Optical magnetic detection of single-neuron action ...walsworth.physics.harvard.edu/publications/2016_Barry_arxiv.pdf · Optical magnetic detection of single-neuron action potentials

Opticalmagneticdetectionofsingle-neuronactionpotentialsusingquantumdefectsindiamond

J.F.Barry1,2,3,M.J.Turner2,3,J.M.Schloss3,4,D.R.Glenn1,2,3,Y.Song5,6,7,M.D.Lukin2,H.Park2,3,8,9,R.L.Walsworth1,2,3*

1Harvard-SmithsonianCenterforAstrophysics,Cambridge,Massachusetts02138,USA.2DepartmentofPhysics,HarvardUniversity,Cambridge,Massachusetts02138,USA.3CenterforBrainScience,HarvardUniversity,Cambridge,Massachusetts02138,USA.

4DepartmentofPhysics,MassachusettsInstituteofTechnology,Cambridge,Massachusetts02139,USA.5MarineBiologicalLaboratory,WoodsHole,Massachusetts02543,USA.

6YaleSchoolofMedicine,DepartmentofGeneticsandHowardHughesMedicalInstitute,BoyerCenter,NewHaven,Connecticut06510,USA.7BostonChildren’sHospital,HarvardMedicalSchool,DepartmentofNeurology/F.M.KirbyNeurobiology,Boston,Massachusetts02115,USA.

8DepartmentofChemistryandChemicalBiology,HarvardUniversity,Cambridge,Massachusetts02138,USA.9BroadInstituteofMITandHarvard,Cambridge,Massachusetts02142,USA.

*Correspondenceto:[email protected]

A key challenge for neuroscience is noninvasive, label-freesensingofactionpotential(AP)dynamicsinwholeorganismswith single-neuron resolution1. Here, we present a newapproach to this problem: using nitrogen-vacancy (NV)quantumdefects in diamond tomeasure the time-dependentmagnetic fields produced by single-neuron APs. Ourtechnique has a unique combination of features: (i) it isnoninvasive, as the light that probes the NV sensors stayswithinthebiocompatiblediamondchipanddoesnotentertheorganism,enablingactivitymonitoringoverextendedperiods;(ii) it is label-free and should be widely applicable to mostorganisms; (iii) it provides high spatial and temporalresolution, allowing precise measurement of the APwaveforms and conduction velocities of individual neurons;(iv) it directly determines AP propagation direction throughthe inherent sensitivityofNVs to theassociatedAPmagneticfield vector; (v) it is applicable to neurons located withinoptically opaque tissue or whole organisms, through whichmagneticfieldspasslargelyunperturbed;and(vi)itiseasy-to-use, scalable, and can be integratedwith existing techniquessuch as wide-field and superresolution imaging. Wedemonstrate our method using excised single neurons fromtwoinvertebratespecies,marinewormandsquid;andthenbysingle-neuron AP magnetic sensing exterior to whole, live,opaquemarineworms for extendedperiodswithnoadverseeffect. The results lay the groundwork for real-time,noninvasive 3D magnetic mapping2 of functional neuronalnetworks,ultimatelywithsynapse-scale(~!"nm)resolution3andcircuit-scale(~!cm)field-of-view4.

There are many established and emerging techniques forprobingneuronalnetworkactivity,eitheratthe ‘micro-scale’withsingle-neuron resolution, or at the ‘macro-scale’ with wholeorganismcompatibility.However,challengesremaintorealizethecomplete set of desired capabilities1 (see SI Table S1). Inparticular, electrophysiology recording methods such as patch-clamping remain the gold standard for measuring individualneuronactionpotentials(APs),withexcellentsignal-to-noiseratio(SNR) and good temporal resolution. Nonetheless, such direct-contactmethodsaretechnicallydelicateand invasive,andarenotscalable to dense recordingwith both high spatial resolution andwide field-of-view5. Microelectrode arrays are more robust andlessinvasive,butspatialresolutionislimitedto~10 µmanderror-pronepost-processingofdataisrequired6.Opticaltechniquesoffermanyadvantages,buttypicallyarelimitedtoprobingtissuedepths~1mmduetoscattering,andcanemployopticalpowerinexcessof photo-damage thresholds7. In addition, calcium imaging ishampered by extraneous intracellular calcium8, and its limited

temporalresolutionprecludesresolvingindividualAPsthatfireatrates > 10 Hz9; voltage sensitive dyes have a tradeoff betweenpoor SNR and high toxicity to the membrane10; functional nearinfrared spectroscopy (fNIRS) cannot resolve single-neuronactivity; and voltage-sensitive fluorescent proteins must begeneticallyexpressed11,whichmayalterneuronalfunction12.

Alternatively, AP magnetic sensing confers importantadvantages: it is noninvasive, label-free, and able to detectneuronalactivitythroughinterveningtissueandwholeorganisms;and itprovides inherent informationonAPpropagationdirectionandconductionvelocityviathecharacteristicAPazimuthalvectormagneticfield(seeFig.1a).Todate,however,magnetictechniquesfor sensing neuronal activity have either operated at the macro-scale with coarse spatial (~1 mm) and temporal (~1 ms)resolution — e.g., functional magnetic resonance imaging (fMRI)and magnetoencephalography (MEG) — or been restricted tobiophysics studies of excised neurons probed with cryogenic orbulky detectors that are not scalable to functional networks orwholeorganisms13.

