Fast nanoscale addressability of nitrogen-vacancy spins via coupling to a dynamic ferromagnetic vortex

Abstract

The core of a ferromagnetic vortex domain creates a strong, localized magnetic field, which can be manipulated on nanosecond timescales, providing a platform for addressing and controlling individual nitrogen-vacancy centre spins in diamond at room temperature, with nanometre-scale resolution. Here, we show that the ferromagnetic vortex can be driven into proximity with a nitrogen-vacancy defect using small applied magnetic fields, inducing significant nitrogen-vacancy spin splitting. We also find that the magnetic field gradient produced by the vortex is sufficient to address spins separated by nanometre-length scales. By applying a microwave-frequency magnetic field, we drive both the vortex and the nitrogen-vacancy spins, resulting in enhanced coherent rotation of the spin state. Finally, we demonstrate that by driving the vortex on fast timescales, sequential addressing and coherent manipulation of spins is possible on ∼100 ns timescales.

ARTICLE

Received 12 Nov 2015 | Accepted 11 Apr 2016 | Published 14 Jun 2016

The core of a ferromagnetic vortex domain creates a strong, localized magnetic eld, which can be manipulated on nanosecond timescales, providing a platform for addressing and controlling individual nitrogen-vacancy centre spins in diamond at room temperature, with nanometre-scale resolution. Here, we show that the ferromagnetic vortex can be driven into proximity with a nitrogen-vacancy defect using small applied magnetic elds, inducing signicant nitrogen-vacancy spin splitting. We also nd that the magnetic eld gradient produced by the vortex is sufcient to address spins separated by nanometre-length scales. By applying a microwave-frequency magnetic eld, we drive both the vortex and the nitrogen-vacancy spins, resulting in enhanced coherent rotation of the spin state. Finally, we demonstrate that by driving the vortex on fast timescales, sequential addressing and coherent manipulation of spins is possible on B100 ns timescales.

DOI: 10.1038/ncomms11584 OPEN

Fast nanoscale addressability of nitrogen-vacancy spins via coupling to a dynamic ferromagnetic vortex

M.S. Wolf1, R. Badea1 & J. Berezovsky1

1 Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106, USA. Correspondence and requests for materials should be addressed to J.B. (email: mailto:[email protected]

Web End [email protected] ).

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Future spintronic devices will require fast, strong, localized magnetic elds (or effective magnetic elds) in an integrated platform1. Ferromagnetic (FM) vortices provide

a route towards this requirement, in particular, when coupled to nitrogen-vacancy (NV) centre spins in diamond. NVs are an increasingly attractive candidate for applications in both spin-based sensing24 and quantum information processing5,6 because of their long coherence times at room temperature79 and nanoscale size. But to take advantage of the NVs small size, individual spins must be addressable on nanometre-length scales, for individual manipulation and read-out of the spin state, and to control coupling between proximal spins.

Previous work has studied the possibility of using a magnetic eld gradient for spin addressability, although without the necessary combination of nanometre-scale resolution, fast control and potential scalability. By using the static fringe eld from a uniformly magnetized micromagnet, spin addressability was demonstrated in coupled gate-dened quantum dots with comparatively large-size scale10. Conned spin-wave modes in such micromagnets have been shown to locally couple to NV spins11. But for nanoscale NV addressability, larger magnetic eld gradients are required than are typically generated by a uniformly magnetized micromagnet. One approach is to use a scanning nanomagnet (that is, a magnetic force microscopy tip) to provide the necessary gradient12,13. The inverse process, scanning NV magnetometry, in which an NV centre is placed on a scanning probe, has proven to be a powerful technique for revealing the fringe elds from magnetic structures, including vortex domains1416. These scanning probe approaches do not permit fast control. Here, we show that a FM vortex can provide a large local magnetic eld and magnetic eld gradient for addressing spins, while also being able to rapidly drive the vortex position for coherent control of the NV spin.

