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. .

Observation of current whirlpools in graphene at room temperature.

Electron-electron interactions in high-mobility conductors can give rise to transport signatures resembling those described by classical hydrodynamics. Using a nanoscale scanning magnetometer, we imaged a distinctive hydrodynamic transport pattern-stationary current vortices-in a monolayer graphene device at room temperature. By measuring devices with increasing characteristic size, we observed the disappearance of the current vortex and thus verified a prediction of the hydrodynamic model. We further observed that vortex flow is present for both hole- and electron-dominated transport regimes but disappears in the ambipolar regime. We attribute this effect to a reduction of the vorticity diffusion length near charge neutrality. Our work showcases the power of local imaging techniques for unveiling exotic mesoscopic transport phenomena.

Multidimensional Spectroscopy of Nuclear Spin Clusters in Diamond.

Optically active spin defects in solids offer promising platforms to investigate nuclear spin clusters with high sensitivity and atomic-site resolution. To leverage near-surface defects for molecular structure analysis in chemical and biological contexts using nuclear magnetic resonance (NMR), further advances in spectroscopic characterization of nuclear environments are essential. Here, we report Fourier spectroscopy techniques to improve localization and mapping of the test bed ^{13}C nuclear spin environment of individual, shallow nitrogen-vacancy centers at room temperature. We use multidimensional spectroscopy, well-known from classical NMR, in combination with weak measurements of single-nuclear-spin precession. We demonstrate two examples of multidimensional NMR: (i) improved nuclear spin localization by separate encoding of the two hyperfine components along spectral dimensions and (ii) spectral editing of nuclear-spin pairs, including measurement of internuclear coupling constants. Our work adds important tools for the spectroscopic analysis of molecular structures by single-spin probes.

Nanoscale Magnets Embedded in a Microstrip.

Nanoscale magnetic resonance imaging (NanoMRI) is an active area of applied research with potential applications in structural biology and quantum engineering. The success of this technological vision hinges on improving the instrument's sensitivity and functionality. A particular challenge is the optimization of the magnetic field gradient required for spatial encoding and of the radio frequency field used for spin control, in analogy to the components used in clinical MRI. In this work, we present the fabrication and characterization of a magnet-in-microstrip device that yields a compact form factor for both elements. We find that our design leads to a number of advantages, among them a 4-fold increase of the magnetic field gradient compared to those achieved with traditional fabrication methods. Our results can be useful for boosting the efficiency of a variety of different experimental arrangements and detection principles in the field of NanoMRI.

Multicone Diamond Waveguides for Nanoscale Quantum Sensing.

The long-lived electronic spin of the nitrogen-vacancy (NV) center in diamonds is a promising quantum sensor for detecting nanoscopic magnetic and electric fields in various environments. However, the poor signal-to-noise ratio (SNR) of prevalent optical spin-readout techniques presents a critical challenge in improving measurement sensitivity. Here, we address this limitation by coupling individual NVs to optimized diamond nanopillars, thereby enhancing the collection efficiency of fluorescence. Guided by near-field optical simulations, we predict improved performance for tall (≥5 µm) pillars with tapered sidewalls. This is subsequently verified by fabricating and characterizing a representative set of structures using a newly developed nanofabrication process. We observe increased SNR for optimized devices, owing to improved emission collimation and directionality. Promisingly, these devices are compatible with low-numerical-aperture collection optics and a reduced tip radius, reducing experimental overhead and facilitating improved spatial resolution for scanning applications.

Imaging ferroelectric domains with a single-spin scanning quantum sensor.

The ability to sensitively image electric fields is important for understanding many nanoelectronic phenomena, including charge accumulation at surfaces1 and interfaces2 and field distributions in active electronic devices3. A particularly exciting application is the visualization of domain patterns in ferroelectric and nanoferroic materials4,5, owing to their potential in computing and data storage6-8. Here, we use a scanning nitrogen-vacancy (NV) microscope, well known for its use in magnetometry9, to image domain patterns in piezoelectric (Pb[Zr0.2Ti0.8]O3) and improper ferroelectric (YMnO3) materials through their electric fields. Electric field detection is enabled by measuring the Stark shift of the NV spin10,11 using a gradiometric detection scheme12. Analysis of the electric field maps allows us to discriminate between different types of surface charge distributions, as well as to reconstruct maps of the three-dimensional electric field vector and charge density. The ability to measure both stray electric and magnetic fields9,13 under ambient conditions opens opportunities for the study of multiferroic and multifunctional materials and devices8,14.

