Sensitive nanoscale magnetic resonance imaging (MRI) of target spins using nitrogen--vacancy (NV) centers in diamond will require a quantitative understanding of dominant noise at the surface. We probe this noise by applying dynamical decoupling to shallow NVs at calibrated depths. Results support a model of NV dephasing by a surface bath of electronic spins having a correlation rate of 200 kHz, much faster than that of the bulk N spin bath. Our method of combining nitrogen delta--doping growth and nanoscale depth imaging paves a way for studying spin noise present in diverse material surfaces.The negatively charged nitrogen--vacancy (NV) center in diamond is a robust quantum sensor of magnetic fields [1--4]. Although an individual NV has the capability to detect small numbers of electronic [5--7] and nuclear spins external to diamond [8--10], its widespread application in spin imaging has been limited by the ability to form shallow NVs that retain spin coherence near the surface. Shallow spins with long coherence time, T 2 , are important because quantum phase accumulation between two electronic spin states of the NV provides signal transduction, and hence the minimum detectable magnetic dipole moment scales as δµ ∝ r 3 / T 2 , with r the NV--target spin distance [3,4]. At odds with this figure of merit is strong evidence that the diamond crystal surface adversely affects T 2 , reducing it from ~2 ms for bulk NVs [11,12] to less than 10 µs for few--nm deep NVs [6,13--16], but the origin of this decoherence is an outstanding question. We consider in this letter a model of surface spin induced decoherence, a theory which has emerged from experiments on other systems [20,21] where long coherence is a requirement, such as in superconducting circuits [17,18] and spin

Spin-labeling of molecules with paramagnetic ions is an important approach for determining molecular structure, however current ensemble techniques lack the sensitivity to detect few isolated spins. In this Letter, we demonstrate two-dimensional nanoscale imaging of paramagnetic gadolinium compounds using scanning relaxometry of a single nitrogen vacancy (NV) center in diamond. Gadopentetate dimeglumine attached to an atomic force microscope tip is controllably interacted with and detected by the NV center, by virtue of the fact that the NV exhibits fast relaxation in the fluctuating magnetic field generated by electron spin flips in the gadolinium. Using this technique, we demonstrate a reduction in the T 1 relaxation time of the NV center by over two orders of magnitude, probed with a spatial resolution of 20 nm. Our result exhibits the viability of the technique for imaging individual spins attached to complex nanostructures or biomolecules, along with studying the magnetic dynamics of isolated spins.

Methods to detect paramagnetic species in biochemical media are discussed in the context of computational approaches to their spectral simulation and property prediction. Theory is discussed throughout in order to guide the reader through fundamental ESR principles and describe the important role computational techniques play in understanding such spectral data. Examples are provided from the literature, including pedagogical studies in order to offer a breadth of coverage for these fundamental computational approaches in analytical science.