ResultsCharacterizing the NV/vortex system. The core of a ferro-magnetic vortex provides a strong, local, controllable magnetic eld for spin addressability and control. The ground-state magnetization of a FM microdisk is a single vortex domain with in-plane magnetization circulating around a central core of magnetization normal to the plane1719. A simulation of vortex magnetization near the core, and the resulting fringe eld, is shown in Fig. 1a. The grey scale represents the normalized out-of-plane magnetization Mz/Ms, where Ms is the saturation magnetization. The scale is oversaturated (completely black) at the central vortex core, where MzEMs, in order to show more detail away from the core. The arrows show the magnetic eld in a plane 20 nm above the disk surface, with the arrow length and colour showing the eld strength on a logarithmic scale. The eld is strongest directly above the vortex core, and then falls off approximately as r 3 with small elds persisting beyond the core due to long-range deformation of the vortex domain.

To demonstrate the vortex-enabled spatial addressability, we need two or more NVs with nanometre-scale separation. Diamond nanoparticles (DNPs) provide a straightforward way to achieve this. We have used DNPs with mean diameter of 25 nm, containing typically one to several NVs. NVs are detected optically in a scanning microscopy setup illustrated in Fig. 1b. Figure 1c shows the two-photon correlation g(2) for the particular DNP we study here. The central dip in g(2)o5/6, indicating that there are roughly 5 or fewer NVs in this DNP. Because the metal substrate also generates some background counts, it is probable that the DNP contains three or four NVs.

NVs and FM vortices are coupled by overcoating a set of Permalloy disks with DNPs. To apply both a microwave (MW)

magnetic eld with amplitude BMW and a rapidly tunable static magnetic eld BCPW, the disks are fabricated atop a gold coplanar waveguide (CPW) as shown in the photoluminescence (PL) scan in Fig. 1d. Diagonally across the scan is a portion (centre) of the CPW. The CPW centre conductor constricts to a 10-mm width for 100 mm at the middle where the Permalloy (Ni0.81Fe0.19) disks

are seen as the array of blue circles. The gold, Permalloy and silicon are distinguishable in the PL scan because of differing background PL counts on these materials. DNPs are dispersed over the entire surface. DNPs generate diffraction limited spots across the image. Their PL intensity is dependent on the number of NVs within the DNP having typically one to several NVs per particle. The specic DNP/vortex system studied is circled in Fig. 1d and a zoomed in PL scan is shown in Fig. 1e. The black circle indicates the edge of a 2-mm-diameter, 40-nm-thick

Permalloy disk. The DNP appears as the bright spot in the lower half of the FM disk.

The vortex core position rv is controlled by the application of an in-plane magnetic eld B. To lowest order, |rv| w0|B|, with

rv>B (refs 20,21). Differential scanning magneto-optical Kerr effect (MOKE) microscopy is used to image the vortex, and to measure its displacement versus applied eld (see the Methods and ref. 22 for details). This technique uses a 15-kHz AC magnetic eld with peak amplitude of 1.25 mT to oscillate the vortex position by E100 nm, and measures the resulting change in magnetization. Here, this results in a positive signal

DyK at the vortex core position, with an amplitude corresponding to the displacement because of the AC eld. A static in-plane magnetic eld can be applied with arbitrary direction using permanent magnets with automated motion control, and time-dependent elds are generated using the CPW. Figure 1fh shows differential MOKE images of the vortex, as it is translated by increasing static eld Bx. The dark spot shows the location of the vortex core, which translates in the y direction as Bx is

increased. These measurements conrm that a single vortex domain is present and provide a measure of the vortex displacement susceptibility w0E80 nm mT 1. The sign of the displacement reveals the sign of the vortex helicity. By comparison to the PL scan in Fig. 1e, we can see that as the eld is increased from Bx 0 to 9 mT, the vortex approaches close

to the nanoparticle, then continues past.

Probing the NV/vortex interaction. NV spins are initialized and read-out via the standard optically detected magnetic resonance (ODMR) technique at room temperature23,24, using the same laser for NV excitation as is used for the MOKE measurements. A typical ODMR spectrum is produced by measuring the PL intensity while sweeping the MW frequency fMW. Dips in

the PL intensity reveal transitions between the ms 0 to ms 1

sublevels of the NV ground state. For a single NV in a magnetic eld, we generally expect to see two dips centred around the zero-eld splitting f0 2.87 GHz. See the Methods for more detail

on the techniques.