Asdemonstratedhere,thebenefitsofAPmagneticsensingcanberealizedwithbothsingle-neuronresolutionandwholeorganismapplicabilityusingnitrogen-vacancy(NV)colorcentersindiamond.NV centers are atomic-scale quantum defects that providenanoscalemagneticfieldsensingandimagingviaopticallydetectedmagnetic resonance (ODMR), with broad applicability to bothphysical14 and biological4,15,16 systems under ambient conditions.We employ a simple, robust apparatus (see Fig. 1b) with amagnetic field sensor consisting of a macroscopic, single-crystaldiamondchipwithauniform13 µmlayercontainingahighdensity(~3×10!" cm-3) of NV centers at the top surface. The biologicalsampleisplacedonorabovetheNV-enrichedsurface. Laserlightat532nmisappliedtothesensingNVlayerthroughthediamondat a sufficently shallow angle that the light reflects off the topdiamond surface (due to total internal reflection) and thereforedoes not irradiate the living sample. Microwaves (MWs) areapplied to the NV sensor via a wire loop located above thediamond, with minimal perturbation to the specimen studied17.Laser-induced fluorescence (LIF) from the NVs is imaged onto aphotodiode; and continuous-wave electron spin resonance (CW-ESR) magnetometry is used to detect the AP magnetic field as atime-varying shift in the center of the ODMR spectrum, withtemporalresolutionof~32 µs(seeSIandSIFig.S7).Weregularlyachieve magnetic field sensitivity ! = 15 ± 1 pT/ Hz from asensingvolumeofabout 13 × 200 × 2000 µm!,whichrepresentsatwenty-foldimprovementoverpreviousbroadbandNV-diamondmagnetometers18andprovidesSNR> 1forasingleAPeventusingmatched filtering (see SI). For each biological specimen we

Figure1:Experimentaloverview.a,Schematicimagedepictingbipolarazimuthalmagneticfieldassociatedwithactionpotential(AP)propagatingfromleft toright. Redarrows indicateaxialcurrentthroughaxonandbluearrowsdepictassociatedmagnetic field. Magnetic fieldprojection isdetectedby13 µmthicknitrogen-vacancy(NV)layerondiamondsubstrate.InsetshowsNVcenterenergyleveldiagram;seeSIfordetails.b,Custom-builtmicroscopeallowssimultaneousmagneticsensingandconventionalimagingofspecimens.NVcentersareexcitedby532nmlaserlightorientedatgrazingincidencetodiamondtopsurface.InvertedasphericcondenserobjectivecollectsNVlaser-inducedfluorescence(LIF).Specimensareplacedontopofdiamond,andindividual APs are stimulated by suction electrode and detected downstream via a pair of bipolar recording electrodes. For clarity, wire loop formicrowave(MW)deliveryandaxonclamparenotshown. c,Top,side,andaxialviewsofNV-diamondsensorandspecimen. TopviewshowssensingregionfromwhichLIFiscollected,aswellasfourcrystallograpicNVaxes. APmagneticfieldprojectsontotwoNVaxesperpendiculartospecimenaxis.Sideviewshows532nmlaser lightenteringdiamondatgrazingangleandexcitingNVlayer. BluearrowinaxialviewdepictsAPmagnetic field;blackarrowsdepictNVaxesinsensingregion.typically acquire repeatedAPmagnetic fieldmeasurements, oftenover extendedperiodsof time (hours). Multiple, consectutiveAPmeasurements(!!"#)canalsobeaveragedtogethertoincreasetheAPSNR(seeMethodsandSI).

We first performed magnetic sensing of single-neuron APsfromexcisedinvertebrategiantaxons,togetherwithsimultaneouselectrophysiologymeasurementsontheaxonsasacomparisonandcheck on the magnetic data. We studied two species, withconsistentresults:themarinefanwormMyxicolainfundibulum;andthe North Atlantic longfin inshore squid Loligo pealeii, a modelorganism for neuroscience. Details of specimen preparation, APstimulation,andelectrophysiologymeasurementsaredescribedinthe Methods. Figure 2a shows a representative measuredintracellularAPvoltagetimetraceΦ!"

!"#$(!)fromM.infundibulum.InasimplemodeloftheelectromagneticdynamicsofAPs(seeSI),themagnetic field!(!) isproportional to the temporalderivativeof the intracellular voltageΦ!"(!):! ! = !"Φ!"/!",where ! is ascaling constant dependent on geometrical parameters (axonradius!!,radialdistanceofthefieldpointtotheaxoncenter!)andelectrophysiological axon parameters (AP conduction velocity !! ,axoplasmelectrical conductivity !). As shown in Figs. 2b and2c,wefindgoodagreementbetween(i)!!"#! ! ,theAPmagneticfieldcalculated from Φ!"