Toward quantum sensing of chiral induced spin selectivity: Probing donor-bridge-acceptor molecules with NV centers in diamond.

Photoexcitable donor-bridge-acceptor (D-B-A) molecules that support intramolecular charge transfer are ideal platforms to probe the influence of chiral induced spin selectivity (CISS) in electron transfer and resulting radical pairs. In particular, the extent to which CISS influences spin polarization or spin coherence in the initial state of spin-correlated radical pairs following charge transfer through a chiral bridge remains an open question. Here, we introduce a quantum sensing scheme to measure directly the hypothesized spin polarization in radical pairs using shallow nitrogen-vacancy (NV) centers in diamond at the single- to few-molecule level. Importantly, we highlight the perturbative nature of the electron spin-spin dipolar coupling within the radical pair and demonstrate how Lee-Goldburg decoupling can preserve spin polarization in D-B-A molecules for enantioselective detection by a single NV center. The proposed measurements will provide fresh insight into spin selectivity in electron transfer reactions.

Distance measurements between 5 nanometer diamonds - single particle magnetic resonance or optical super-resolution imaging?

5 nanometer sized detonation nanodiamonds (DNDs) are studied as potential single-particle labels for distance measurements in biomolecules. Nitrogen-vacancy (NV) defects in the crystal lattice can be addressed through their fluorescence and optically-detected magnetic resonance (ODMR) of a single particle can be recorded. To achieve single-particle distance measurements, we propose two complementary approaches based on spin-spin coupling or optical super-resolution imaging. As a first approach, we try to measure the mutual magnetic dipole-dipole coupling between two NV centers in close DNDs using a pulse ODMR sequence (DEER). The electron spin coherence time, a key parameter to reach long distance DEER measurements, was prolonged using dynamical decoupling reaching T 2,DD ≈ 20 µs, extending the Hahn echo decay time T 2 by one order of magnitude. Nevertheless, an inter-particle NV-NV dipole coupling could not be measured. As a second approach, we successfully localize the NV centers in DNDs using STORM super-resolution imaging, achieving a localization precision of down to 15 nm, enabling optical nanometer-scale single-particle distance measurements.

Diamond surface engineering for molecular sensing with nitrogen-vacancy centers.

Quantum sensing using optically addressable atomic-scale defects, such as the nitrogen-vacancy (NV) center in diamond, provides new opportunities for sensitive and highly localized characterization of chemical functionality. Notably, near-surface defects facilitate detection of the minute magnetic fields generated by nuclear or electron spins outside of the diamond crystal, such as those in chemisorbed and physisorbed molecules. However, the promise of NV centers is hindered by a severe degradation of critical sensor properties, namely charge stability and spin coherence, near surfaces (< ca. 10 nm deep). Moreover, applications in the chemical sciences require methods for covalent bonding of target molecules to diamond with robust control over density, orientation, and binding configuration. This forward-looking Review provides a survey of the rapidly converging fields of diamond surface science and NV-center physics, highlighting their combined potential for quantum sensing of molecules. We outline the diamond surface properties that are advantageous for NV-sensing applications, and discuss strategies to mitigate deleterious effects while simultaneously providing avenues for chemical attachment. Finally, we present an outlook on emerging applications in which the unprecedented sensitivity and spatial resolution of NV-based sensing could provide unique insight into chemically functionalized surfaces at the single-molecule level.

Soft-Clamped Silicon Nitride String Resonators at Millikelvin Temperatures.

We demonstrate that soft-clamped silicon nitride strings with a large aspect ratio can be operated at mK temperatures. The quality factors (Q) of two measured devices show consistent dependency on the cryostat temperature, with soft-clamped mechanical modes reaching Q>10^{9} at roughly 46 mK. For low optical readout power, Q is found to saturate, indicating good thermalization between the sample and the stage it is mounted on. Our best device exhibits a calculated force sensitivity of 9.6 zN/sqrt[Hz] and a thermal decoherence time of 0.38 s, which bode well for future applications such as nanomechanical force sensing.

Single-Nitrogen-Vacancy NMR of Amine-Functionalized Diamond Surfaces.