When the vortex core is brought near an NV (separation dv NVo100 nm), the NV spin experiences a signicant magnetic

eld from the vortex. Figure 2a shows ODMR versus fMW as the

vortex is swept past the NVs by increasing the magnetic eld Bx.

The path of the vortex rv(B) is shown schematically in the inset (also see Fig. 1fh for details). The largest splitting occurs around Bx 5 mT, where the MOKE images show that dv

NV is small.

Here, the transitions to the ms 1 and ms 1 states are split

by E900 MHz, corresponding to a projection of E16 mT along the NV symmetry axis. The orientations of the symmetry axes of these NVs are unknown, so this sets a lower bound on the actual magnetic eld seen by the NV. Given the applied eld Bx 5 mT,

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Figure 1 | Characterization of the NV/vortex system. (a) Micromagnetic simulation near the vortex core with in-plane applied eld B 3 mT showing

normalized out-of-plane magnetization Mz/Ms (grey scale), and the magnetic eld 20 nm above the surface (arrows, logarithmic scale). Scale bar, 100 nm. (b) Schematic of the setup. A continuous-wave 532 nm laser is sent through an acousto-optical modulator (AOM) for pulsing. The reected laser from the sample is sent to a magneto-optical Kerr effect microscopy (MOKE) setup for imaging the vortex core. The PL is directed to either an electron-multiplied charge-coupled device (EMCCD) camera for imaging or sent to a pair of avalanche photodiodes (APDs) connected to a time-correlated single photon counter (TCSPC). (c) A g(2) measurement of the nanoparticle indicating multiple NV centres. (d) PL scan of the sample. Scale bar, 5 mm. (e) PL map of the NV/vortex system studied here. The circle indicates the edge of the Permalloy disk, and the double arrow indicates the direction of BCPW. Scale bar, 1 mm. (fh) Differential magneto-optical Kerr effect measurements showing the vortex core positions at different applied elds Bx 0, 5 and 9 mT, respectively.

the vortex must be contributing BZ11 mT to the NV spin splitting. As the NV/vortex interaction increases, increased broadening of the resonance is also visible, with linewidths exceeding 100 MHz in some cases. We will show below that this can be explained by power-broadening because of strong vortex-induced amplication of the MW eld. A distinct feature of the data in Fig. 2a is that the measured spin splittings do not change continuously with Bx, but instead undergo frequent steps.

This is a result of vortex pinning caused by defects in the Permalloy, with steps occurring when the vortex becomes unpinned and jumps to a new equilibrium position21.

The strength of the magnetic eld gradient from the vortex can be roughly estimated from the slope geff df/dBx of the

resonances versus Bx in Fig. 2a. (Specically, geff is related to the gradient in the direction of vortex motion.) Between Bx 4

and 5 mT, we observe the highest geffE320 MHz mT 1. For comparison, the splitting from the applied magnetic eld alone is at most g 28 MHz mT 1. The observed geff

corresponds to a gradient of the magnetic eld projected on the NV axis B0 geff/gw0E0.14 mT nm 1. For two NVs with the

same axis, separated by 10 s of nm, this gradient would cause splitting B100 MHz.

The general trends of the resonances versus vortex position can be understood via comparison to simulation. We obtain the fringe eld above a FM vortex domain using micromagnetic (object-oriented micromagnetic framework) simulation25, as a

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Figure 2 | Mapping the NV/vortex interaction. (a) Optically detected magnetic resonance (ODMR) spectra versus Bx of the NVs contained within the DNP. As Bx increases, the vortex (black dot) follows a path past the NVs (red dot) as illustrated in the inset. (b) Simulated ODMR spectra of two NV centres with the same orientation, separated by 10 nm, and 20 nm above the FM disk. Inset shows the same simulation but with no FM disk. The inset axes cover the same range as the main axes.