!"#$(!) for a typical value of ! for M.infundibulum,and(ii)arepresentativemeasuredAPmagneticfieldtime trace !!"#$ ! . This correspondence demonstrates theconsistency of NV-diamond magnetic AP measurements withstandardelectrophysiology techniquesand theory. Note that thisexample!!"#$ ! data has a peak-to-peak amplitude= 4.1 ± 0.2nTfor!!"# = 150,correspondingtoanSNRof1.2 ± 0.1forasingleAPfiring,i.e.,!!"# = 1(seeSI).Using!!"# = 6yieldsanSNRof3,which is sufficient for AP event detection. Furthermore, wedemonstrated that our method has multi-species capability viamagnetic sensing of APs from the squid L. pealeii (Fig. 2d). Nochange to the apparatusormagnetic sensingprotocol is requireduponswitchingorganisms.

We next demonstrated single-neuron AP magnetic sensingexterior to a whole, live, opaque organism — an undissectedspecimenofM.infundibulum(Fig.3a)—forextendedperiods,with

minimaladverseeffectontheanimal(seeSIandSIFig.S8b). Forexample, Fig. 3b shows an example measured AP magnetic fieldtimetrace!!"#$ ! foraliveintactspecimen,whichistothebestof ourknowledge the firstdemonstrationof ‘single-neuronMEG’fromtheexteriorofawholeanimal. ThemeasuredAPwaveforminFig.3bissimilartothatofanexcisedaxon(Fig.2c),withroughlyfour times smaller peak-to-peak amplitude (≈ 1 nT), which isconsistentwith theseparationof~1.2mmfromthecenterof theaxon inside the animal to the NV sensing layer (see transversesections and diagrams in Fig. 4a-d and in SI Fig. S1d, and SI). Inaddition,werecorded!!"#$ ! fromaliveintactwormafter> 24hours of continuous exposure to the experimental conditions,including applied MWs and optical illumination of the diamondsensor. WeobservedlittletonochangeinthemagneticAPsignalorintheanimalbehavior(seeSIFig.S8bandSI).

WealsousedwholelivewormstodemonstratethecapabilityofNV-diamondmagneticsensingtodeterminetheAPpropagationdirectionanddistinguishdifferencesinAPconductionvelocity(!!)from a single-point measurement. NV-diamond provides fullvectormagnetometrybysensingthemagneticfieldprojectionontoalinearcombinationofthefourNVcenterorientationswithinthediamond crystal lattice (see SI). AneuronAPproduces a bipolarazimuthal magnetic field waveform, with the time-varying fieldorientationsetbythedirectionofAPpropagation(seeFigs.1aand4d). Thus,as shown inFig.4e, f, themeasuredAPmagnetic fieldtimetrace!!"#$ ! fromanintactwormhasaninvertedwaveformfor anterior versus posterior AP stimulation, demonstrating cleardistinguishability between oppositely-propagating APs.Furthermore, the amplitude of the AP magnetic field, at a givenradialdistancefromanaxon,isexpectedfromcabletheory(seeSI)to scale inversely with AP conduction velocity (i.e., as ~ 1/!!),which could enable NV-diamond magnetometry as a sensitiveprobe of axon demylination as well as other neurophysiologicaleffects affecting !! . For example, the giant axon radius in M.infundibulum is tapered over the organism’s length19, which ispredictedtoinduceapropagation-direction-dependentasymmetryin!!20. Specifically,!! isexpectedtobesmaller,andthus! ! tobe larger, for anAPpropagating in thedirectionofpositive taper

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Figure2:Measuredactionpotentialvoltageandmagneticfieldfromexcisedsingle-neurons.a,Measuredtimetraceofactionpotential(AP)voltageΦ!"!"#$(!)forgiantaxonfromMyxicolainfundibulum(worm).b,CalculatedtimetraceofAPmagneticfield!!"#! ! forM.infundibulumextractedfromdata

inFig.2a. c,MeasuredtimetraceofAPmagneticfield!!"#$ ! forM.infundibulumgiantaxonwith!!"# = 150. d,MeasuredtimetraceofAPmagneticfield!!"#$ ! forLoligopealeii(squid)giantaxonwith!!"# = 375.Grayboxindicatesmagneticartifactfromstimulationcurrent.(increasing axon radius) than for an AP propagating in thedirectionofnegativetaper(decreasingradius).Ourmeasurementsin whole worms are consistent with this prediction: transversesections show a taper in the axon radius from smaller near theposteriorto largerneartheanterior(Fig.4a,b),correlatedwithalarger amplitude of!!"#$ ! at a fixedmeasurement point alongthe axon for posterior versus anterior AP stimulation (Fig. 4e, f).Weobservethisasymmetryinall threewormstestedinthisway,with amplitude differences of 47% ± 20% (see SI Fig. S8a).Independent two-point electrophysiology measurements (see SI)provideconsistentresults,withsmallermeasured!! (ratio≈ 0.6)forposteriorversusanteriorstimulation.

