High-gradient nanomagnets on cantilevers for sensitive detection of nuclear magnetic resonance

Mass and Stiffness Deconvolution in Nanomechanical Resonators for Precise Mass Measurement and In Vivo Biosensing

Nanomechanical sensors, due to their small size and high sensitivity to the environment, hold significant promise for various sensing applications. These sensors enable rapid, highly sensitive, and selective detection of biological and biochemical entities as well as mass spectrometry by utilizing the frequency shift of nanomechanical resonators. Nanomechanical systems have been employed to measure the mass of cells and biomolecules and study the fundamentals of surface science such as phase transitions and diffusion. Here, we develop a methodology using both experimental measurements and numerical simulations to explore the characteristics of nanomechanical resonators when the detection entities are absorbed on the cantilever surface and quantify the mass, density, and Young's modulus of adsorbed entities. Moreover, based on this proposed concept, we present an experimental method for measuring the mass of molecules and living biological entities in their physiological environment. This approach could find applications in predicting the behavior of bionanoelectromechanical resonators functionalized with biological capture molecules, as well as in label-free, nonfunctionalized micro/nanoscale biosensing and mass spectrometry of living bioentities.

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.

A Review of the Current State of Magnetic Force Microscopy to Unravel the Magnetic Properties of Nanomaterials Applied in Biological Systems and Future Directions for Quantum Technologies

Magnetism plays a pivotal role in many biological systems. However, the intensity of the magnetic forces exerted between magnetic bodies is usually low, which demands the development of ultra-sensitivity tools for proper sensing. In this framework, magnetic force microscopy (MFM) offers excellent lateral resolution and the possibility of conducting single-molecule studies like other single-probe microscopy (SPM) techniques. This comprehensive review attempts to describe the paramount importance of magnetic forces for biological applications by highlighting MFM's main advantages but also intrinsic limitations. While the working principles are described in depth, the article also focuses on novel micro- and nanofabrication procedures for MFM tips, which enhance the magnetic response signal of tested biomaterials compared to commercial nanoprobes. This work also depicts some relevant examples where MFM can quantitatively assess the magnetic performance of nanomaterials involved in biological systems, including magnetotactic bacteria, cryptochrome flavoproteins, and magnetic nanoparticles that can interact with animal tissues. Additionally, the most promising perspectives in this field are highlighted to make the reader aware of upcoming challenges when aiming toward quantum technologies.

A Non-Perturbative, Low-Noise Surface Coating for Sensitive Force-Gradient Detection of Electron Spin Resonance in Thin Films

The sensitivity of magnetic resonance force microscopy (MRFM) is limited by surface noise. Coating a thin-film polymer sample with metal has been shown to decrease, by orders of magnitude, sample-related force noise and frequency noise in MRFM experiments. Using both MRFM and inductively detected measurements of electron-spin resonance, we show that thermally evaporating a 12 nm gold layer on a 40 nm nitroxide-doped polystyrene film inactivates the nitroxide spin labels to a depth of 20 nm, making single-spin measurements difficult or impossible. We introduce a "laminated sample" protocol in which the gold layer is first evaporated on a sacrificial polymer. The sample is deposited on the room-temperature gold layer, removed using solvent lift-off, and placed manually on a coplanar waveguide. Electron spin resonance (ESR) of such a laminated sample was detected via MRFM at cryogenic temperatures using a high-compliance cantilever with an integrated 100-nm-scale cobalt tip. A 20-fold increase of spin signal was observed relative to a thin-film sample prepared instead with an evaporated metal coating. The observed signal is still somewhat smaller than expected, and we discuss possible remaining sources of signal loss.

Efficient Entanglement of Spin Qubits Mediated by a Hot Mechanical Oscillator

Localized electronic and nuclear spin qubits in the solid state constitute a promising platform for storage and manipulation of quantum information, even at room temperature. However, the development of scalable systems requires the ability to entangle distant spins, which remains a challenge today. We propose and analyze an efficient, heralded scheme that employs a parity measurement in a decoherence free subspace to enable fast and robust entanglement generation between distant spin qubits mediated by a hot mechanical oscillator. We find that high-fidelity entanglement at cryogenic and even ambient temperatures is feasible with realistic parameters and show that the entangled pair can be subsequently leveraged for deterministic controlled-NOT operations between nuclear spins. Our results open the door for novel quantum processing architectures for a wide variety of solid-state spin qubits.