Nuclear magnetic resonance (NMR) imaging with shallow nitrogen-vacancy (NV) centers in diamond offers an exciting route toward sensitive and localized chemical characterization at the nanoscale. Remarkable progress has been made to combat the degradation in coherence time and stability suffered by near-surface NV centers using suitable chemical surface termination. However, approaches that also enable robust control over adsorbed molecule density, orientation, and binding configuration are needed. We demonstrate a diamond surface preparation for mixed nitrogen- and oxygen-termination that simultaneously improves NV center coherence times for <10 nm-deep emitters and enables direct and recyclable chemical functionalization via amine-reactive cross-linking. Using this approach, we probe single NV centers embedded in nanopillar waveguides to perform 19F NMR sensing of covalently bound fluorinated molecules with detection on the order of 100 molecules. This work signifies an important step toward nuclear spin localization and structure interrogation at the single-molecule level.

Current-driven dynamics and ratchet effect of skyrmion bubbles in a ferrimagnetic insulator.

Magnetic skyrmions are compact chiral spin textures that exhibit a rich variety of topological phenomena and hold potential for the development of high-density memory devices and novel computing schemes driven by spin currents. Here, we demonstrate the room-temperature interfacial stabilization and current-driven control of skyrmion bubbles in the ferrimagnetic insulator Tm3Fe5O12 coupled to Pt, showing the current-induced motion of individual skyrmion bubbles. The ferrimagnetic order of the crystal together with the interplay of spin-orbit torques and pinning determine the skyrmion dynamics in Tm3Fe5O12 and result in a strong skyrmion Hall effect characterized by a negative deflection angle and hopping motion. Further, we show that the velocity and depinning threshold of the skyrmion bubbles can be modified by exchange coupling Tm3Fe5O12 to an in-plane magnetized Y3Fe5O12 layer, which distorts the spin texture of the skyrmions and leads to directional-dependent rectification of their dynamics. This effect, which is equivalent to a magnetic ratchet, is exploited to control the skyrmion flow in a racetrack-like device.

Strong Parametric Coupling between Two Ultracoherent Membrane Modes.

We demonstrate parametric coupling between two modes of a silicon nitride membrane. We achieve the coupling by applying an oscillating voltage to a sharp metal tip that approaches the membrane surface to within a few 100 nm. When the voltage oscillation frequency is equal to the mode frequency difference, the modes exchange energy periodically and faster than their free energy decay rate. This flexible method can potentially be useful for rapid state control and transfer between modes, and is an important step toward parametric spin sensing experiments with membrane resonators.

Spatial Correlation between Fluctuating and Static Fields over Metal and Dielectric Substrates.

We report spatially resolved measurements of static and fluctuating electric fields over conductive (Au) and nonconductive (SiO_{2}) surfaces. Using an ultrasensitive "nanoladder" cantilever probe to scan over these surfaces at distances of a few tens of nanometers, we record changes in the probe resonance frequency and damping that we associate with static and fluctuating fields, respectively. We find static and fluctuating fields to be spatially correlated. Furthermore, the fields are of similar magnitude for the two materials. We quantitatively describe the observed effects on the basis of trapped surface charges and dielectric fluctuations in an adsorbate layer. Our results are consistent with organic adsorbates significantly contributing to surface dissipation that affects nanomechanical sensors, trapped ions, superconducting resonators, and color centers in diamond.

High-speed domain wall racetracks in a magnetic insulator.

Recent reports of current-induced switching of ferrimagnetic oxides coupled to heavy metals have opened prospects for implementing magnetic insulators into electrically addressable devices. However, the configuration and dynamics of magnetic domain walls driven by electrical currents in insulating oxides remain unexplored. Here we investigate the internal structure of the domain walls in Tm3Fe5O12 (TmIG) and TmIG/Pt bilayers, and demonstrate their efficient manipulation by spin-orbit torques with velocities of up to 400 ms-1 and minimal current threshold for domain wall flow of 5 × 106 A cm-2. Domain wall racetracks are defined by Pt current lines on continuous TmIG films, which allows for patterning the magnetic landscape of TmIG in a fast and reversible way. Scanning nitrogen-vacancy magnetometry reveals that the domain walls of TmIG thin films grown on Gd3Sc2Ga3O12 exhibit left-handed Néel chirality, changing to an intermediate Néel-Bloch configuration upon Pt deposition. These results indicate the presence of interfacial Dzyaloshinskii-Moriya interaction in magnetic garnets, opening the possibility to stabilize chiral spin textures in centrosymmetric magnetic insulators.