It is worth highlighting that, in contrast to our method ofvector magnetic field sensing using NV-diamond, existingtechniquesforAPdetectionwithsingle-neuronresolutionmeasureascalarquantity,e.g. ionconcentrationorelectricpotential. Suchscalarmeasurementsdonotprovidesingle-pointdeterminationofAP conduction velocity magnitude or direction; instead, spatiallyseparated differential scalar measurements must be performed,

Figure 3: Single-neuronaction potential magneticsensing exterior to wholeliveorganism. a,Overheadview of intact livingspecimenofM. infundibulum(worm) on top of NV-diamond sensor. Inconfiguration shown, animalis stimulated from posteriorend by suction electrode;action potentials (APs)

propagatetowardworm’santeriorend;andbipolarelectrodesconfirmAPstimulationandpropagation.Scalebaris20mm.b,Recordedtimetraceofsingle-neuron APmagnetic field!!"#$ ! from live intact specimen ofM.infundibulumfor!!"# = 1650events.

with sufficiently high temporal resolution and SNR to distinguishsmall timing differences between the two detected signals.Specifically, when the AP spatial extent is long compared to theaxon (as inmany systems of interest in neuroscience), the delaybetween the detected scalar signals at two measurement pointsalong the axon is significantly shorter than the duration of eachsignal. As a result, determiningAP conductionvelocity via scalartechniques requires a much higher SNR than with vectormagnetometry.

Buildingonourpresentresults,NV-diamondmagneticsensingshouldbeapplicabletononinvasivemonitoringofAPactivity inabroadrangeofsystemssuchasculturedneurons,tissueslices,andwholeorganisms,includingspeciesforwhichgeneticencodingandviral transduction of voltage-sensitive proteins is not currentlypossible. An example near-term application is single-pointmeasurements of AP conduction velocity,which could greatly aidthe study of demyelinating diseases such as multiple sclerosis.Furthermore, NV-diamond magnetic sensing could be combinedwith optical stimulationmethods21 to provide individual-neuron-targeted excitation and noninvasive AP detection, enablinglongitudinal studies of environmental and developmental effects,and tests of models used to interpret conventional MEG signalsfrom macroscopic brain circuits. Key technical challenges forneuroscience applications of NV-diamond include: (i) improvingthemagnetic field sensitivity to enable real-time, single AP eventdetectionfromindividualmammalianneurons,whichareexpectedtogeneratepeakAPmagnetic fields~1nTat theNVsensor layer(see SI); and (ii) incorporating magnetic imaging. The imagingchallenge can be met by integrating techniques from our recentsuccessful demonstrations using NV-diamond for wide-fieldparallel magnetic imaging of biological cells4,15, andsuperresolution magnetic imaging3, as well as tomographicmethods for extending the depth-of-field2. The sensitivitychallenge can be addressed by using optimized diamonds withhigher NV density and longer spin-dephasing times !!∗, and byimplementingpulsed-Ramsey22andquantum-beat23measurementprotocols; a sensitivity and AP SNR gain of~10! per unit sensorvolumeisexpected,alongwithtemporalresolutiondownto~1 µs(see SI). To realize further sensitivity enhancements we willinvestigate quantum-assisted techniques, which should enablemeasurements approaching fundamental quantum limits. Ourpresent NV-diamond instrument has a photon-shot-noise-limitedmagnetic field sensitivity ~3000 times worse than the quantumspin-projection limit (see SI), highlighting the potential for largesensitivity gains. For example, we recently demonstrated thatspin-to-charge-state readout for NV centers provides enhancedmagnetic fieldsensitivity that isonlya factorof3abovethespin-projectionlimit24.

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Figure 4: Single-point sensing of action potential propagationdirection and conduction velocity exterior to whole live organism.Transverse sections ofM. infundibulum nearmid-point ofworm illustrategiant axon radius tapering from smaller near posterior (a) to larger nearanterior(b).Sectionstaken~1cmapart.Encircledwhitestructureisgiantaxon. Scalebarsare400 µm. c,Cartooncross-sectionsideviewofwholelive worm and NV-diamond sensor. Black dashed lines indicate taperedgiant axon. Cartoon time traces of action potential (AP) voltage indicatethey are typically identical forposterior stimulation (left-propagatingAP)andanterior stimulation (right-propagatingAP). d, Cartoon cross-sectionaxialview looking fromanteriorend. Bluearrowsencirlingaxon indicateopposite azimuthal AP magnetic field vectors for oppositely propagatingAPs. e, Top: Expected AP magnetic field time trace for posterior wormstimulation, indicating effect of AP propagation direction and conductionvelocity on sign of bipolar magnetic field waveform and magnetic fieldamplitude,respectively. Bottom:RecordedtimetraceofAPmagneticfield!!"#$ ! from intact live specimen of M. infundibulum for posteriorstimulation and!!"# = 1650 events. f, Top: Expected AP magnetic fieldtimetraceforanteriorwormstimulation. Bottom:RecordedtimetraceofAP magnetic field !!"#$ ! from the same intact live specimen of M.infundibulum as in (e) for anterior stimulation and !!"# = 1650 events.Note that the observed sign of !!"#$ ! is reversed depending on APpropagationdirection;andthemagneticsignalamplitudeislargerbyabout50% for posterior-stimulated APs, consistent with two-pointelectrophysiology measurements of smaller AP conduction velocity forposteriorstimulation.

