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Stacking van der Waals magnets holds promise for creating new hybrid materials with properties that do not exist in bulk materials. Here we investigate orthogonally twisted stacks of the van der Waals antiferromagnet CrSBr, aiming to exploit an extreme misalignment of magnetic anisotropy across the twisted interface.Using nitrogen-vacancy centre microscopy, we construct vector maps of the magnetisation, and track their evolution under an external field, in a range of twisted compensated and uncompensated configurations differing by the number of layers. We show that twisted stacking consistently modifies the local magnetic switching behaviour of constituent flakes, and that these modifications are spatially non-uniform. In the case of compensated component flakes (even number of layers), we demonstrate that the combination of dipolar coupling and stacking-induced strain can reduce the switching field by over an order of magnitude. Conversely, in uncompensated component flakes (odd number of layers), we observe indications of a non-zero interlayer exchange interaction between twisted flakes during magnetization reversal, which can persistently modify magnetic order. This work highlights the importance of spatial imaging in investigating stacking-induced magnetic effects, particularly in the case of twistronics where spatial variation is expected and can be conflated with structural imperfections., Comment: 6 main text pages, 4 figures plus 8 supplementary information pages, 9 figures

The inhomogeneous magnetic stray field of micromagnets has been extensively used to manipulate electron spin qubits. By means of micromagnetic simulations and scanning superconducting quantum interference device microscopy, we show that the polycrystallinity of the magnet and non-uniform magnetization significantly impact the stray field and corresponding qubit properties. We find that the random orientation of the crystal axis in polycrystalline Co magnets alters the qubit frequencies by up to 0.5 GHz, compromising single qubit addressability and single gate fidelities. We map the stray field of Fe micromagnets with an applied magnetic field of up to 500 mT (mimicking conditions when operating qubits), finding field gradients above 1 mT/nm. The measured gradients and the lower magnetocrystalline anisotropy of Fe demonstrate the advantage of using Fe instead of Co for magnets in spin qubit devices. These properties of Fe also enabled us to design a 2D arrangement of nanomagnets for driving spin qubits distributed on a 2D lattice.

Two-dimensional materials are extraordinarily sensitive to external stimuli, making them ideal for studying fundamental properties and for engineering devices with new functionalities. One such stimulus, strain, affects the magnetic properties of the layered magnetic semiconductor CrSBr to such a degree that it can induce a reversible antiferromagnetic-to-ferromagnetic phase transition. Given the pervasiveness of non-uniform strain in exfoliated two-dimensional magnets, it is crucial to understand its impact on their magnetic behavior. Using scanning SQUID-on-lever microscopy, we directly image the effects of spatially inhomogeneous strain on the magnetization of layered CrSBr as it is polarized by a field applied along its easy axis. The evolution of this magnetization and the formation of domains is reproduced by a micromagnetic model, which incorporates the spatially varying strain and the corresponding changes in the local interlayer exchange stiffness. The observed sensitivity to small strain gradients along with similar images of a nominally unstrained CrSBr sample suggest that unintentional strain inhomogeneity influences the magnetic behavior of exfoliated samples and must be considered in the design of future devices., Comment: 15 pages, 4 figures, 1 supplementary section

Many bacteria share the fascinating ability to sense Earth's magnetic field -- a process known as magnetotaxis. These bacteria synthesize magnetic nanoparticles, called magnetosomes, within their own cell body and arrange them to form a linear magnetic chain. The chain, which behaves like a compass needle, aligns the microorganisms with the geomagnetic field. Here, we measure the magnetic hysteresis of an individual bacterium of the species Magnetospirillum gryphiswaldense via ultrasensitive torque magnetometry. These measurements, in combination with transmission electron microscopy and micromagnetic simulations, reveal the magnetic configurations of the magnetosomes, their progression as a function of applied field, as well as the total remanent magnetic moment and effective magnetic anisotropy of a chain within a single bacterium. Knowledge of magnetic properties is crucial both for understanding the mechanisms behind magnetotaxis and for the design of systems exploiting magnetotactic bacteria in biomedical applications., Comment: 8 pages, 4 figures, 5-page supplemental material

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.

