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Photoluminescent defects in diamond, like the nitrogen-vacancy (NV) color center, are at the forefront of emerging optical quantum technologies. Most emit in the visible and near-infrared spectral region below 1000 nm (NIR-I), limiting their applications in photonics, fiber communications, and biology. Here, we show that the nitrogen-vacancy-nitrogen ($N_2V$) center, which emits in the visible and near-infrared-II (NIR-II, 1000-1700 nm), is ubiquitous in as-synthesized and processed nitrogen-doped diamond from bulk samples to nanoparticles. We demonstrate that $N_2V$ is also present in commercially available state-of-the-art NV diamond sensing chips made via chemical vapor deposition (CVD). In high-pressure high-temperature (HPHT) diamonds, the photoluminescence (PL) intensity of both $N_2V$ charge states, $N_2V^0$ in the visible and $N_2V^-$ in the NIR-II, increases with increasing substitutional nitrogen concentration. We determine the PL lifetime of $N_2V^-$ to be 0.3 ns and compare a quantum optical and density functional theory model of the $N_2V^-$ with experimental PL spectra. Finally, we show that detonation nanodiamonds (DND) show stable PL in the NIR-II, which we attribute to the $N_2V$ color center, and use this NIR-II PL to image DNDs inside skin cells. Our results will contribute to the scientific and technological exploration and development of the $N_2V$ color center and inspire more research into its effect on other color centers in diamond.

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

Optically addressable solid-state spins are an important platform for practical quantum technologies. Van der Waals material hexagonal boron nitride (hBN) is a promising host as it contains a wide variety of optical emitters, but thus far observations of addressable spins have been sparse, and most of them lacked a demonstration of coherent spin control. Here we demonstrate robust optical readout of spin pairs in hBN with emission wavelengths spanning from violet to the near-infrared. We find these broadband spin pairs exist naturally in a variety of hBN samples from bulk crystals to powders to epitaxial films, and can be coherently controlled across the entire wavelength range. Furthermore, we identify the optimal wavelengths for independent readout of spin pairs and boron vacancy spin defects co-existing in the same sample. Our results establish the ubiquity of the optically addressable spin pair system in hBN across a broad parameter space, making it a versatile playground for spin-based quantum technologies.

Widefield quantum diamond microscopy is a powerful technique for imaging magnetic fields with high sensitivity and spatial resolution. However, current methods to approach the ultimate spatial resolution ($<500\,$nm) are impractical for routine use as they require time-consuming fabrication or transfer techniques to precisely interface the diamond sensor with the sample to be imaged. To address this challenge, we have designed a co-axial sensor holder that enables simple, repeatable sensor-sample interfacing while being compatible with high numerical aperture (NA) optics. With our new design we demonstrate low standoffs $<500\,$nm with a millimetre sized sensor. We also explore the relationship between spatial resolution and NA spanning from 0.13 to 1.3. The spatial resolution shows good agreement with the optical diffraction limit at low NA but deviates at high NA, which is shown to be due to optical aberrations. Future improvements to our design are discussed, which should enable magnetic imaging with $<500\,$nm resolution in an accessible, easy-to-use instrument.

Optically detected magnetic resonance (ODMR) has been observed from emitters in hexagonal boron nitride across a broad range of wavelengths, but so far an understanding of their microscopic structure and the physical origin of ODMR has been lacking. Here we perform comprehensive measurements and modelling of the spin-resolved photodynamics of ensembles and single emitters, and uncover a universal model that accounts, and provides an intuitive physical explanation, for all key experimental features. The model assumes a pair of nearby point defects -- a primary optically active defect and a secondary defect. Charge transfer between the two defects creates a metastable weakly coupled spin pair with ODMR naturally arising from selection rules. Our optical-spin defect pair (OSDP) model resolves several previously open questions including the asymmetric envelope of the Rabi oscillations, the large variability in ODMR contrast amplitude and sign, and the wide spread in emission wavelength. It may also explain similar phenomena observed in other wide bandgap semiconductors such as GaN. The presented framework will be instrumental in guiding future theoretical and experimental efforts to study and engineer solid-state spin pairs and unlock their potential for quantum technology applications.