Ultimately, we envision that NV centers or other quantumdefects in diamond25 will enable a qualitatively new imagingmodalityforneuroscience—a‘quantumdiamondmicroscope’thatprovidesfast(~1 µs),real-time,3Dmagneticmappingoffunctionalactivity, connectivity, and directionality in neuronal networks,including in whole organisms and with single-neuron resolution;and which is integrable with superresolution methods to yield~10nm spatial resolution3, or with wide-field imaging4 andtomographic techniques2 to study tissue volumes ~1 cm3. Thisnew functional imaging modality could be applied to detailedstudies of the relationship between microscopic neuronalconnectivity and circuit development and function: e.g., the gainand loss of branches and synapses as well as the adaptivestrengtheningandweakeningof connectionsat the levelof singlecells, as governed by intrinsic neuronal cell behaviors andspatiotemporal patterns of neuronal signals and biochemicalrewards, and the resulting effect on and feedback from overallcircuitfunction26,27.Attheextremesoftechnicalperformance,onemight also observe opening and closing events of single ionchannels28, detect spatial heterogeneity in the radial AP currentsdue to nodes of Ranvier29, and map sub-threshold currents inneuraldendritesandsoma30.Acknowledgements|WethankElementSixfordiamondsamplesused in this work; E. R. Soucy and J. Greenwood for machiningassistance and advice on electrophysiology techniques; S. G.Turney, M. G. Shapiro, P. Ramesh, and H. Davis for technicalguidance and fruitful discussions; D. Bowman and B. Faulkner-Jones of the Dept. of Pathology at Beth Israel DeaconessMedicalCenter for tissue processing and imaging of transverse sections;and the Center for Brain Science at Harvard University forinfrastructureandsupport. J.M.S.wassupportedbyaFannieandJohnHertzFoundationGraduateFellowshipandaNationalScienceFoundation Graduate Research Fellowship under Grant No.1122374. This work was financially supported by the DARPAQuASAR program, theMURI biological transduction program, theNSF,andtheSmithsonianInstitution.

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MethodsM.infundibulumpropertiesandacquisitionM.infundibulumspecimenspossessalargegiantaxon19,arereadilyavailable year-round, and can be kept for long periods of time inlaboratoryenvironments. Thegiantaxonmediatesarapidescapereflex; electrical or physical stimulus elicits a violent muscularcontraction, which can shorten the worm by 50% or morecompared to the relaxed state. Specimens are obtained from acommercialsupplier(GulfofMaineInc.,BayofFundy,Maine,USA)or a research laboratory (UC Davis Bodega Bay Marine BiologyLaboratory, California, USA). Worms are housed in a 208 Laquarium filledwithartificial seawater (ASW) froma commercialsupplier (Instant Ocean Sea Salt), and temperature stabilized to7.5 ± 0.5 ℃. Worms are fed a plankton-based food source (SeraMarinCoraliquid) every14days. Large specimensof length~60mmanddiameter> 5mm(bothmeasuredwhenfullycontracted)wereusedinthepresentstudies.M. infundibulum specimen preparation and action potentialstimulationForstudiesoftheexcisedgiantaxonofM.infundibulum,amodifiedversion of theBinstock andGoldmanmethodwas followed31. (i)The ventral side ofM. infundibulum is identified by a triangularstructure on the thorax32. (ii) The worm is pinned ventral sidedown in a glass dish spray-painted flat black (Kyrlon Ultra FlatBlack #1602) and filled with PDMS (Dow Corning Sylgard 184).The specimen is illuminated with broadband white light at ashallow grazing angle. The painted dish and lighting increasecontrast between the axon and the surrounding tissue for bettervisibility. The preparation is submerged in chilled ASWthroughout.(iii)Amediandorsalincisionoflength~2cmismadethrough the bodywall at themid-section of the animal. Furthercuts sever connective tissue between the body wall and the gut.(iv)ThefreedbodywallispinnedtothePDMSawayfromtheaxonwith substantial tension as described in ref. 31. (v) The gut ispartially lifted (vertically up) from the body wall, allowing finevanassasscissorstocuttheconnectivetissueconnectingtheguttothebodywall.Thegutisexcisedfromthespecimen,revealingthedorsalsideoftheventralnervecordcontainingthegiantaxon.(vi)The ventral blood vessels and additional tissue close to the axonarecarefullystrippedawaywithfineforceps,furtherexposingthenervecordasshowninSIFig.S1a,b.(vii)AdditionalcutsthroughthebodywallremovetissuearoundthenervecordasshowninSIFig. S1c. (viii) The excised nerve cord (still connected to theundissected worm anterior and posterior) is then placed dorsal-side-downon the diamond sensor chip. In this configuration thewormisalive,andactionpotential(AP)firingcancontinuefor72hoursorlonger.Aflexibleacrylicclampholdsthenervecordfixedagainst the diamond chip to restrain the worm’s musclecontractions. Axon viability is checked periodically throughphysical or electrical stimulus at the worm posterior andconfirmationofmuscle responseat thewormanterior. Note thatfor studies of intact specimens ofM. infundibulum, the worm iscleanedofaccumulatedmucusandplacedinanacrylicjigtofixthedorsal side of the animal against the diamond. For both excisedaxons and whole live worms, the specimen preparation iscontinuously perfused with 10 ℃ ASW with a gaseous solute of99.5%O2and0.5%CO2.