Dynamical Magnetic Field Accompanying the Motion of Ferroelectric Domain Walls.

The recently proposed dynamical multiferroic effect describes the generation of magnetization from temporally varying electric polarization. Here, we show that the effect can lead to a magnetic field at moving ferroelectric domain walls, where the rearrangement of ions corresponds to a rotation of ferroelectric polarization in time. We develop an expression for the dynamical magnetic field, and calculate the relevant parameters for the example of 90° and 180° domain walls, as well as for polar skyrmions, in BaTiO_{3}, using a combination of density functional theory and phenomenological modeling. We find that the magnetic field reaches the order of several µT at the center of the wall, and we propose two experiments to measure the effect with nitrogen-vacancy center magnetometry.

Rapid Flipping of Parametric Phase States.

We experimentally demonstrate flipping the phase state of a parametron within a single period of its oscillation. A parametron is a binary logic element based on a driven nonlinear resonator. It features two stable phase states that define an artificial spin. The most basic operation performed on a parametron is a bit flip between these two states. Thus far, this operation involved changing the energetic population of the resonator and therefore required a number of oscillations on the order of the quality factor Q. Our technique takes a radically different approach and relies on rapid control of the underlying potential. Our work represents a paradigm shift for phase-encoded logic operations by boosting the speed of a parametron bit flip to its ultimate limit.

Parametric Symmetry Breaking in a Nonlinear Resonator.

Much of the physical world around us can be described in terms of harmonic oscillators in thermodynamic equilibrium. At the same time, the far-from-equilibrium behavior of oscillators is important in many aspects of modern physics. Here, we investigate a resonating system subject to a fundamental interplay between intrinsic nonlinearities and a combination of several driving forces. We have constructed a controllable and robust realization of such a system using a macroscopic doubly clamped string. We experimentally observe a hitherto unseen double hysteresis in both the amplitude and the phase of the resonator's response function and present a theoretical model that is in excellent agreement with the experiment. Our work unveils that the double hysteresis is a manifestation of an out-of-equilibrium symmetry breaking between parametric phase states. Such a fundamental phenomenon, in the most ubiquitous building block of nature, paves the way for the investigation of new dynamical phases of matter in parametrically driven many-body systems and motivates applications ranging from ultrasensitive force detection to low-energy computing memory units.

Magnetometry of Individual Polycrystalline Ferromagnetic Nanowires.

Ferromagnetic nanowires are finding use as untethered sensors and actuators for probing micro- and nanoscale biophysical phenomena, such as for localized sensing and application of forces and torques on biological samples, for tissue heating through magnetic hyperthermia, and for microrheology. Quantifying the magnetic properties of individual isolated nanowires is crucial for such applications. Dynamic cantilever magnetometry is used to measure the magnetic properties of individual sub-500 nm diameter polycrystalline nanowires of Ni and Ni80 Co20 fabricated by template-assisted electrochemical deposition. The values are compared with bulk, ensemble measurements when the nanowires are still embedded within their growth matrix. It is found that single-particle and ensemble measurements of nanowires yield significantly different results that reflect inter-nanowire interactions and chemical modifications of the sample during the release process from the growth matrix. The results highlight the importance of performing single-particle characterization for objects that will be used as individual magnetic nanoactuators or nanosensors in biomedical applications.

Surface Chemical Tuning of Phonon and Electron Transport in Free-Standing Silicon Nanowire Arrays.

We report electronic and phononic transport measurements of monocrystalline batch-fabricated silicon nanowire (SiNW) arrays functionalized with different surface chemistries. We find that hydrogen-terminated SiNWs prepared by vapor HF etching of native-oxide-covered devices show increased electrical conductivity but decreased thermal conductivity. We used the kinetic Monte Carlo method to solve the Boltzmann transport equation and also numerically examine the effect of phonon boundary scattering. Surface transfer doping of the SiNWs by cobaltocene or decamethylcobaltocene drastically improves the electrical conductivity by 2 to 4 orders of magnitude without affecting the thermal conductivity. The results showcase surface chemical control of nanomaterials as a potent pathway that can complement device miniaturization efforts in the quest for more efficient thermoelectric materials and devices.