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, $T_c$, sensitivity to atmospheric conditions and difficulties in preparing clean large-area samples still present major limitations to further progress. The remarkably stable high-$T_c$ 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 address the spin-flip transition in bilayer CrSBr by direct imaging of the emerging antiferromagnetic (AFM) to ferromagnetic (FM) phase wall and elucidate the magnetic properties of CrSBr around its ordering temperature. Our work will enable the engineering of exotic electronic and magnetic phases in CrSBr and the realisation of novel nanomagnetic devices based on this highly promising vdW magnet., Comment: 8 pages, 4 figures, plus supplementary material. Questions and comments are welcome

Cold ions in traps are well-established, highly controllable quantum systems with a wide variety of applications in quantum information, precision spectroscopy, clocks and chemistry. Nanomechanical oscillators are used in advanced sensing applications and for exploring the border between classical and quantum physics. Here, we report on the implementation of a hybrid system combining a metallic nanowire with laser-cooled ions in a miniaturised ion trap. We demonstrate resonant and off-resonant coupling of the two systems and the coherent motional excitation of the ion by the mechanical drive of the nanowire. The present results open up avenues for mechanically manipulating the quantum motion of trapped ions, for the development of ion-mechanical hybrid quantum systems and for the sympathetic cooling of mechanical systems by trapped ions and vice versa.

Magnetic ordering in two-dimensional (2D) materials has recently emerged as a promising platform for data storage, computing, and sensing. To advance these developments, it is vital to gain a detailed understanding of how the magnetic order evolves on the nanometer-scale as a function of the number of atomic layers and applied magnetic field. Here, we image few-layer $\text{Cr}_2\text{Ge}_2\text{Te}_6$ using a combined scanning superconducting quantum interference device and atomic force microscopy probe. Maps of the material's stray magnetic field as a function of applied magnetic field reveal its magnetization per layer as well as the thickness-dependent magnetic texture. Using a micromagnetic model, we correlate measured stray-field patterns with the underlying magnetization configurations, including labyrinth domains and skyrmionic bubbles. Comparison between real-space images and simulations demonstrates that the layer dependence of the material's magnetic texture is a result of the thickness-dependent balance between crystalline and shape anisotropy. These findings represent an important step towards 2D spintronic devices with engineered spin configurations and controlled dependence on external magnetic fields., Comment: 15 pages, 4 figures, and supplementary information

Mobile electrons in the semiconductor monolayer-MoS$_2$ form a ferromagnetic state at low temperature. The Fermi sea consists of two circles, one at the $K$-point, the other at the $\tilde{K}$-point, both with the same spin. Here, we present an optical experiment on gated MoS$_2$ at low electron-density in which excitons are injected with known spin and valley quantum numbers. The resulting trions are identified using a model which accounts for the injection process, the formation of antisymmetrized trion states, electron-hole scattering from one valley to the other, and recombination. The results are consistent with a complete spin polarization. From the splittings between different trion states, we measure the exchange energy, $\Sigma$, the energy required to flip a single spin within the ferromagnetic state, as well as the intervalley Coulomb exchange energy, $J$. We determine $\Sigma=11.2\,$meV and $J=5\,$meV at $n=1.5 \times 10^{12}\,$cm$^{-2}$, and find that $J$ depends strongly on the electron density, $n$., Comment: 13 pages, 11 figures

Focused-electron-beam-induced deposition is a promising technique for patterning nanomagnets for spin qubit control in a single step. We fabricate cobalt nanomagnets in such a process, obtaining cobalt contents and saturation magnetizations comparable to or higher than those typically obtained using electron-beam lithography. We characterize the nanomagnets using transmission electron microscopy and image their stray magnetic field using scanning NV magnetometry, finding good agreement with micromagnetic simulations. The magnetometry reveals the presence of magnetic domains and halo side-deposits, which are common for this fabrication technique. Finally, we estimate dephasing times for electron spin qubits in the presence of disordered stray fields due to these side-deposits.