APs are evoked for duration Δ!!"#$ by a suction electrodeengagingeither thespecimenposteriororanterior,anddrivenbyanisolatedpulsestimulator(A-MSystemsModel2100)producingbiphasic pulses (positive polarity first) with 10 mA amplitude.Posteriorstimulationisusedunlessotherwisenoted.ThevalueofΔ!!"#$istypicallysettotwicethestimulationthreshold,andranges

from 100 µs to 1 ms depending on the size and health of theorganism and the degree of contact between thewormbody andthesuctionelectrode. Stimulationpulsesareappliedatrepetitionrate!!"#$ ≈ 0.4Hz.SuccessfulAPstimulationandpropagationareverifiedwithapairofbipolarplatinumrecordingmicroelectrodes(World Precision Instruments PTM23B10 or PTM23B05)connected to a differential amplifier (A-M Systems Model 1800Headstage),whichis furtheramplified(A-MsystemsModel1800)and then digitized (National Instruments USB-6259) at 250 kHz.For the intactworm studies, the same recording electrodesweregently positioned in contact with the worm skin near the axon,allowing verification of AP propagation. Care was taken to notpuncturetheskintoavoiddamagingthespecimen.

L. pealeii acquisition, preparation, and action potentialstimulationSpecimens of L. pealeii are acquired seasonally from the MarineBiological Laboratory in Woods Hole, Massachusetts, USA, withmediumtolargesquid(0.3mto0.5minoveralllength)chosenforthepresentstudies. Followingdecapitationofthesquid,thepost-synapticgiantaxonsare isolated following theprotocoldescribedin ref. 33. The axons are placed in vials containing calcium-freesaline solution and stored on ice. The iced vials are transportedfrom Woods Hole to our laboratory at Harvard University (90-minutedrive). The isolated axonsmaintain viability forup to12hoursafterinitialexcision.

ForstudiesoftheexcisedgiantaxonofL.pealeii,asquidbuffersolution(475mMNaCl,115mMMgCl2,10mMCaCl2,10mMKCl,3mMNaHCO3,10mMHEPES)chilledto10 ℃ perfusestheaxon.APstimulation and extracellular voltage detection is accomplishedthrough the samemethods used forM. infundibulum, save for anincrease in the stimulation repetition rate!!"#$. The squid giantaxoncanbefiredasoftenas100HzwithoutreducingdetectedAPsignalquality. Forincreasedlongevityofsquidaxons,stimulationisappliedat!!"#$ = 25Hzfor15sfollowedbyarestperiodof15s.ElectrophysiologyDetermination of!!"#!(!) requires recording the intracellular APvoltage Φ!"(!). Intracellular microelectrodes are pulled fromcommercial glass (World Precision Instruments 1B150-4) to aresistanceof20-40MΩonapipettepuller(DaganDMZUniversalPuller), filled with 3M KCl, and fitted into a headstage (AxonInstrumentsHS-2A) connected to an amplifier (Axon InstrumentsAxoProbe 1B). The microelectrode is mounted to a micro-manipulator for precise insertion into the axon. M. infundibulumspecimensaredissectedasdescribedpreviouslybutremainpinnedin the dissection dish during this measurement so that themicroelectrode remains sealed to the axon despite the worm’scontractions. APstimulationoccursasdescribedpreviously. Thetime trace Φ!"

!"#$(!) is digitized (Tektronix TDS2004B), andsubsequently low-pass-filtered at 2 kHz. Axon resting potentialvaluesΦ!of-60mVto-85mVandpeakAPamplitudesof100mVto110mVareobservedforM.infundibulum,consistentwithtypicalvaluesintheliterature31.ForM.infundibulum,APswerefoundtobeabolishedforvaluesof!!"#$ ≳ 5Hz,andmaximalAPamplitudesrealizedfor!!"#$ ≲ 1Hz,bothinagreementwithpreviousreportsintheliterature34.ForL.pealeii, consistentAP stimulationwas observedup to!!"#$ = 300Hz, although eventual axon degradation was observed over ~15minutes at suchhigh rates. L. pealeii exhibits a refractoryperiodfollowing theAP,wherein thepotential experiences anovershootbelow the resting voltage. The overshoot is not present in M.infundibulum.