Boron vacancy centre ($V_{\rm B}^-$) ensembles in hexagonal boron nitride (hBN) have attracted recent interest for their potential as two-dimensional solid-state quantum sensors. Irradiation is necessary for $V_{\rm B}^-$ creation, however, to date only limited attention has been given to optimising the defect production process, especially in the case of bulk irradiation with high-energy particles, which offers scalability through the potential for creating ensembles in large volumes of material. Here we systematically investigate the effect of electron irradiation by varying the dose delivered to a range of hBN samples, which differ in their purity, and search for an optimum in measurement sensitivity. We find that moderate electron irradiation doses ($\approx 5\times 10^{18}$~cm$^{-2}$) appear to offer the best sensitivity, and also observe a dependence on the initial crystal purity. These results pave the way for the scalable and cost-effective production of hBN quantum sensors, and provide insight into the mechanisms limiting $V_{\rm B}^-$ spin properties., Comment: 8pages, 5 figures

We derive sharp-interface models for one-dimensional brittle fracture via the inverse-deformation approach. Methods of Gamma-convergence are employed to obtain the singular limits of previously proposed models. The latter feature a local, non-convex stored energy of inverse strain, augmented by small interfacial energy, formulated in terms of the inverse-strain gradient. They predict spontaneous fracture with exact crack-opening discontinuities, without the use of damage (phase) fields or pre-existing cracks; crack faces are endowed with a thin layer of surface energy. The models obtained herewith inherit the same properties, except that surface energy is now concentrated at the crack faces. Accordingly, we construct energy-minimizing configurations. For a composite bar with a breakable layer, our results predict a pattern of equally spaced cracks whose number is given as an increasing function of applied load., Comment: 12 pages, 8 figures

We propose a model for nonlinearly elastic membranes undergoing finite deformations while confined to a regular frictionless surface in $\mathbb{R}^3$. This is a physically correct model of the analogy sometimes given to motivate harmonic maps between manifolds. The proposed energy density function is convex in the strain pair comprising the deformation gradient and the local area ratio. If the target surface is a plane, the problem reduces to 2-dimensional, polyconvex nonlinear elasticity addressed by J.M. Ball. On the other hand, the energy density is not rank-one convex for unconstrained deformations into $\mathbb{R}^3$. We show that the problem admits an energy-minimizing configuration when constrained to lie on the given surface. For a class of Dirichlet problems, we demonstrate that the minimizing deformation is a homeomorphism onto its image on the given surface and establish the weak Eulerian form of the equilibrium equations., Comment: 13 pages

Magnetic van der Waals materials are often proposed for use in future spintronic devices, aiming to leverage the combination of long-range magnetic order and near-atomic thinness to produce energy-efficient components. One class of material that has been discussed in this context are the iron halides FeCl$_2$ and FeBr$_2$, which are A-type antiferromagnets with strong uniaxial magnetocrystalline anisotropy. However, despite characterization of the bulk materials, the possibility for sustaining the magnetic behaviors that would underpin such applications in thin flakes has not been investigated. In this work, we use nitrogen-vacancy (NV) center microscopy to quantitatively image magnetism in individual exfoliated flakes of these iron halides, revealing the absence of magnetic remanence, a weak induced magnetization under bias field and variable behavior versus temperature. We show that our results are consistent with the antiferromagnetic behavior of the bulk material with a soft ferromagnetic uncompensated layer, indicating that extended ($>1~\mu$m) ferromagnetic domains are not sustained even at low temperatures (down to 4 K). Finally, we find that the magnetic order is strongly affected by the sample preparation, with a surprising diamagnetic order observed in a thin, hydrated sample., Comment: 15 pages, 13 figures

Detecting magnetic noise from small quantities of paramagnetic spins is a powerful capability for chemical, biochemical, and medical analysis. Quantum sensors based on optically addressable spin defects in bulk semiconductors are typically employed for such purposes, but the 3D crystal structure of the sensor inhibits the sensitivity by limiting the proximity of the defects to the target spins. Here we demonstrate the detection of paramagnetic spins using spin defects hosted in hexagonal boron nitride (hBN), a van der Waals material which can be exfoliated into the 2D regime. We first create negatively charged boron vacancy (V$_{\rm B}^-$) defects in a powder of ultrathin hBN nanoflakes ($<10$~atomic monolayers thick on average) and measure the longitudinal spin relaxation time ($T_1$) of this system. We then decorate the dry hBN nanopowder with paramagnetic Gd$^{3+}$ ions and observe a clear $T_1$ quenching, under ambient conditions, consistent with the added magnetic noise. Finally, we demonstrate the possibility of performing spin measurements including $T_1$ relaxometry using solution-suspended hBN nanopowder. Our results highlight the potential and versatility of the hBN quantum sensor for a range of sensing applications, and pave the way towards the realisation of a truly 2D, ultrasensitive quantum sensor., Comment: 19 pages, 11 figures

