Roadmap on nanoscale magnetic resonance imaging.

The field of nanoscale magnetic resonance imaging (NanoMRI) was started 30 years ago. It was motivated by the desire to image single molecules and molecular assemblies, such as proteins and virus particles, with near-atomic spatial resolution and on a length scale of 100 nm. Over the years, the NanoMRI field has also expanded to include the goal of useful high-resolution nuclear magnetic resonance (NMR) spectroscopy of molecules under ambient conditions, including samples up to the micron-scale. The realization of these goals requires the development of spin detection techniques that are many orders of magnitude more sensitive than conventional NMR and MRI, capable of detecting and controlling nanoscale ensembles of spins. Over the years, a number of different technical approaches to NanoMRI have emerged, each possessing a distinct set of capabilities for basic and applied areas of science. The goal of this roadmap article is to report the current state of the art in NanoMRI technologies, outline the areas where they are poised to have impact, identify the challenges that lie ahead, and propose methods to meet these challenges. This roadmap also shows how developments in NanoMRI techniques can lead to breakthroughs in emerging quantum science and technology applications.

Multiple flat bands and topological Hofstadter butterfly in twisted bilayer graphene close to the second magic angle.

Moiré superlattices in two-dimensional van der Waals heterostructures provide an efficient way to engineer electron band properties. The recent discovery of exotic quantum phases and their interplay in twisted bilayer graphene (tBLG) has made this moiré system one of the most renowned condensed matter platforms. So far studies of tBLG have been mostly focused on the lowest two flat moiré bands at the first magic angle θm1 ∼ 1.1°, leaving high-order moiré bands and magic angles largely unexplored. Here we report an observation of multiple well-isolated flat moiré bands in tBLG close to the second magic angle θm2 ∼ 0.5°, which cannot be explained without considering electron-election interactions. With high magnetic field magnetotransport measurements we further reveal an energetically unbound Hofstadter butterfly spectrum in which continuously extended quantized Landau level gaps cross all trivial band gaps. The connected Hofstadter butterfly strongly evidences the topologically nontrivial textures of the multiple moiré bands. Overall, our work provides a perspective for understanding the quantum phases in tBLG and the fractal Hofstadter spectra of multiple topological bands.

Mechanical Mode Imaging of a High-Q Hybrid hBN/Si3N4 Resonator.

We image and characterize the mechanical modes of a 2D drum resonator made of hBN suspended over a high-stress Si3N4 membrane. Our measurements demonstrate hybridization between various modes of the hBN resonator and those of the Si3N4 membrane. The measured resonance frequencies and spatial profiles of the modes are consistent with finite-element simulations based on idealized geometry. Spectra of the thermal motion reveal that, depending on the degree of hybridization with modes of the heavier and higher-quality-factor Si3N4 membrane, the quality factors and the motional mass of the hBN drum modes can be shifted by orders of magnitude. This effect could be exploited to engineer hybrid drum/membrane modes that combine the low motional mass of 2D materials with the high quality factor of Si3N4 membranes for optomechanical or sensing applications.

Optimized single-shot laser ablation of concave mirror templates on optical fibers.

We realize mirror templates on the tips of optical fibers using a single-shot CO2 laser ablation procedure and perform a systematic study of the influence of the pulse power, pulse duration, and laser spot size on their geometry. This investigation provides new insights into CO2 laser ablation of optical fibers and should help improve current models. We notably find that the radius of curvature, depth, and diameter of the templates exhibit extrema as a function of the power and duration of the ablation pulse, and observe that compound convex-concave shapes can be obtained. We additionally identify regimes of ablation parameters that lead to mirror templates with favorable geometries for use in cavity quantum electrodynamics and optomechanics.

Quantum dot opto-mechanics in a fully self-assembled nanowire.

We show that optically active quantum dots (QDs) embedded in MBE-grown GaAs/AlGaAs core-shell nanowires (NWs) are coupled to the NW mechanical motion. Oscillations of the NW modulate the QD emission energy in a broad range exceeding 14 meV. Furthermore, this opto-mechanical interaction enables the dynamical tuning of two neighboring QDs into resonance, possibly allowing for emitter-emitter coupling. Both the QDs and the coupling mechanism, i.e. material strain, are intrinsic to the NW structure and do not depend on any functionalization or external field. Such systems open up the prospect of using QDs to probe and control the mechanical state of a NW, or conversely of making a quantum nondemolition readout of a QD state through a position measurement.

Scanning Nitrogen-Vacancy Magnetometry of Focused-Electron-Beam-Deposited Cobalt Nanomagnets.