Single-Spin Magnetomechanics with Levitated Micromagnets

We demonstrate a new mechanical transduction platform for individual spin qubits. In our approach, single micromagnets are trapped using a type-II superconductor in proximity of spin qubits, enabling direct magnetic coupling between the two systems. Controlling the distance between the magnet and the superconductor during cooldown, we demonstrate three-dimensional trapping with quality factors around 1×10^{6} and kHz trapping frequencies. We further exploit the large magnetic moment to mass ratio of this mechanical oscillator to couple its motion to the spin degrees of freedom of an individual nitrogen vacancy center in diamond. Our approach provides a new path towards interfacing individual spin qubits with mechanical motion for testing quantum mechanics with mesoscopic objects, realization of quantum networks, and ultrasensitive metrology.

Magnetic Resonance Force Microscopy with a One-Dimensional Resolution of 0.9 Nanometers

Magnetic resonance force microscopy (MRFM) is a scanning probe technique capable of detecting MRI signals from nanoscale sample volumes, providing a paradigm-changing potential for structural biology and medical research. Thus far, however, experiments have not reached sufficient spatial resolution for retrieving meaningful structural information from samples. In this work, we report MRFM imaging scans demonstrating a resolution of 0.9 nm and a localization precision of 0.6 nm in one dimension. Our progress is enabled by an improved spin excitation protocol furnishing us with sharp spatial control on the MRFM imaging slice, combined with overall advances in instrument stability. From a modeling of the slice function, we expect that our arrangement supports spatial resolutions down to 0.3 nm given sufficient signal-to-noise ratio. Our experiment demonstrates the feasibility of subnanometer MRI and realizes an important milestone toward the three-dimensional imaging of macromolecular structures.

Single Rare-Earth Ions as Atomic-Scale Probes in Ultrascaled Transistors

Continued scaling of semiconductor devices has driven information technology into vastly diverse applications. The performance of ultrascaled transistors is strongly influenced by local electric field and strain. As the size of these devices approaches fundamental limits, it is imperative to develop characterization techniques with nanometer resolution and three-dimensional (3D) mapping capabilities for device optimization. Here, we report on the use of single erbium (Er) ions as atomic probes for the electric field and strain in a silicon ultrascaled transistor. Stark shifts on the Er³⁺ spectra induced by both the overall electric field and the local charge environment are observed. Changes in strain smaller than 3 × 10^-6 are detected, which is around 2 orders of magnitude more sensitive than the standard techniques used in the semiconductor industry. These results open new possibilities for 3D mapping of the local strain and electric field in the channel of ultrascaled transistors.

Growth of magnetic nanowires along freely selectable 〈hkl〉 crystal directions

The production of nanowire materials, uniformly oriented along any arbitrarily chosen crystal orientation, is an important, yet unsolved, problem in material science. Here, we present a generalizable solution to this problem. The solution is based on the technique of glancing angle deposition combined with a rapid switching of the deposition direction between crystal symmetry positions. Using iron-cobalt as an example, we showcase the simplicity and capabilities of the process in one-step fabrications of 〈100〉, 〈110〉, 〈111〉, 〈210〉, 〈310〉, 〈320〉, and 〈321〉-oriented nanowires, three-dimensional nanowire spirals, core-shell heterostructures, and axial hybrids. Our results provide a new capability for tailoring the properties of nanowires, and should be generalizable to any material that can be grown as a single-crystal biaxial film.