We consider a class of models motivated by previous numerical studies of wrinkling in highly stretched, thin rectangular elastomer sheets. The model used is characterized by a finite-strain hyperelastic membrane energy perturbed by small bending energy. Without bending energy, the stored-energy density is not rank-one convex for general spatial deformations but reduces to a polyconvex function when restricted to the plane, i.e., two-dimensional hyperelasticity. In addition, it grows unbounded as the local area ratio approaches zero. The small-bending component of the model is the same as that in the classical von K\'arm\'an model. Here we prove the existence of energy minima for a general class of such models.

We study the nucleation and development of crack patterns in thin composite fibers under tension in this work. A fiber comprises an elastic core and an outer layer of a weaker brittle material. In recent tensile experiments on such composites, multiple cracks were observed to develop simultaneously on the outer layer. We propose here a simple one-dimensional model to predict such phenomenon. We idealize the problem as two axially loaded rods coupled by a linear interfacial condition. The latter can be regarded as an adhesive that resists slip between the two materials. One rod is modeled as a brittle material, and the other a linearly elastic material, both undergoing finite deformations.

Dense, near-surface (within 10 nm) ensembles of nitrogen-vacancy (NV) centres in diamond are rapidly moving into prominence as the workhorse of a variety of envisaged applications, ranging from the imaging of fast-fluctuating magnetic signals to the facilitation of nuclear hyperpolarisation. Unlike their bulk counterparts, near-surface ensembles suffer from charge stability issues and reduced NV formation efficiency due to the diamond surface's role as a vacancy sink during annealing and an electron sink afterwards. To this end, work is ongoing to determine the best methods for producing high-quality ensembles in this regime. Here we examine the prospects for creating such ensembles cost-effectively by implanting nitrogen-rich type Ib diamond with electron donors, aiming to exploit the high bulk nitrogen density to combat surface-induced band bending in the process. This approach has previously been successful at creating deeper ensembles, however we find that in the near-surface regime there are fewer benefits over nitrogen implantation into pure diamond substrates. Our results suggest that control over diamond surface termination during annealing is key to successfully creating high-yield near-surface NV ensembles generally, and implantation into type Ib diamond may be worth revisiting once that has been accomplished., Comment: 7 pages, 3 figures

We consider a class of single-director Cosserat shell models accounting for both curvature and finite mid-plane strains. We assume a polyconvexity condition for the stored-energy function that reduces to a physically correct membrane model in the absence of bending. With appropriate growth conditions, we establish the existence of energy minimizers. The local orientation of a minimizing configuration is maintained via the blowup of the stored energy as a version of the local volume ratio approaches zero. Finally, we specialize our results to three constrained versions of the theory commonly employed in the subject., Comment: 10 pages

Predicting measurement outcomes from an underlying structure often follows directly from fundamental physical principles. However, a fundamental challenge is posed when trying to solve the inverse problem of inferring the underlying source-configuration based on measurement data. A key difficulty arises from the fact that such reconstructions often involve ill-posed transformations and that they are prone to numerical artefacts. Here, we develop a numerically efficient method to tackle this inverse problem for the reconstruction of magnetisation maps from measured magnetic stray field images. Our method is based on neural networks with physically inferred loss functions to efficiently eliminate common numerical artefacts. We report on a significant improvement in reconstruction over traditional methods and we show that our approach is robust to different magnetisation directions, both in- and out-of-plane, and to variations of the magnetic field measurement axis orientation. While we showcase the performance of our method using magnetometry with Nitrogen Vacancy centre spins in diamond, our neural-network-based approach to solving inverse problems is agnostic to the measurement technique and thus is applicable beyond the specific use-case demonstrated in this work., Comment: 11 pages, 6 figures