Focused-electron-beam-induced deposition is a promising technique for patterning nanomagnets in a single step. We fabricate cobalt nanomagnets in such a process and characterize their content, saturation magnetization, and stray magnetic field profiles by using a combination of transmission electron microscopy and scanning nitrogen-vacancy (NV) magnetometry. We find agreement between the measured stray field profiles and saturation magnetization with micromagnetic simulations. We further characterize magnetic domains and grainy stray magnetic fields in the nanomagnets and their halo side-deposits. This work may aid in the evaluation of Co nanomagnets produced through focused electron-beam-induced deposition for applications in spin qubits, magnetic field sensing, and magnetic logic.

Mapping the phase-separated state in a 2D magnet.

Intrinsic 2D magnets have recently been established as a playground for studies on fundamentals of magnetism, quantum phases, and spintronic applications. The inherent instability at low dimensionality often results in coexistence and/or competition of different magnetic orders. Such instability of magnetic ordering may manifest itself as phase-separated states. In 4f 2D materials, magnetic phase separation is expressed in various experiments; however, the experimental evidence is circumstantial. Here, we employ a high-sensitivity MFM technique to probe the spatial distribution of magnetic states in the paradigmatic 4f 2D ferromagnet EuGe2. Below the ferromagnetic transition temperature, we discover the phase-separated state and follow its evolution with temperature and magnetic field. The characteristic length-scale of magnetic domains amounts to hundreds of nanometers. These observations strongly shape our understanding of the magnetic states in 2D materials at the monolayer limit and contribute to engineering of ultra-compact spintronics.

Imaging nanomagnetism and magnetic phase transitions in atomically thin CrSBr.

Since their first observation in 2017, atomically thin van der Waals (vdW) magnets have attracted significant fundamental, and application-driven attention. However, their low ordering temperatures, Tc, sensitivity to atmospheric conditions and difficulties in preparing clean large-area samples still present major limitations to further progress, especially amongst van der Waals magnetic semiconductors. The remarkably stable, high-Tc vdW magnet CrSBr has the potential to overcome these key shortcomings, but its nanoscale properties and rich magnetic phase diagram remain poorly understood. Here we use single spin magnetometry to quantitatively characterise saturation magnetization, magnetic anisotropy constants, and magnetic phase transitions in few-layer CrSBr by direct magnetic imaging. We show pristine magnetic phases, devoid of defects on micron length-scales, and demonstrate remarkable air-stability down the monolayer limit. We furthermore address the spin-flip transition in bilayer CrSBr by imaging the phase-coexistence of regions of antiferromagnetically (AFM) ordered and fully aligned spins. Our work will enable the engineering of exotic electronic and magnetic phases in CrSBr and the realization of novel nanomagnetic devices based on this highly promising vdW magnet.

Energy dissipation on magic angle twisted bilayer graphene.

Traditional Joule dissipation omnipresent in today's electronic devices is well understood while the energy loss of the strongly interacting electron systems remains largely unexplored. Twisted bilayer graphene (tBLG) is a host to interaction-driven correlated insulating phases, when the relative rotation is close to the magic angle (1.08∘). We report on low-temperature (5K) nanomechanical energy dissipation of tBLG measured by pendulum atomic force microscopy (p-AFM). The ultrasensitive cantilever tip acting as an oscillating gate over the quantum device shows dissipation peaks attributed to different fractional fillings of the flat energy bands. Local detection allows to determine the twist angle and spatially resolved dissipation images showed the existence of hundred-nanometer domains of different doping. Application of magnetic fields provoked strong oscillations of the dissipation signal at 3/4 band filling, identified in analogy to Aharonov-Bohm oscillations, a wavefunction interference present between domains of different doping and a signature of orbital ferromagnetism.

A tunable fiber Fabry-Perot cavity for hybrid optomechanics stabilized at 4 K.

We describe an apparatus for the implementation of hybrid optomechanical systems at 4 K. The platform is based on a high-finesse, micrometer-scale fiber Fabry-Perot cavity, which can be widely tuned using piezoelectric positioners. A mechanical resonator can be positioned within the cavity in the object-in-the-middle configuration by a second set of positioners. A high level of stability is achieved without sacrificing either performance or tunability, through the combination of a stiff mechanical design, passive vibration isolation, and an active Pound-Drever-Hall feedback lock incorporating a reconfigurable digital filter. The stability of the cavity length is demonstrated to be better than a few picometers over many hours both at room temperature and at 4 K.

Stray-Field Imaging of a Chiral Artificial Spin Ice during Magnetization Reversal.