p (g 28 MHz mT 1) is also shown, which is the

maximum possible fR for the NVs alone, in the absence of vortex-induced enhancement. Both G and fR show the same roughly linear trend versus BMW. In the limit of strong MW-power broadening, the linewidth is expected to be G b

p =2 f

function of applied eld. We then calculate the NV resonances in that eld, for NVs in particular locations, in particular orientations. Figure 2b shows the simulated resonances from a pair of NVs, both oriented with polar and azimuthal angles (f, y) p/4. The two NVs are separated by 10 nm, and are located at

positions (x, y, z) (10, 300, 20) nm and (20, 300, 20) nm,

relative to the centre of the disk surface. Note that this simulation does not take into account vortex pinning or broadening of the resonances. The broadening may be due to coherent driving of spin-wave modes of the vortex, which is an effect not included in these static simulations. This will be further discussed below. Although the position and orientation of the measured NVs are not precisely known, the simulation captures some general features. The largest splitting is observed when dv NV is near its

minimum, around Bx 5 mT. In this region where the vortex is

strongly coupled to the NVs, same resonance in different NVs are split B100 MHz. When the vortex core is far from the NVs, the resonances tend towards the frequencies expected with no vortex present, shown for comparison in the inset. The experimental data show the same trends, although the experiment displays greater splitting when the vortex core is far from the NVs. This suggests that the fringe eld contains higher gradients away from the core, perhaps due to irregularities in the FM lm.

Coherent manipulation of vortex-coupled NV spins. The rst step towards fast addressability is to map the NV resonances in response to BCPW. Sweeping BCPW with an additional static eld

Bx moves the vortex along the paths illustrated in the insets to Fig. 3ac. The NV resonances that result from these vortex paths are shown by the corresponding ODMR scans (see the Methods for more detail on the experimental protocol).

The ODMR scans in Fig. 3ac provide a more detailed look at the NV/vortex coupling. The resonances show a general trend of greater splitting at smaller dv NV. The scan in Fig. 3c, closest

to the vortex, was taken with reduced BMW, which reduces the power broadening that obscured the features at small dv NV

in Fig. 2a. Sets of resonances with qualitatively different behaviour versus BCPW likely arise from NVs with different orientation within the DNP. When lines are split into parallel doublets, this suggests that the transitions of NVs with the same orientation have become addressable. From these maps, we can design a path of rv that will sequentially address one or more of the NV transitions.

To demonstrate that the broadening of the resonances is caused by vortex-enhanced power broadening, we measure both the half-width at half maximum G and the Rabi frequency fR of a spin transition at different BMW. Figure 3d displays the ODMR spectrum of one of the transitions at the magnetic eld indicated by the solid arrow in Fig. 3b. The resonance dip is shown at increasing BMW with a corresponding increase in linewidth.

A Lorentzian t yields G at these and other BMW, shown as circles in Fig. 3e (left axis). G is roughly linear with BMW, as expected if linewidth is dominated by MW-eld-induced power broadening. We conrm the broadening mechanism by measuring coherent Rabi oscillations of this spin transition (see the Methods for details). Figure 3f shows Rabi oscillations with MW pulses at fMW 2,688 MHz, and the same BMW as used in Fig. 3d. The Rabi

frequency fR, extracted via a Fourier transform, is shown as squares in Fig. 3e (right axis). For comparison, the line f gBMW= 2

R, where

b is the ratio between optical excitation rate and spin initialization rate26. From the data in Fig. 3e, we nd bE10, consistent with typical values for this ratio. It is possible that this linewidth broadening and Rabi frequency enhancement are caused by coherent MW-induced excitation of spin wave modes in the disk, which in turn drive the spin transitions11,27.