Widefield quantum microscopy based on nitrogen-vacancy (NV) centres in diamond has emerged as a powerful technique for quantitative mapping of magnetic fields with a sub-micron resolution. However, the accuracy of the technique has not been characterised in detail so far. Here we show that optical aberrations in the imaging system may cause large systematic errors in the measured quantity beyond trivial blurring. We introduce a simple theoretical framework to model these effects, which extends the concept of a point spread function to the domain of spectral imaging. Using this model, the magnetic field imaging of test magnetic samples is simulated under various scenarios, and the resulting errors quantified. We then apply the model to previously published data, show that apparent magnetic anomalies can be explained by the presence of optical aberrations, and demonstrate a post-processing technique to retrieve the source quantity with improved accuracy. This work presents a guide to predict and mitigate aberration induced artefacts in quantitative NV-based widefield imaging and in spectral imaging more generally., Comment: The following article has been submitted to/accepted by AVS Quantum Science. After it is published, it will be found at https://publishing.aip.org/resources/librarians/products/journals/

Van der Waals (vdW) magnets are appealing candidates for realising spintronic devices that exploit current control of magnetization (e.g. switching or domain wall motion), but so far experimental demonstrations have been sparse, in part because of challenges associated with imaging the magnetization in these systems. Widefield nitrogen-vacancy (NV) microscopy allows rapid, quantitative magnetic imaging across entire vdW flakes, ideal for capturing changes in the micromagnetic structure due to an electric current. Here we use a widefield NV microscope to study the effect of current injection in thin flakes ($\sim10$nm) of the vdW ferromagnet Fe$_3$GeTe$_2$ (FGT). We first observe current-reduced coercivity on an individual domain level, where current injection in FGT causes substantial reduction in the magnetic field required to locally reverse the magnetisation. We then explore the possibility of current-induced domain-wall motion, and provide preliminary evidence for such a motion under relatively low current densities, suggesting the existence of strong current-induced torques in our devices. Our results illustrate the applicability of widefield NV microscopy to imaging spintronic phenomena in vdW magnets, highlight the possibility of efficient magnetization control by direct current injection without assistance from an adjacent conductor, and motivate further investigations of the effect of currents in FGT and other vdW magnets., Comment: 18 pages, 9 figures

We present a general approach to the bifurcation analysis of elastic frameworks with symmetry. While group-theoretic methods for bifurcation problems with symmetry are well known, their actual implementation in the context of elastic frameworks is not straightforward. We consider frames comprising assemblages of Cosserat rods, and the main difficulty arises from the nonlinear configuration space, due to the presence of (cross-sectional) rotation fields. We avoid this via a single-rod formulation, developed earlier by one of the authors, whereby the governing equations are embedded in a linear space. The field equations comprise the assembly of all rod equations, supplemented by compatibility and equilibrium conditions at the joints. We demonstrate their equivariance under the symmetry-group action, and the implementation of group-theoretic methods is now natural within the linear-space context. All potential generic, symmetry-breaking bifurcations are predicted apriori. We then employ an open-source path-following code, which can detect and compute simple, onedimensional bifurcations; multiple bifurcation points are beyond its capabilities. For the latter, we construct symmetry-reduced problems implemented by appropriate substructures. Multiple bifurcations are rendered simple, and the path-following code is again applicable. We first analyze a simple tripod framework, providing all details of our methodology. We then treat a hexagonal space frame via the same approach. The tripod and the hexagonal dome both exhibit simple and double bifurcation points., Comment: preprint

Interest in van der Waals materials often stems from a desire to miniaturise existing technologies by exploiting their intrinsic layered structure to create near atomically-thin components that do not suffer from surface defects. One appealing property is easily-switchable yet robust magnetic order, a quality only sparsely demonstrated in the case of in-plane anisotropy. In this work, we use widefield nitrogen-vacancy (NV) center magnetic imaging to measure the properties of individual flakes of CuCrP$_2$S$_6$, a multiferroic van der Waals magnet known to exhibit weak easy-plane anisotropy in the bulk. We chart the crossover between in-plane ferromagnetism in thin flakes down to the trilayer, and the bulk behaviour dominated by a low-field spin-flop transition. Further, by exploiting the directional dependence of NV center magnetometry, we are able to observe an instance of a predominantly out-of-plane ferromagetic phase near zero field, in contradiction with expectation and previous experiments on the bulk material. We attribute this to the presence of surface anisotropies arising from the sample preparation process or exposure to the ambient environment, which is expected to have more general implications for a broader class of weakly anisotropic van der Waals magnets., Comment: 24 pages, 20 figures (including supplementary information)

