SUPPLEMENTARY INFORMATION

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1 Figure S. Experimental set-up

2 Figure S2. Dependence of ESR frequencies (GHz) on a magnetic field (G) applied in different directions with respect to NV axis ( θ 2π). The angle with respect to NV axis (in degrees) is indicated along resonant surface. h rêr Figure S3. The radial cross-section of the magnetic tip. 2

3 9 Magnetic Field (Arb. Units) B Bz Br Lorentzian Fit Radial Distance (μm) Figure S4 Simulated magnetic field of the tip having the following parameters: apex curvature radius 5nm, height 7μm, and radius of the base 2.5μm. The apex of the tip is 5nm above the plane of interest. The magnetization direction is along the tip axis. The field can be well fitted by a Lorentzian. A B y HμmL y HμmL x HμmL.5.5 x HμmL Figure S5. Shapes of isofrequency resonance lines for the S z => S z =+>transition as the magnetic cantilever is scanned above the NV center: (A) both NV axis and the cantilever magnetization are perpendicular to the surface of scan and (B) θ B =π/, θ NV =π/4, and ϕ=π/2. Each contour represents a resonant line corresponding to a particular microwave frequency. 3

4 One-dimensional imaging and magnetometry experiments. In a first set of experiments an inhomogeneous external magnetic field (gradient field) created by a thin metal wire causes a spatially dependent shift of the Zeeman levels of the NV marker that varies according to their location relative to the wire. A single diamond nanocrystal containing two NV defects was selected as test object for demonstrating the resolving power of our approach. Note that the two NV defects were irresolvable by confocal microscopy owing to their close spacing, but the presence of two emitters was confirmed by photon correlation measurements. Local Magnetic Field (G) Fluorescence Intensity I=25 ma NV2 NV MW frequency (MHz) Line Position (GHz) Current (A) Current (ma) NV 8G NV2 NV 37.5 o NV2 5. o Magnetic field (G) NV 2nm 7nm 5 nm NV2 8G μm I=6mA 66nm 54nm Distance from the wire (μm) Figure S6. One-dimensional imaging demonstration using a magnetic field gradient generated by a wire. The main graph shows the magnetic field experienced by two closely spaced NV defects in the nanocrystal for different currents flowing through wire. Inset at left upper corner shows a typical ESR spectrum of nanocrystal containing two NV defects. Lower inset shows resonant frequencies of NV defects used to calculate the main graph. Right graph shows. a simulated magnetic field profile of the wire, along with the relative radial positions of the two NV defects. The inset in Figure S6 shows the optically detected ESR spectrum of this diamond nanocrystal. Four lines mark the electron spin resonance transitions of the two centres. The amplitude and orientation of the magnetic field experienced by each NV defect was calculated as described above for different values of wire current. As expected for 4

5 immobilized nanocyrstals, the angle Θ for the quantization axes of the two NV centres (NV and NV2) with respect to external field was not dependent on current, and we have obtained Θ =37.5 and Θ 2 =5. for NV and NV2, respectively. The calculated values of the local magnetic fields experienced by NV and NV2 differed by 6% for all currents: B /B 2 =.6. This difference is related to the different distance of NV and NV2 from the wire and the inhomogeneous magnetic field generated by the wire. Since the geometry of wire was known (measured independently by atomic force microscopy) the radial distribution of the magnetic field can be accurately simulated. Knowing the magnitudes of the magnetic field at a given current (B =32G and B 2 =33G at I=6mA) it was possible to determine the distances of the two NVs from the wire edge: d =54nm and d 2 =66nm, respectively. The precision of determining the distances is defined by the accuracy of finding the resonance frequencies. The latter is given by the width of the ESR resonance 5MHz FWHM for the two defects (note that apart from magnetic field fluctuations, the driving microwave field also contributes to the finite linewidth of ESR transition). Based on this width we calculate a limiting resolution of 2nm as a crude estimate under the present experimental conditions (field gradient of.25 G/nm for the present structure at 6mA of current). 5

6 Broadening of resonance lines related to cantilever vibrations. All the imaging experiments presented in this letter were performed using either a magnetic AFM cantilever or a diamond nanocrystal attached to the AFM cantilever. In both cases we have used 3 2 tapping mode (AC mode) to scan the Intensity (A.U) 2 3 surface. In this mode the cantilever is driven to oscillate at its resonant frequency and the deflection feedback is set to keep the amplitude at a desired MW frequency (MHz) Figure S7. Broadening of ODMR lines related to vibrations of magnetic cantilever. value. Usually the amplitude of vibration of the cantilever is on the order of few tens of angstroms. When the probe is brought in close proximity to a region of high magnetic field gradients, this vibration causes the NV centre in the nanocrystal to experience an oscillating magnetic field. This causes the ODMR resonant lines to become broader. It is evident from the Figure S7 that sharp ODMR lines become broad on entering the high magnetic field gradient region and eventually change into a square shape in regions of very high magnetic field gradient. Although decoherence of NV spin is for the limiting cause of ESR line broadening, in the present experiment the vibrating cantilever dominates the linewidth at regions of high gradients, which in turn limits the apparent resolution. However, since this vibrational broadening is coherent, advanced echo based techniques synchronised with the vibration could be implemented to achieve the higher resolutions projected in the main manuscript. 6