Fast NV addressability and coherent manipulation of spins. We now demonstrate the capability to sequentially move the vortex and perform coherent operations on one of the NVs in the DNP. The pulse sequence for this operation is shown in Fig. 4a. The laser serves to rst initialize, and nally measure all of the NV spins in the DNP. During the spin initialization, BCPW 0, so

the vortex is in the position indicated by the dashed arrow in Fig. 3b. After the initialization pulse has ended, BCPW is stepped

to the solid arrow in Fig. 3b. A MW pulse at fMW 2,688 MHz

then coherently rotates the spin. The MW pulse has duration tp,

and is delayed from the BCPW pulse by t0. From the map in Fig. 3b, we see that at the initial vortex position, no NV transitions are resonant with fMW. After the step in BCPW, the vortex position undergoes some dynamics, nally relaxing to a position where a spin transition is now resonant with fMW. The

vortex position is reset after the spin read-out (resetting the vortex position before the read-out does not affect the outcome).

The timescale for addressing an NV with the vortex and performing coherent spin rotation is demonstrated by the Rabi oscillations shown in Fig. 4b. The ODMR contrast is plotted versus t0 tp with different t0. Sinusoidal ts performed at t0

tp4200 ns yield the oscillation amplitudes AR (Fig. 4c). When the MW pulse begins t0 200 ns after the BCPW step, clear Rabi

oscillations are observed, with AR equal to the value observed for static vortex position (dashed line in Fig. 4c). As t0 is reduced, the oscillation contrast is reduced. At t0r50 ns, a non-oscillating decay of the signal is visible at t0 tpr100 ns. The observed NV

spin behaviour can be understood in terms of the dynamic coupling of the vortex and NV transitions. The relaxation time for gyrotropic vortex dynamics in these structures is B50 ns, as

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Figure 3 | Coherent control of vortex-coupled NV spins. (ac) ODMR spectra with static Bx plus variable BCPW translating the vortex along the diagonal paths shown in the inset illustrations. Bx 0, 2, 5 mT, respectively. (d) ODMR spectra with Lorentzian ts of the NV spin transition at the eld indicated by

the solid arrow in b with BMW 70 mT ( ), 280 mT (~) and 690 mT (m). (e) (Left axis, ) Half-width at half-maximum G of the resonance in d versus BMW.

(Right axis, ) Rabi frequencies fR versus BMW from the data in f. Dashed line indicates upper bound of fR with no vortex-induced enhancement. (f) Rabi oscillations at the same resonance and the same three BMW as in d. The oscillations are offset for a clear comparison.

measured by time-resolved MOKE (not shown) and in agreement with previous work28. Once the gyrotropic precession has fully decayed and the vortex has fully relaxed to its new equilibrium position at t0Z200 ns, the NV transition is on resonance, and coherent rotation proceeds as usual. During the vortex relaxation, the NV spin experiences a time-dependent spin splitting. If the MW pulse is present during these dynamics, the spin follows a more complex path on the Bloch sphere.

DiscussionThe NV/vortex system opens a path towards large-scale quantum registers, in which the vortex can be repositioned to address a single NV within the register. Specically, tuning the vortex position to maximally split the spin transitions of one NV will separate those transitions from all other NVs in the register. As shown, the vortex can be repositioned on B100 ns timescales, allowing for operations on many NVs within typical

coherence times. Technical challenges that remain to be studied and addressed, however, include the effects of pinning on the freedom to position the vortex, and the possible presence of vortex-induced spin dephasing or decoherence.

It is interesting to ask whether the Bloch sphere dynamics that occur when the MW pulse is applied while the vortex is moving are coherent (as in the top curve of Fig. 4b). The time evolution of the spin splitting here is similar to that required for adiabatic passage, suggesting that it may be possible to use the vortex dynamics to generate robust spin rotations. The coupled NV/ vortex dynamics will provide a rich system for future study, opening new possibilities for coherent spin control with nanoscale addressability.

Methods

Experimental setup. ODMR and MOKE measurements were performed on a home-built scanning microscopy setup at room temperature. A schematic of the setup is shown in Fig. 1b. A continuous wave (CW) 532 nm laser is sent through an

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a c

0.03

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300

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t 0 = 50 ns

t 0 = 100 ns

t 0 = 200 ns

At each fMW, many modulations occur (for example, T0 1 ms with measurement

time 1 s) and a marker is placed at the beginning of each period of M. This allows

us to separate the time-tagged PL counts, {ti}, into bins such that the PL signal counts, Csig P

i M ti

, and PL reference counts, Cref P

i 1 M ti

. Cref reects

the PL count rate when the spins are initialized, with no MW eld applied. Csig

reects the PL count rate when the spins are initialized, and also acted on by the MW eld. The ODMR signal is then dened as S Csig/Cref.