Magnetic imaging with nitrogen-vacancy centers in diamond, also known as quantum diamond microscopy, has emerged as a useful technique for the spatial mapping of charge currents in solid-state devices. In this work, we investigate an application to photovoltaic (PV) devices, where the currents are induced by light. We develop a widefield nitrogen-vacancy microscope that allows independent stimulus and measurement of the PV device, and test our system on a range of prototype crystalline silicon PV devices. We first demonstrate micrometer-scale vector magnetic field imaging of custom PV devices illuminated by a focused laser spot, revealing the internal current paths in both short-circuit and open-circuit conditions. We then demonstrate time-resolved imaging of photocurrents in an interdigitated back-contact solar cell, detecting current build-up and subsequent decay near the illumination point with microsecond resolution. This work presents a versatile and accessible analysis platform that may find distinct application in research on emerging PV technologies., Comment: 14 pages, 9 figures

Quantum microscopes based on solid-state spin quantum sensors have recently emerged as powerful tools for probing material properties and physical processes in regimes not accessible to classical sensors, especially on the nanoscale. Such microscopes have already found utility in a variety of problems, from imaging magnetism and charge transport in nanoscale devices, to mapping remanent magnetic fields from ancient rocks and biological organisms. However, applications of quantum microscopes have so far relied on sensors hosted in a rigid, three-dimensional crystal, typically diamond, which limits their ability to closely interact with the sample under study. Here we demonstrate a versatile and robust quantum microscope using quantum sensors embedded within a thin layer of a van der Waals (vdW) material, hexagonal boron nitride (hBN). To showcase the capabilities of this platform, we assemble several active vdW heterostructures, with an hBN layer acting as the quantum sensor. We demonstrate time-resolved, simultaneous temperature and magnetic imaging near the Curie temperature of a vdW ferromagnet as well as apply this unique microscope to map out charge currents and Joule heating in graphene. By enabling intimate proximity between sensor and sample, potentially down to a single atomic layer, the hBN quantum sensor represents a paradigm shift for nanoscale quantum sensing and microscopy. Moreover, given the ubiquitous use of hBN in modern materials and condensed matter physics research, we expect our technique to find rapid and broad adoption in these fields, further motivated by the prospect of performing in-situ chemical analysis and noise spectroscopy using advanced quantum sensing protocols.

The widefield diamond nitrogen-vacancy (NV) microscope is a powerful instrument for imaging magnetic fields. However, a key limitation impeding its wider adoption is its complex operation, in part due to the difficulty of precisely interfacing the sensor and sample to achieve optimum spatial resolution. Here we demonstrate a solution to this interfacing problem that is both practical and reliably minimizes NV-sample standoff. We built a compact widefield NV microscope which incorporates an integrated widefield diamond probe with full position and angular control, and developed a systematic alignment procedure based on optical interference fringes. Using this platform, we imaged an ultrathin (1 nm) magnetic film test sample, and conducted a detailed study of the spatial resolution. We reproducibly achieved an estimated NV-sample standoff (and hence spatial resolution) of at most $\sim2~\mu$m across a $\sim0.5$ mm field of view. Guided by these results, we suggest future improvements for approaching the optical diffraction limit. This work is a step towards realizing a widefield NV microscope suitable for routine high-throughput mapping of magnetic fields.

A dense layer of nitrogen-vacancy (NV) centers near the surface of a diamond can be interrogated in a widefield optical microscope to produce spatially resolved maps of local quantities such as magnetic field, electric field and lattice strain, providing potentially valuable information about a sample or device placed in proximity. Since the first experimental realization of such a widefield NV microscope in 2010, the technology has seen rapid development and demonstration of applications in various areas across condensed matter physics, geoscience and biology. This Perspective analyzes the strengths and shortcomings of widefield NV microscopy in order to identify the most promising applications and guide future development. We begin with a brief review of quantum sensing with ensembles of NV centers, and the experimental implementation of widefield NV microscopy. We then compare this technology to alternative microscopy techniques commonly employed to probe magnetic materials and charge flow distributions. Current limitations in spatial resolution, measurement accuracy, magnetic sensitivity, operating conditions and ease of use, are discussed. Finally, we identify the technological advances that solve the aforementioned limitations, and argue that their implementation would result in a practical, accessible, high-throughput widefield NV microscope., Comment: 22 pages, 8 figures