Artificial spin ices are a class of metamaterials consisting of magnetostatically coupled nanomagnets. Their interactions give rise to emergent behavior, which has the potential to be harnessed for the creation of functional materials. Consequently, the ability to map the stray field of such systems can be decisive for gaining an understanding of their properties. Here, we use a scanning nanometer-scale superconducting quantum interference device (SQUID) to image the magnetic stray field distribution of an artificial spin ice system exhibiting structural chirality as a function of applied magnetic fields at 4.2 K. The images reveal that the magnetostatic interaction gives rise to a measurable bending of the magnetization at the edges of the nanomagnets. Micromagnetic simulations predict that, owing to the structural chirality of the system, this edge bending is asymmetric in the presence of an external field and gives rise to a preferred direction for the reversal of the magnetization. This effect is not captured by models assuming a uniform magnetization. Our technique thus provides a promising means for understanding the collective response of artificial spin ices and their interactions.

Resonant driving of a single photon emitter embedded in a mechanical oscillator.

Coupling a microscopic mechanical resonator to a nanoscale quantum system enables control of the mechanical resonator via the quantum system and vice-versa. The coupling is usually achieved through functionalization of the mechanical resonator, but this results in additional mass and dissipation channels. An alternative is an intrinsic coupling based on strain. Here we employ a monolithic semiconductor system: the nanoscale quantum system is a semiconductor quantum dot (QD) located inside a nanowire. We demonstrate the resonant optical driving of the QD transition in such a structure. The noise spectrum of the resonance fluorescence signal, recorded in the single-photon counting regime, reveals a coupling to mechanical modes of different types. We measure a sensitivity to displacement of 65 fm/[Formula: see text] limited by charge noise in the device. Finally, we use thermal excitation of the different modes to determine the location of the QD within the trumpet, and calculate the contribution of the Brownian motion to the dephasing of the emitter.Resonant driving of a nanoscale quantum system coupled to a microscopic mechanical resonator may have uses in precision sensing and quantum information. The authors realize this by tailoring the geometry of a semiconductor nanowire embedding a quantum dot, detecting sub-picometre displacements.

Vectorial scanning force microscopy using a nanowire sensor.

Self-assembled nanowire (NW) crystals can be grown into nearly defect-free nanomechanical resonators with exceptional properties, including small motional mass, high resonant frequency and low dissipation. Furthermore, by virtue of slight asymmetries in geometry, a NW's flexural modes are split into doublets oscillating along orthogonal axes. These characteristics make bottom-up grown NWs extremely sensitive vectorial force sensors. Here, taking advantage of its adaptability as a scanning probe, we use a single NW to image a sample surface. By monitoring the frequency shift and direction of oscillation of both modes as we scan above the surface, we construct a map of all spatial tip-sample force derivatives in the plane. Finally, we use the NW to image electric force fields distinguishing between forces arising from the NW charge and polarizability. This universally applicable technique enables a form of atomic force microscopy particularly suited to mapping the size and direction of weak tip-sample forces.

Role of the electron spin in determining the coherence of the nuclear spins in a quantum dot.

A huge effort is underway to develop semiconductor nanostructures as low-noise qubits. A key source of dephasing for an electron spin qubit in GaAs and in naturally occurring Si is the nuclear spin bath. The electron spin is coupled to each nuclear spin by the hyperfine interaction. The same interaction also couples two remote nuclear spins via a common coupling to the delocalized electron. It has been suggested that this interaction limits both electron and nuclear spin coherence, but experimental proof is lacking. We show that the nuclear spin decoherence time decreases by two orders of magnitude on occupying an empty quantum dot with a single electron, recovering to its original value for two electrons. In the case of one electron, agreement with a model calculation verifies the hypothesis of an electron-mediated nuclear spin-nuclear spin coupling. The results establish a framework to understand the main features of this complex interaction in semiconductor nanostructures.

Manipulation of the nuclear spin ensemble in a quantum dot with chirped magnetic resonance pulses.

The nuclear spins in nanostructured semiconductors play a central role in quantum applications. The nuclear spins represent a useful resource for generating local magnetic fields but nuclear spin noise represents a major source of dephasing for spin qubits. Controlling the nuclear spins enhances the resource while suppressing the noise. NMR techniques are challenging: the group III and V isotopes have large spins with widely different gyromagnetic ratios; in strained material there are large atom-dependent quadrupole shifts; and nanoscale NMR is hard to detect. We report NMR on 100,000 nuclear spins of a quantum dot using chirped radiofrequency pulses. Following polarization, we demonstrate a reversal of the nuclear spin. We can flip the nuclear spin back and forth a hundred times. We demonstrate that chirped NMR is a powerful way of determining the chemical composition, the initial nuclear spin temperatures and quadrupole frequency distributions for all the main isotopes. The key observation is a plateau in the NMR signal as a function of sweep rate: we achieve inversion at the first quantum transition for all isotopes simultaneously. These experiments represent a generic technique for manipulating nanoscale inhomogeneous nuclear spin ensembles and open the way to probe the coherence of such mesoscopic systems.