We image and characterize the mechanical modes of a 2D drum resonator made of hBN suspended over a high-stress Si$_3$N$_4$ membrane. Our measurements demonstrate hybridization between various modes of the hBN resonator and those of the Si$_3$N$_4$ membrane. The measured resonance frequencies and spatial profiles of the modes are consistent with finite-element simulations based on an idealized geometry. Spectra of the thermal motion reveal that, depending on the degree of hybridization with modes of the heavier and higher-quality-factor Si$_3$N$_4$ 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 Si$_3$N$_4$ membranes for optomechanical or sensing applications., Comment: 16 pages, 4 figure, 1 supplementary section (6 pages, 3 figures)

We developed a process to fabricate nanoscale metallic gate electrodes on scanning probe cantilevers, including on the irregular surface of protruding cantilever tips. The process includes a floating-layer technique to coat the cantilevers in electron-beam resist. We demonstrate gate definition through a lift-off process, as well as through an etching process. The cantilevers maintain a high force sensitivity after undergoing the patterning process. Our method allows the patterning of nanoscale devices on fragile scanning probes, extending their functionality as sensors.

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., Comment: 10 pages, 6 figures, 1 table

Nanometer-scale imaging of magnetization and current density is the key to deciphering the mechanisms behind a variety of new and poorly understood condensed matter phenomena. The recently discovered correlated states hosted in atomically layered materials such as twisted bilayer graphene or van der Waals heterostructures are noteworthy examples. Manifestations of these states range from superconductivity, to highly insulating states, to magnetism. Their fragility and susceptibility to spatial inhomogeneities limits their macroscopic manifestation and complicates conventional transport or magnetization measurements, which integrate over an entire sample. In contrast, techniques for imaging weak magnetic field patterns with high spatial resolution overcome inhomogeneity by measuring the local fields produced by magnetization and current density. Already, such imaging techniques have shown the vulnerability of correlated states in twisted bilayer graphene to twist-angle disorder and revealed the complex current flows in quantum Hall edge states. Here, we review the state-of-the-art techniques most amenable to the investigation of such systems, because they combine the highest magnetic field sensitivity with the highest spatial resolution and are minimally invasive: magnetic force microscopy, scanning superconducting quantum interference device microscopy, and scanning nitrogen-vacancy center microscopy. We compare the capabilities of these techniques, their required operating conditions, and assess their suitability to different types of source contrast, in particular magnetization and current density. Finally, we focus on the prospects for improving each technique and speculate on its potential impact, especially in the rapidly growing field of two-dimensional (2D) materials., Comment: 24 pages, 4 figures, 3 boxes, 1 table

Moir\'e superlattices in two-dimensional (2D) van der Waals (vdW) heterostructures provide 20 an efficient way to engineer electron band properties. The recent discovery of exotic quantum phases and their interplay in twisted bilayer graphene (tBLG) has built this moir\'e system one of the most renowned condensed matter platforms (1-10). So far the studies of tBLG has been mostly focused on the lowest two flat moir\'e bands at the first magic angle {\theta}m1 ~ 1.1{\deg}, leaving high-order moir\'e bands and magic angles largely unexplored. Here we report 25 an observation of multiple well-isolated flat moir\'e bands in tBLG close to the second magic angle {\theta}m2 ~ 0.5{\deg}, which cannot be explained without considering electron-election interactions. With high magnetic field magneto-transport measurements, we further reveal a qualitatively new, energetically unbound Hofstadter butterfly spectrum in which continuously extended quantized Landau level gaps cross all trivial band-gaps. The 30 connected Hofstadter butterfly strongly evidences the topologically nontrivial textures of the multiple moir\'e bands. Overall, our work provides a new perspective for understanding the quantum phases in tBLG and the fractal Hofstadter spectra of multiple topological bands.