The nitrogen-vacancy (NV) centre in diamond has emerged as a candidate to non-invasively hyperpolarise nuclear spins in molecular systems to improve the sensitivity of nuclear magnetic resonance (NMR) experiments. Several promising proof of principle experiments have demonstrated small-scale polarisation transfer from single NVs to hydrogen spins outside the diamond. However, the scaling up of these results to the use of a dense NV ensemble, which is a necessary prerequisite for achieving realistic NMR sensitivity enhancement, has not yet been demonstrated. In this work, we present evidence for a polarising interaction between a shallow NV ensemble and external nuclear targets over a micrometre scale, and characterise the challenges in achieving useful polarisation enhancement. In the most favourable example of the interaction with hydrogen in a solid state target, a maximum polarisation transfer rate of $\approx 7500$ spins per second per NV is measured, averaged over an area containing order $10^6$ NVs. Reduced levels of polarisation efficiency are found for liquid state targets, where molecular diffusion limits the transfer. Through analysis via a theoretical model, we find that our results suggest implementation of this technique for NMR sensitivity enhancement is feasible following realistic diamond material improvements.

After initial proof-of-principle demonstrations, optically pumped nitrogen-vacancy (NV) centres in diamond have been proposed as a non-invasive platform to achieve hyperpolarisation of nuclear spins in molecular samples over macroscopic volumes and enhance the sensitivity in nuclear magnetic resonance (NMR) experiments. In this work, we model the process of polarisation of external samples by NV centres and theoretically evaluate their performance in a range of scenarios. We find that average nuclear spin polarisations exceeding 10% can in principle be generated over macroscopic sample volumes ($\gtrsim\mu$L) with a careful engineering of the system's geometry to maximise the diamond-sample contact area. The fabrication requirements and other practical challenges are discussed. We then explore the possibility of exploiting local polarisation enhancements in nano/micro-NMR experiments based on NV centres. For micro-NMR, we find that modest signal enhancements over thermal polarisation (by 1-2 orders of magnitude) can in essence be achieved with existing technology, with larger enhancements achievable via micro-structuring of the sample/substrate interface. However, there is generally no benefit for nano-NMR where the detection of statistical polarisation provides the largest signal-to-noise ratio. This work will guide future experimental efforts to integrate NV-based hyperpolarisation to NMR systems.

We consider a class of models for nonlinearly elastic surfaces in this work. We have in mind thin, highly deformable structures modeled directly as two-dimensional nonlinearly elastic continua, accounting for finite membrane and bending strains and thickness change. We assume that the stored-energy density is polyconvex with respect to the second gradient of the deformation, and we require that it grow unboundedly as the local area ratio approaches zero. For sufficiently fast growth, we show that the latter is uniformly bounded away from zero at an energy minimizer. With this in hand, we rigorously derive the weak form of the Euler-Lagrange equilibrium equations., Comment: 11 pages

We propose a one-dimensional, nonconvex elastic constitutive model with higher gradients that can predict spontaneous fracture at a critical load via a bifurcation analysis. It overcomes the problem of discontinuous deformations without additional field variables, such as damage or phase-field variables, and without a priori specified surface energy. Our main tool is the use of the inverse deformation, which can be extended to be a piecewise smooth mapping even when the original deformation has discontinuities describing cracks opening. We exploit this via the inverse-deformation formulation of finite elasticity due to Shield and Carlson, including higher gradients in the energy. The problem is amenable to a rigorous global bifurcation analysis in the presence of a unilateral constraint. Fracture under hard loading occurs on a bifurcating solution branch at a critical applied stretch level and fractured solutions are found to have surface energy arising from higher gradient effects., Comment: 30 pages, 9 figures

Thin layers of near-surface nitrogen-vacancy (NV) defects in diamond substrates are the workhorse of NV-based widefield magnetic microscopy, which has applications in physics, geology and biology. Several methods exist to create such NV layers, which generally involve incorporating nitrogen atoms (N) and vacancies (V) into the diamond through growth and/or irradiation. While there have been detailed studies of individual methods, a direct side-by-side experimental comparison of the resulting magnetic sensitivities is still missing. Here we characterise, at room and cryogenic temperatures, $\approx100$ nm thick NV layers fabricated via three different methods: 1) low-energy carbon irradiation of N-rich high-pressure high-temperature (HPHT) diamond, 2) carbon irradiation of $\delta$-doped chemical vapour deposition (CVD) diamond, 3) low-energy N$^+$ or CN$^-$ implantation into N-free CVD diamond. Despite significant variability within each method, we find that the best HPHT samples yield similar magnetic sensitivities (within a factor 2 on average) to our $\delta$-doped samples, of $<2$~$\mu$T Hz$^{-1/2}$ for DC magnetic fields and $<100$~nT Hz$^{-1/2}$ for AC fields (for a $400$~nm~$\times~400$~nm pixel), while the N$^+$ and CN$^-$ implanted samples exhibit an inferior sensitivity by a factor 2-5, at both room and low temperature. We also examine the crystal lattice strain caused by the respective methods and discuss the implications this has for widefield NV imaging. The pros and cons of each method, and potential future improvements, are discussed. This study highlights that low-energy irradiation of HPHT diamond, despite its relative simplicity and low cost, is a competitive method to create thin NV layers for widefield magnetic imaging.