TransversesectionsTransverse sections shown in Fig. 4a, b were prepared from atypical M. infundibulum specimen, which was anesthetized andfixed inasolutionof4%paraformaldehyde(PFA)overnight. Thefixed worm was mounted to a paraffin block and sectioned,yielding slices of width ~4 µm. The slices were treated with ahematoxylin and eosin stain (H&E stain) to illustrate the tissuestructure. Representative slices from three different sections areshown (https://slide-atlas.org/link/mn74xw). By comparison

with the literature19, we verified the structure observed in thesectionsandconfirmedthelocationofthegiantaxon.Thesectionsshowadistance from thegiant axon center to the skin surfaceof900 ± 200 µm, and a taper in the axonwith decreasing diameterfromanteriortoposterior.

SupportingInformationNV-diamondphysicsandmagnetometrymethodNV colour centers are localized quantum defects in diamondconsistingofasubstitutionalnitrogenadjacenttoavacancyinthelattice. TheNV center has an! = 1 (triplet) ground statewith azero-field splittingof 2.87GHzbetween the!! = 0 and!! = ±1spinprojections.Thesestateshaveadditionalhyperfinestructure,whicharisesfromthecouplingofthe14Nnuclearspin! = 1totheunpairedNVelectronspin. AlocalmagneticfieldinducesZeemanshifts, lifting the degeneracy of the !! = ±1 energy levels.Optically-inducedelectronic transitions to theexcited tripletstateand fluorescent decay back to the ground electronic state aremainly spin-conserving35. Fluorescent readout and opticalpolarization of the NV spin state are made possible through anonradiativedecaypath fromthe!! = ±1 excitedstates throughmetastablesingletstatesandpreferentiallytothe!! = 0state35.

TheNVspinisquantizedalongoneoffourcrystallographicNVsymmetryaxesinthediamondcrystal,whichareequallypopulatedfor a typical ensembleofNVcenters36. Thus thediamondsensorchipused in thepresentwork, containinga largeensembleofNVcenters,providesacompletebasisforvectormagnetometry:alocalmagnetic field’s magnitude and direction can be reconstructedfrom its measured projections onto each of the NV axes37,15. APmagnetic fields are expected to encircle the axon andbedirectedperpendicular to the axon axis and hence the direction of APpropagation.Inthisworktheaxonswereorientedroughlylinearlyon the diamond and normal to two NV axes, maximizing theprojectionoftheAPmagneticfield!(!)ontothoseaxes,asshownin Fig. S2a, with the projection along the other two NV axesexpected tobenear-zero. In this configuration the componentof!(!)paralleltotheNVsurfacelayerandperpendiculartotheaxonaxis is detected. In future incarnations of an instrument formagnetic imaging of networks of neurons oriented arbitrarily onthediamondsurface, the componentof!(!) perpendicular to theNVlayerateachpointonthediamondsurfacewouldbesensed,asshowninFig.S2b. Themagnetic fieldprojectionontoasingleNVaxiswouldhaveoppositesignformeasurementpointsondifferentsides of the axon, and !(!) would in general have nonzeroprojectiononeachofthefourNVaxes.

A modified CW-ESR technique is employed for NV-diamondODMR,whereinopticalNVspinpolarization,MWdrive,andspin-statereadoutviaLIFoccursimultaneously.Continuousgreenlaserexcitation at 532 nm polarizes the NV center into the !! = 0ground state. Applied MWs, when tuned to resonance with thetransitionbetweentheopticallybright!! = 0spinstateandoneofthelessbright!! = +1or−1states,causeNVspinprecessionintoamixed state and a detectable reduction in LIF. A change in thelocalmagneticfieldshiftstheODMRfeatureand,fornear-resonantMWdrive,isdetectedasachangeinthefluorescencerate.

A single ODMR feature of Lorentzian lineshapewith angularfrequency !! (where ! ≡ 2!"), linewidth Γ, and contrast ! isdetected in fluorescence as ! ! = !! 1 − ! !/! !

!/! !! !!!! ! (see

Fig.S3a), ignoringMWandopticalbroadeninghereforsimplicity.As themajority of noise in the systemhas1/! character, greaterSNRisachievedbyshiftingthemeasurementbandwidthtohigherfrequency via a lock-in technique, which generates a dispersion-like signalwith a characteristic zero-crossing feature: i.e., a rapidchange of the lock-in amplifier (LIA) voltage and sign withfrequency. The applied MWs are square-wave frequencymodulatedat!!"#(typically18kHz)aboutthecenterfrequency!! with frequency deviation !!"#: i.e.,!!"(!) = !! + !!"#square 2!!!"#! . The collected fluorescenceis then! !!" . Afterdemodulationby theLIAwith a reference

signal!!"# sin 2!!!"#! , theDCoutput is a dispersion-type signalwithazero-crossingat!!:

!!"# !! ,!!"# ∝ ! !! + !!"# − ! !! − !!"#2

= !!!2 − (Γ/2)!

Γ/2 ! + !! + !!"# − !!!

+ (Γ/2)!

Γ/2 ! + !! − !!"# − !!! ,

where!! is a prefactor voltage determined by!! and the outputsettingsof theLIA. Setting!!"# = !

! !maximizestheslopeof the

zero-crossing!!!"#!!! !!"#!!

in the absence of power broadening38.