Cryogenic positioning and alignment with micrometer precision in a magnetic resonance force microscope

Aligning a microcantilever to an area of interest on a sample is a critical step in many scanning probe microscopy experiments, particularly those carried out on devices and rare, precious samples. We report a series of protocols that rapidly and reproducibly align a high-compliance microcantilever to a <10 μm sample feature under high vacuum and at cryogenic temperatures. The first set of protocols, applicable to a cantilever oscillating parallel to the sample surface, involve monitoring the cantilever resonance frequency while laterally scanning the tip to map the sample substrate through electrostatic interactions of the substrate with the cantilever. We demonstrate that when operating a cantilever a few micrometers from the sample surface, large shifts in the cantilever resonance frequency are present near the edges of a voltage-biased sample electrode. Surprisingly, these "edge-finder" frequency shifts are retained when the electrode is coated with a polymer film and a ∼10 nm thick metallic ground plane. The second series of methods, applicable to any scanning probe microscopy experiment, integrate a single-optical fiber to image line scans of the sample surface. The microscope modifications required for these methods are straightforward to implement, provide reliable micrometer-scale positioning, and decrease the experimental setup time from days to hours in a vacuum, cryogenic magnetic resonance force microscope.

Instrumentation and control of harmonic oscillators via a single-board microprocessor-FPGA device

We report the development of an instrumentation and control system instantiated on a microprocessor-field programmable gate array (FPGA) device for a harmonic oscillator comprising a portion of a magnetic resonance force microscope. The specific advantages of the system are that it minimizes computation, increases maintainability, and reduces the technical barrier required to enter the experimental field of magnetic resonance force microscopy. Heterodyne digital control and measurement yields computational advantages. A single microprocessor-FPGA device improves system maintainability by using a single programming language. The system presented requires significantly less technical expertise to instantiate than the instrumentation of previous systems, yet integrity of performance is retained and demonstrated with experimental data.

A High-Performance Nb Nano-Superconducting Quantum Interference Device with a Three-Dimensional Structure

A superconducting quantum interference device (SQUID) miniaturized into the nanoscale is promising in the inductive detection of a single electron spin. A nano-SQUID with a strong spin coupling coefficient, a low flux noise, and a wide working magnetic field range is highly desired in a single spin resonance measurement. Nano-SQUIDs with Dayem bridge junctions excel in a high working field range and in the direct coupling from spins to the bridge. However, the common planar structure of nano-SQUIDs is known for problems such as a shallow flux modulation depth and a troublesome hysteresis in current-voltage curves. Here, we developed a fabrication process for creating three-dimensional (3-D) niobium (Nb) nano-SQUIDs with nanobridge junctions that can be tuned independently. Characterization of the device shows up to 45.9% modulation depth with a reversible current-voltage curve. Owning to the large modulation depth, the measured flux noise is as low as 0.34 μΦ₀/Hz^1/2. The working field range of the SQUID is greater than 0.5 T parallel to the SQUID plane. We believe that 3-D Nb nano-SQUIDs provide a promising step toward effective single-spin inductive detection.

Signal enhancement in cantilever magnetometry based on a co-resonantly coupled sensor

Cantilever magnetometry is a measurement technique used to study magnetic nanoparticles. With decreasing sample size, the signal strength is significantly reduced, requiring advances of the technique. Ultrathin and slender cantilevers can address this challenge but lead to increased complexity of detection. We present an approach based on the co-resonant coupling of a micro- and a nanometer-sized cantilever. Via matching of the resonance frequencies of the two subsystems we induce a strong interplay between the oscillations of the two cantilevers, allowing for a detection of interactions between the sensitive nanocantilever and external influences in the amplitude response curve of the microcantilever. In our magnetometry experiment we used an iron-filled carbon nanotube acting simultaneously as nanocantilever and magnetic sample. Measurements revealed an enhancement of the commonly used frequency shift signal by five orders of magnitude compared to conventional cantilever magnetometry experiments with similar nanomagnets. With this experiment we do not only demonstrate the functionality of our sensor design but also its potential for very sensitive magnetometry measurements while maintaining a facile oscillation detection with a conventional microcantilever setup.