We revisit the classic stability problem of the buckling of an inextensible, axially compressed beam on a nonlinear elastic foundation with a semi-analytical approach to understand how spatially localized deformation solutions emerge in many applications in mechanics. Instead of a numerical search for such solutions using arbitrary imperfections, we propose a systematic search using branch-following and bifurcation techniques along with group-theoretic methods to find all the bifurcated solution orbits (primary, secondary, etc.) of the system and to examine their stability and hence their observability. Unlike previously proposed methods that use multi-scale perturbation techniques near the critical load, we show that to obtain a spatially localized deformation equilibrium path for the perfect structure, one has to consider the secondary bifurcating path with the longest wavelength and follow it far away from the critical load. The novel use of group-theoretic methods here illustrates a general methodology for the systematic analysis of structures with a high degree of symmetry., Comment: Accepted for publication in Journal of Elasticity

Transverse wrinkles are known to appear in thin rectangular elastic sheets when stretched in the long direction. Numerically computed bifurcation diagrams for extremely thin, highly stretched films indicate entire orbits of wrinkling solutions, cf. Healey, et. al. [J. Nonlinear Sci., 23 (2013), pp.~777--805]. These correspond to arbitrary phase shifts of the wrinkled pattern in the transverse direction. While such behavior is normally associated with problems in the presence of a continuous symmetry group, an unloaded rectangular sheet possesses only a finite symmetry group. In order to understand this phenomenon, we consider a simpler problem more amenable to analysis -- a finite-length beam on a nonlinear softening foundation under axial compression. We first obtain asymptotic results via amplitude equations, that are valid as a certain non-dimensional beam length becomes sufficiently large. We deduce that any two phase-shifts of a solution differ from one another by exponentially small terms in that length. We validate this observation with numerical computations, indicating the presence of solution orbits for sufficiently long beams. We refer to this as "hidden asymptotic symmetry"., Comment: 20 pages, 10 figures

We consider a general class of parametrized displacement boundary value problems in incompressible nonlinear elasticity. We prove the existence of an unbounded solution branch of classical injective solutions emanating from the unforced stress-free reference configuration, which constitutes a sharp global implicit function theorem. The ramifications of this are: There exists at least one solution for any given applied loading, and or there exists solutions of arbitrarily large norm for some finite loading. We refer to this as solutions in the large. The nonlinear constraint equation enforcing incompressibility obviates the direct use of either the Leray-Schauder degree or an oriented degree previously developed for compressible problems. Instead we employ the nonlinear Fredholm degree for proper maps developed by Fitzpatrick, et. al. We establish the requisite admissibility properties in the presence of the constraint equation before proving the main results.

Recent work demonstrates that finite-deformation nonlinear elasticity is essential in the accurate modeling of wrinkling in highly stretched thin films. Geometrically exact models predict an isola-center bifurcation, indicating that for a bounded interval of aspect ratios only, stable wrinkles appear and then disappear as the macroscopic strain is increased. This phenomenon has been verified in experiments. In addition, recent experiments revealed the following striking phenomenon: For certain aspect ratios for which no wrinkling occurred upon the first loading, wrinkles appeared during the first unloading and again during all subsequent cyclic loading. Our goal here is to present a simple pseudo-elastic model, capturing the stress softening and residual strain observed in the experiments, that accurately predicts wrinkling behavior on the first loading that differs from that under subsequent cyclic loading. In particular for specific aspect ratios, the model correctly predicts the scenario of no wrinkling during first loading with wrinkling occurring during unloading and for all subsequent cyclic loading., Comment: 15 pages, 9 figures