We realize mirror templates on the tips of optical fibers using a single-shot CO$_2$ laser ablation procedure. We perform a systematic study of the influence of the pulse power, pulse duration, and laser spot size on the radius of curvature, depth, and diameter of the mirror templates. We find that these geometrical characteristics can be tuned to a larger extent than has been previously reported, and notably observe that compound convex-concave shapes can be obtained. This detailed investigation should help further the understanding of the physics of CO$_2$ laser ablation processes and help improve current models. We additionally identify regimes of ablation parameters that lead to mirror templates with favorable geometries for use in cavity quantum electrodynamics and optomechanics.

Classically coherent dynamics analogous to those of quantum two-level systems are studied in the setting of force sensing. We demonstrate quantitative control over the coupling between two orthogonal mechanical modes of a nanowire cantilever, through measurement of avoided crossings as we deterministically position the nanowire inside an electric field. Furthermore, we demonstrate Rabi oscillations between the two mechanical modes in the strong coupling regime. These results give prospects of implementing coherent two-mode control techniques for force sensing signal enhancement., Comment: 16 pages, 4 figures

Coupling a microscopic mechanical resonator to a nano-scale 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. We employ here a monolithic semiconductor system. The nano-scale quantum system is a quantum dot; the mechanical resonator a microscopic trumpet which simultaneously optimizes the mechanical and photonic properties. The quantum dot transition is driven resonantly. Via the resonance fluorescence, we observe mechanical Brownian motion even at 4K, and demonstrate a coupling to mechanical modes of different types. We identify a mechanical mode with a cooperativity larger than one. We show analytically that the Heisenberg limit on displacement measurement can be reached with an embedded two-level system in the case of a transform-limited optical emitter with perfect photon detection. We argue that operation close to the Heisenberg limit is achievable with state-of-the-art quantum dot devices.

We present the experimental realization of a quantum fiber-pigtail. The device consists of a semiconductor quantum-dot embedded into a conical photonic wire that is directly connected to the core of a fiber-pigtail. We demonstrate a photon collection efficiency at the output of the fiber of 5.8% and suggest realistic improvements for the implementation of a useful device in the context of quantum information. We finally discuss potential applications in scanning probe microscopy.

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., Comment: 8 pages, 4 figures

Solid-state systems which mimic two-level atoms are being actively developed. Improving the quantum coherence of these systems, for instance spin qubits or single photon emitters using semiconductor quantum dots, involves dealing with noise. The sources of noise are inherent to the semiconductor and are complex. Charge noise results in a fluctuating electric field, spin noise in a fluctuating magnetic field at the location of the qubit, and both can lead to dephasing and decoherence of optical and spin states. We investigate noise in an ultra-pure semiconductor using a minimally-invasive, ultra-sensitive, local probe: resonance fluorescence from a single quantum dot. We distinguish between charge noise and spin noise via a crucial difference in their optical signatures. Noise spectra for both electric and magnetic fields are derived. The noise spectrum of the charge noise can be fully described by the fluctuations in an ensemble of localized charge defects in the semiconductor. We demonstrate the "semiconductor vacuum" for the optical transition at frequencies above 50 kHz: by operating the device at high enough frequencies, we demonstrate transform-limited quantum dot optical linewidths.

We discuss hybrid systems in which a mechanical oscillator is coupled to another (microscopic) quantum system, such as trapped atoms or ions, solid-state spin qubits, or superconducting devices. We summarize and compare different coupling schemes and describe first experimental implementations. Hybrid mechanical systems enable new approaches to quantum control of mechanical objects, precision sensing, and quantum information processing., Comment: To cite this review, please refer to the published book chapter (see Journal-ref and DOI). This v2 corresponds to the published version

We propose an implementation for quantum information processing based on coherent manipulations of nuclear spins I=3/2 in GaAs semiconductors. We describe theoretically an NMR method which involves multiphoton transitions and which exploits the non-equidistance of nuclear spin levels due to quadrupolar splittings. Starting from known spin anisotropies we derive effective Hamiltonians in a generalized rotating frame, valid for arbitrary I, which allow us to describe the non-perturbative time evolution of spin states generated by magnetic rf fields. We identify an experimentally accessible regime where multiphoton Rabi oscillations are observable. In the nonlinear regime, we find Berry phase interference effects., Comment: 4 pages, 6 EPS figures, REVTex