The second method is the same as the rst, but we also modulate the vortex position via BCPW (as in Fig. 3ac.) This is done to avoid thermal depinning of the vortex. When the vortex is at a position close to a transition between pinning congurations, it can stochastically jump to a new position, in a thermally activated process. Using the rst method, the vortex may sit in such a position for many minutes. If a jump occurs during this time, discontinuities can appear in the data in a single fMW scan. If the vortex can jump back and forth between two congurations, the scan features can be smeared. To avoid this, we want to reduce the dwell time of the vortex at these unstable positions. Modulating the vortex position back to some reference position essentially resets the vortex. It can still undergo thermal jumps, but if it does, the situation is quickly remedied. Here, both BCPW(t) BCPWM(t) and BMW(t) BMWM(t) are modulated at 1 kHz. In this case,

Cref pertains to vortex position set by BCPW 0 with no MW applied, and Csig

pertains to the vortex with position set by the desired value of BCPW, with the MW

eld applied. Because the signal and reference here are measured in different static elds (from both BCPW and the vortex eld), Cref may differ from Csig even if no

MW eld is applied. To account for this, the ODMR signal for each line scan is normalized to have the off-resonant signal, S 1.

In the third method, pulsed measurements are carried out, separating the spin initialization, manipulation and measurement in time. We use a measurement protocol with a period of 1.5 ms. The laser is on during the time intervaltON (0 1) ms and off during the interval tOFF (1 1.5) ms. The measurement

time interval (read-out) is dened as tm (0 300) ns and the reference time

interval is dened as tr (700 1,000) ns. Csig is then the number of {ti} in the

range tm and Cref is the number of {ti} in the range tr. The MW eld is also pulsed and is on either during tOFF (for coherent manipulation, as in Figs 3f and 4b) or during tON (for incoherent depolarization, as in Fig. 3d).

References

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5. Dutt, M.V. Gurudev et al. Quantum register based on individual electronic and nuclear spin qubits in diamond. Science 316, 13121316 (2007).

6. Wrachtrup, J. & Jelezko, F. Processing quantum information in diamond.J. Phys. Condens. Matter 18, S807S824 (2006).7. Balasubramanian, G. et al. Ultralong spin coherence time in isotopically engineered diamond. Nat. Mater. 8, 383387 (2009).

8. Childress, L. et al. Coherent dynamics of coupled electron and nuclear spin qubits in diamond. Science 314, 281285 (2006).

9. Jelezko, F., Gaebel, T., Popa, I., Gruber, A. & Wrachtrup, J. Observation of coherent oscillations in a single electron Spin. Phys. Rev. Lett. 92, 076401 (2004).

10. Pioro-Ladrire, M. et al. Electrically driven single-electron spin resonance in a slanting Zeeman eld. Nat. Phys. 4, 776779 (2008).

11. van der Sar, T., Casola, F., Walsworth, R. & Yacoby, A. Nanometre-scale probing of spin waves using single-electron spins. Nat. Commun. 6, 7886 (2015).

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0 100 200 300 400 t 0 + t p (ns)

Figure 4 | Fast NV addressability and coherent control. (a) Pulse timing for NV initialization, and read-out (laser), vortex-enabled addressing (BCPW)

and manipulation BMW. t0 is the delay between BCPW and BMW and tp is the BMW pulse duration. (b) Rabi oscillations following a vortex translation with different t0. The oscillations are offset for a clear comparison. (c) The Rabi amplitude, AR, versus t0. Dashed line indicates AR with static vortex position.