Dynamic nuclear polarization in a magnetic resonance force microscope experiment

We report achieving enhanced nuclear magnetization in a magnetic resonance force microscope experiment at 0.6 tesla and 4.2 kelvin using the dynamic nuclear polarization (DNP) effect. In our experiments a microwire coplanar waveguide delivered radiowaves to excite nuclear spins and microwaves to excite electron spins in a 250 nm thick nitroxide-doped polystyrene sample. Both electron and proton spin resonance were observed as a change in the mechanical resonance frequency of a nearby cantilever having a micron-scale nickel tip. NMR signal, not observable from Curie-law magnetization at 0.6 T, became observable when microwave irradiation was applied to saturate the electron spins. The resulting NMR signal's size, buildup time, dependence on microwave power, and dependence on irradiation frequency was consistent with a transfer of magnetization from electron spins to nuclear spins. Due to the presence of an inhomogeneous magnetic field introduced by the cantilever's magnetic tip, the electron spins in the sample were saturated in a microwave-resonant slice 10's of nm thick. The spatial distribution of the nuclear polarization enhancement factor ε was mapped by varying the frequency of the applied radiowaves. The observed enhancement factor was zero for spins in the center of the resonant slice, was ε = +10 to +20 for spins proximal to the magnet, and was ε = -10 to -20 for spins distal to the magnet. We show that this bipolar nuclear magnetization profile is consistent with cross-effect DNP in a ∼10(5) T m(-1) magnetic field gradient. Potential challenges associated with generating and using DNP-enhanced nuclear magnetization in a nanometer-resolution magnetic resonance imaging experiment are elucidated and discussed.

Single-Crystal Diamond Nanowire Tips for Ultrasensitive Force Microscopy

We report the fabrication, integration, and assessment of sharp diamond tips for ultrasensitive force microscopy experiments. Two types of tips, corresponding to the upper and lower halves of a diamond nanowire, were fabricated by top-down plasma etching from a single-crystalline substrate. The lower, surface-attached halves can be directly integrated into lithographically defined nanostructures, like cantilevers. The upper, detachable halves result in diamond nanowires with a tunable diameter (50-500 nm) and lengths of a few microns. Tip radii were around 10 nm and tip apex angles around 15°. We demonstrate the integration of diamond nanowires for use as scanning tips onto ultrasensitive pendulum-style silicon cantilevers. We find the noncontact friction and frequency jitter to be exceptionally low, with no degradation in the intrinsic mechanical quality factor (Q ≈ 130,000) down to tip-to-surface distances of about 10 nm. Our results are an encouraging step toward further improvement of the sensitivity and resolution of force-detected magnetic resonance imaging.

Nanotube mechanical resonators with quality factors of up to 5 million

Carbon nanotube mechanical resonators have attracted considerable interest because of their small mass, the high quality of their surfaces, and the pristine electronic states they host. However, their small dimensions result in fragile vibrational states that are difficult to measure. Here, we observe quality factors Q as high as 5 × 10(6) in ultra-clean nanotube resonators at a cryostat temperature of 30 mK, where we define Q as the ratio of the resonant frequency over the linewidth. Measuring such high quality factors requires the use of an ultra-low-noise method to rapidly detect minuscule vibrations, as well as careful reduction of the noise of the electrostatic environment. We observe that the measured quality factors fluctuate because of fluctuations of the resonant frequency. We measure record-high quality factors, which are comparable to the highest Q values reported in mechanical resonators of much larger size, a remarkable result considering that reducing the size of resonators is usually concomitant with decreasing quality factors. The combination of ultra-low mass and very large Q offers new opportunities for ultra-sensitive detection schemes and quantum optomechanical experiments.

Long-lived frequency shifts observed in a magnetic resonance force microscope experiment following microwave irradiation of a nitroxide spin probe

We introduce a spin-modulation protocol for force-gradient detection of magnetic resonance that enables the real-time readout of longitudinal magnetization in an electron spin resonance experiment involving fast-relaxing spins. We applied this method to observe a prompt change in longitudinal magnetization following the microwave irradiation of a nitroxide-doped perdeuterated polystyrene film having an electron spin-lattice relaxation time of [Formula: see text]. The protocol allowed us to discover a large, long-lived cantilever frequency shift. Based on its magnitude, lifetime, and field dependence, we tentatively attribute this persistent signal to deuteron spin magnetization created via transfer of polarization from nitroxide spins.