An Atomic-Scale Vector Network Analyzer.

Electronic devices have been ever-shrinking toward atomic dimensions and have reached operation frequencies in the GHz range, thereby outperforming most conventional test equipment, such as vector network analyzers (VNA). Here the capabilities of a VNA on the atomic scale in a scanning tunneling microscope are implemented. Nonlinearities present in the voltage-current characteristic of atoms and nanostructures for phase-resolved microwave spectroscopy with unprecedented spatial resolution at GHz frequencies are exploited. The amplitude and phase response up to 9.3 GHz is determined, which permits accurate de-embedding of the transmission line and application of distortion-corrected waveforms in the tunnel junction itself. This enables quantitative characterization of the complex-valued admittance of individual magnetic iron atoms which show a lowpass response with a magnetic-field-tunable cutoff frequency.

Quantum stochastic resonance of individual Fe atoms.

Stochastic resonance, where noise synchronizes a system's response to an external drive, is a wide-reaching phenomenon found in noisy systems spanning from the dynamics of neurons to the periodicity of ice ages. Quantum tunneling can extend stochastic resonance to the quantum realm. We demonstrate quantum stochastic resonance for magnetic transitions in atoms by inelastic electron tunneling with a scanning tunneling microscope. Stochastic resonance is shown deep in the quantum regime, where spin-state fluctuations are driven by tunneling of the magnetization, and in a semiclassical crossover region, where thermally excited electrons drive transitions between ground and excited states. Inducing synchronization by periodically modulating transition rates provides a general mechanism to determine real-time spin dynamics ranging from milliseconds to picoseconds.

Tunable Spin-Superconductor Coupling of Spin 1/2 Vanadyl Phthalocyanine Molecules.

Atomic-scale magnetic moments in contact with superconductors host rich physics based on the emergence of Yu-Shiba-Rusinov (YSR) magnetic bound states within the superconducting condensate. Here, we focus on a magnetic bound state induced into Pb nanoislands by individual vanadyl phthalocyanine (VOPc) molecules deposited on the Pb surface. The VOPc molecule is characterized by a spin magnitude of 1/2 arising from a well-isolated singly occupied d xy-orbital and is a promising candidate for a molecular spin qubit with long coherence times. X-ray magnetic circular dichroism (XMCD) measurements show that the molecular spin remains unperturbed even for molecules directly deposited on the Pb surface. Scanning tunneling spectroscopy and density functional theory (DFT) calculations identify two adsorption geometries for this "asymmetric" molecule (i.e., absence of a horizontal symmetry plane): (a) oxygen pointing toward the vacuum with the Pc laying on the Pb, showing negligible spin-superconductor interaction, and (b) oxygen pointing toward the Pb, presenting an efficient interaction with the Pb and promoting a Yu-Shiba-Rusinov bound state. Additionally, we find that in the first case a YSR state can be induced smoothly by exerting mechanical force on the molecules with the scanning tunneling microscope (STM) tip. This allows the interaction strength to be tuned continuously from an isolated molecular spin case, through the quantum critical point (where the bound state energy is zero) and beyond. DFT indicates that a gradual bending of the VO bond relative to the Pc ligand plane promoted by the STM tip can modify the interaction in a continuously tunable manner. The ability to induce a tunable YSR state in the superconductor suggests the possibility of introducing coupled spins on superconductors with switchable interaction.

Tunable geometrical frustration in magnonic vortex crystals.

A novel approach to investigate geometrical frustration is introduced using two-dimensional magnonic vortex crystals. The frustration of the crystal can be manipulated and turned on and off dynamically on the timescale of milliseconds. The vortices are studied using scanning transmission x-ray microscopy and ferromagnetic resonance spectroscopy. They are arranged analogous to the nanomagnets in artificial spin-ice systems. The polarization state of the vortices is tuned in a way that geometrical frustration arises. We demonstrate that frustrated polarization states and non-frustrated states can be tuned to the crystal by changing the frequency of the state formation process.

Collective modes in three-dimensional magnonic vortex crystals.

Collective modes in three-dimensional crystals of stacked permalloy disks with magnetic vortices are investigated by ferromagnetic resonance spectroscopy and scanning transmission X-ray microscopy. The size of the arrangements is increased step by step to identify the different contributions to the interaction between the vortices. These contributions are the key requirement to understand complex dynamics of three dimensional vortex crystals. Both vertical and horizontal coupling determine the collective modes. In-plane dipoles strongly influence the interaction between the disks in the stacks and lead to polarity-dependent resonance frequencies. Weaker contributions discern arrangements with different polarities and circularities that result from the lateral coupling of the stacks and the interaction of the core regions inside a stack. All three contributions are identified in the experiments and are explained in a rigid particle model.