The error bars are determined by the sinusoidal ts.

acousto-optical modulator (Gooch and Housego) for laser pulsing and directed into an oil immersion objective (Olympus 100, 1.3 numerical aperture) by a

dichroic mirror. The objective focuses the laser onto the sample and both the PL and reected laser are collected back through the same objective. The reected laser can be sent to the longitudinal MOKE measurement to map the magnetization component perpendicular to BCPW (ref. 22). The magnetization maps are produced by raster scanning the disk while measuring the change in magnetization due to the 15-kHz applied BCPW at each pixel. The PL proceeds to an electron-multiplication charge-coupled device camera for imaging or sent to a pair of avalanche photodiodes (PDM-50ct) connected to a time-correlated single-photon counting system (TCSPC, Hydraharp 400).

Sample preparation. The sample is mounted on a three-dimensional nanopositioning stage (Physik Instrumente P-517.3CL). Permanent magnets are placed on automated translation stages that are positioned to move in the x- and y-directions indicated in Fig. 1d,e. The static eld is measured in situ by a two-dimensional hall probe integrated in the sample holder. The sample consists of a 200-nm-thick gold CPW patterned via photo-lithography and thermal evaporation on a silicon substrate. The CPW centre conductor constricts to a10 mm width for 100 mm at the middle. In this region, Permalloy (Ni0.81Fe0.19) disks

are fabricated via electron beam lithography, electron beam evaporation and liftoff, atop of the gold CPW. Last, DNPs are dispersed over the entire surface.

The DNPs (DiaScence, Quantum Particles), E25 nm in diameter, are mixed with a 1.0% solution of polyvinyl alcohol, MW 85,000124,000 (Aldrich 363,146)

in de-ionized water. Spin coating this solution directly on top of the CPW/ Permalloy disks yields a lm thickness E35 nm.

Microwave eld generation. MW elds are produced by a signal generator (SRS SG386) and amplied (Pasternack PE15A4017). MW signals are either CW, internally modulated at low frequency, or pulsed at higher frequency using I/Q modulation. An arbitrary function generator (Tektronix AFG3052C) and a digital delay pulse generator (SRS DG645) are used to provide signals at direct current (DC) or with square amplitude modulation with fast rise time B1 ns. The MW eld is combined with DC or square-modulated current with a resistive splitter (MicroCircuits ZFRSC-42-S ) and sent to the CPW. The MW magnetic eld

(with amplitude referred to as BMW) produced by the CPW drives both the vortex and the NV spin transitions. The DC or low-frequency-modulated magnetic eld (referred to as BCPW) shifts the NV transition frequencies, and moves the vortex.

ODMR techniques. There are three types of ODMR scans performed in the main text. The rst two methods involve simultaneous spin initialization, measurement and incoherent MW-induced depolarization, whereas the third is a pulsed

technique that permits coherent spin control. In all three, a timing scheme is used to provide signal and reference levels, as described below.

During an ODMR scan, the TCSPC continuously measures and time-tags each PL photon count in real time, {t1, t2, t3y}. The TCSPC also places event markers that are synced with the timing of the laser pulses and/or MW eld modulation. A time interval is dened as the measurement time, and another interval is dened as the reference time (see below). The markers are then used to determine which counts arrived in which interval.

The generalized measurement described above is employed in three ways. In the rst method, NVs are under CW laser excitation with the static magnetic eld xed, while sweeping fMW, as in Fig. 2a. The MW eld amplitude is modulated

BMW(t) BMWM(t), where M(t) is a square wave with one period

M t

0 0 toT0=2

1 T0=2 toT0

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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms11584 ARTICLE

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Acknowledgements

This work was supported by the US Department of Energy, Ofce of Science, Basic Energy Sciences, under Award #DE-SC008148.

Author contributions

J.B. conceived and supervised the research, analysed data and performed simulations. R.B. designed and fabricated the samples and performed the MOKE measurements. M.S.W. set up and performed the NV measurements. J.B. and M.S.W. wrote the manuscript and designed the gures.

Additional information

Competing nancial interests: The authors declare no competing nancial interests.

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How to cite this article: Wolf, M. S. et al. Fast nanoscale addressability of nitrogen-vacancy spins via coupling to a dynamic ferromagnetic vortex. Nat. Commun. 7:11584 doi: 10.1038/ncomms11584 (2016).

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