The recent discovery of ferromagnetism in 2D van der Waals (vdW) crystals has generated widespread interest, owing to their potential for fundamental and applied research. Advancing the understanding and applications of vdW magnets requires methods to quantitatively probe their magnetic properties on the nanoscale. Here, we report the study of atomically thin crystals of the vdW magnet CrI 3 down to individual monolayers using scanning single-spin magnetometry, and demonstrate quantitative, nanoscale imaging of magnetisation, localised defects and magnetic domains. We determine the magnetisation of CrI 3 monolayers to be ≈ 16 µ B /nm 2 and find comparable values in samples with odd numbers of layers, whereas the magnetisation vanishes when the number of layers is even. We also establish that this inscrutable even-odd effect is intimately connected to the material structure, and that structural modifications can induce switching between ferro-and anti-ferromagnetic interlayer ordering. Besides revealing new aspects of magnetism in atomically thin CrI 3 crystals, these results demonstrate the power of single-spin scanning magnetometry for the study of magnetism in 2D vdW magnets.Magnetism in individual monolayers of vdW crystals has recently been observed in a range of materials, including semiconducting [3,4] and metallic [5][6][7] compounds. The discovery of such two dimensional magnetic order is per se non-trivial [8] and has triggered significant attention owing to emerging exotic phenomena including Kitaev spin liquids [9,10], or novel magneto-electric effects [11][12][13][14]. Remarkable efforts have led to the use of two-dimensional magnets as functional elements in spintronics, such as spin-filters [15, 16], spin-transistors [17], tunnelling magnetoresistance devices [18,19] or magnetoelectric switches [12][13][14]. Further advances hinge on methods for the quantitative study of the magnetic response of these atomically thin crystals at the nanoscale, but despite their central importance, the required experimental methods are still lacking. Indeed, transport ex-A z NV e NV z θ NV 3 µm 3 l a y e r s 2 l a y e r s B C, D 0.35 -0.35 0 B NV -B NV (mT) C 2 µm Magne�c stray-field map bias D 20 -20 0 σ (µ B /nm 2 ) 2 µm Magne�sa�on map FIG. 1.Nanoscale imaging of magnetism in twodimensional van der Waals magnets. A Schematic of the scanning single spin magnetometry technique employed in this work. A single Nitrogen-Vacancy (NV) electronic spin is scanned across few layer flakes of encapsulated CrI3 (encapsulation not shown). Stray magnetic fields from the sample are sensed by optically detected Zeeman shifts of the NV spin states, and imaged with nanoscale resolution (set by the sensor-sample separation zNV) by lateral scanning of the NV. The method detects magnetic fields along the NV spin quantisation axis eNV, at an angle θNV ∼ 54 • from the sample normal. B Optical micrograph of the CrI3 bi-and tri-layer flake of sample D1. C Magnetic field map of BNV across sample D1 recorded in a bias field B bias NV = 172.5...

Magnetic resonance imaging (MRI) has revolutionized biomedical science by providing non-invasive, three-dimensional biological imaging. However, spatial resolution in conventional MRI systems is limited to tens of micrometres, which is insufficient for imaging on molecular scales. Here, we demonstrate an MRI technique that provides subnanometre spatial resolution in three dimensions, with single electron-spin sensitivity. Our imaging method works under ambient conditions and can measure ubiquitous 'dark' spins, which constitute nearly all spin targets of interest. In this technique, the magnetic quantum-projection noise of dark spins is measured using a single nitrogen-vacancy (NV) magnetometer located near the surface of a diamond chip. The distribution of spins surrounding the NV magnetometer is imaged with a scanning magnetic-field gradient. To evaluate the performance of the NV-MRI technique, we image the three-dimensional landscape of electronic spins at the diamond surface and achieve an unprecedented combination of resolution (0.8 nm laterally and 1.5 nm vertically) and single-spin sensitivity. Our measurements uncover electronic spins on the diamond surface that can potentially be used as resources for improved magnetic imaging. This NV-MRI technique is immediately applicable to diverse systems including imaging spin chains, readout of spin-based quantum bits, and determining the location of spin labels in biological systems.

Microscopic studies of superconductors and their vortices play a pivotal role in understanding the mechanisms underlying superconductivity. Local measurements of penetration depths or magnetic stray fields enable access to fundamental aspects such as nanoscale variations in superfluid densities or the order parameter symmetry of superconductors. However, experimental tools that offer quantitative, nanoscale magnetometry and operate over large ranges of temperature and magnetic fields are still lacking. Here, we demonstrate the first operation of a cryogenic scanning quantum sensor in the form of a single nitrogen-vacancy electronic spin in diamond, which is capable of overcoming these existing limitations. To demonstrate the power of our approach, we perform quantitative, nanoscale magnetic imaging of Pearl vortices in the cuprate superconductor YBa2Cu3O7-δ. With a sensor-to-sample distance of ∼10 nm, we observe striking deviations from the prevalent monopole approximation in our vortex stray-field images, and find excellent quantitative agreement with Pearl's analytic model. Our experiments provide a non-invasive and unambiguous determination of the system's local penetration depth and are readily extended to higher temperatures and magnetic fields. These results demonstrate the potential of quantitative quantum sensors in benchmarking microscopic models of complex electronic systems and open the door for further exploration of strongly correlated electron physics using scanning nitrogen-vacancy magnetometry.

We demonstrate the use of shortcuts to adiabaticity protocols for initialisation, readout, and coherent control of dressed states generated by closed-contour, coherent driving of a single spin. Such dressed states have recently been shown to exhibit efficient coherence protection, beyond what their two-level counterparts can offer. Our state transfer protocols yield a transfer fidelity of ∼ 99.4(2) % while accelerating the transfer speed by a factor of 2.6 compared to the adiabatic approach. We show bi-directionality of the accelerated state transfer, which we employ for direct dressed state population readout after coherent manipulation in the dressed state manifold. Our results enable direct and efficient access to coherence-protected dressed states of individual spins and thereby offer attractive avenues for applications in quantum information processing or quantum sensing.