequence of the unoccupied V 3d orbitals sensitively depend on the interaction with the surface and TiOPc interlayer. We validate the atomic orbital picture obtained from the multiplet model by comparison with DFT, which further allows us to understand the VOPc electronic properties using a molecular orbital description.

cond-mat.mtrl-sci↗