Time-varying magnetic fields ! ! are sensed by setting !! =!! !!! and detecting resonance frequency shifts !! ! = !! +!" ! ,where!" ! = !!!!

ℏ ! ! ,as:

!!"# ! = !!"# !! −!!!!ℏ ! !

= !!!2 − Γ/2 !

Γ/2 ! + Γ2 3 −

!!!!ℏ ! !

!

+ Γ/2 !

Γ/2 ! + Γ2 3 +

!!!!ℏ ! !

!

≈ − 3 34

!!!Γ!!!!ℏ ! ! .

The NV spin resonance has three features separated by thehyperfine (HF) splitting of Δ!!" = 2! × 2.16 MHz, as shown inFig.S3b.ForasingleMWfrequencysweepingacrossthefeatures,andagainignoringMWpowerbroadening,wefind

! ! = !! 1 − ! Γ/2 !

Γ/2 ! + ! − (!! + !Δ!!") !

!

!!!!.

AddressingallthreeNVHFfeaturessimultaneouslywiththreeMWfrequenciesalsoseparatedbyΔ!!"yields! !,Δ!!"

= !! 1 − ! Γ/2 !

Γ/2 ! + (! + !Δ!!") − (!! + !Δ!!" )!!

!!!!

!

!!!!.

AsdisplayedinFig.S3c,theobservedNVfluorescencesignalshowsfiveODMRpeaks. Theouter twopeaks correspond tooneof thethreeMWfrequenciesonresonance; thesecondand fourthpeakscorrespondtotwoofthethreefrequenciestunedtoresonance;andthe innermost peak corresponds to all three MW frequenciesresonantly addressing the HF features. The dispersion signal isthen:!!"# !,Δ!!",!!"#

= !! −! Γ/2 !

Γ/2 ! + (! + !Δ!!" − !!"#) − (!! + !Δ!!" )!!

!!!!

!

!!!!

+ ! Γ/2 !

Γ/2 ! + (! + !Δ!!" + !!"#) − (!! + !Δ!!" )!.

InthissimpletreatmentinwhichMWpowerbroadeningisignored,ourmeasurementtechniqueincreasesthecontrastofthecentralNVHFfeaturebyafactorof3.Inpractice,acontrastimprovementfactorof≈ 1.9isachievedcomparedtothecaseofaddressingasingleHFfeature.

The overall measurement contrast is further improved byorientingthebias field!! tohaveequalprojectionsalongtwoNVaxes.ProjectingalongtwoNVaxesdoublesthecontrastasshownby comparing Fig. S3c and d, although the angle between theNVaxesand!(!)causesthesensitivityimprovementtobe2cos[!/2 −!!"!/2]where!!"! = 109.4712∘isthetetrahedralbondangleinthediamondlattice.NV-diamondmagnetometerdetailsThediamondusedinthisworkisanelectronicgrade(N<5ppb)single crystal chip, with rectangular dimensions 4mm x 4mm x500 µm,grownusingchemicalvapordeposition(CVD)byElementSix. The 13 µm thick top-surface NV sensing layer consists of99.99% 12Cwith25ppm 14N,whichwas irradiatedwith4.6MeVelectronswith1.3 ×10!"cm-2s-1fluxfor5hoursandsubsequentlyannealed in vacuum at 800 ∘C for 12 hours. The measurednitrogen-to-NVconversionefficiency is~7%. Thediamond is cutso that the 500 µm x 4mm faces are perpendicular to the [110]crystal axis. The sides are mechanically ground to an optical-qualitypolish. Thediamondismountedtoa2”diameter,330 µmthicksiliconcarbide(SiC)heatspreaderviathermalepoxy(EpotekH20E) as shown in Fig. S5a. A 2 mm x 25 mm slot in the SiCprovides access to the diamond surface for the dissected axonstudies.

ForNVmagnetometry, the diamond sensor is illuminated by2.75-4.5Wof532nmlaserlight(CoherentVerdiV-5)asshowninFig. S4b. Laser light is guided into the diamond via an in-housefabricatedUV fused silica coupler,making a~ 3 ∘ angle to theNVlayer.A13 µmthickand1mmwidereflectivealuminumlayeronthe diamond surface blocks both excitation light scattered bysurfacedefectsandLIFfromimpinginguponthespecimen.Arareearth magnet (1” x 1” x 1” N42 K&J Magnetics) with south polefacing the experiment creates a biasmagnetic field!!with equalprojections of 7 gauss along the twoNV axes normal to the axonaxis, shifting theMW resonance between the!! = 0 and!! = 1sublevelsto≈ 2.89GHz.FigureS4ashowsaschematicoftheMWsetup.AcommercialMWsource(AgilentE8257D)outputsasinglenear-resonant frequency, which is square-wave modulated atfrequency !!"# = 18 kHz with frequency deviation !!"# = 2! × 360 kHz (Rigol DG1022U). The modulated MWs passthroughanisolator(TeledyneMicrowaveT-2S73T-II)anda-10dBcoupler beforemixing (RELCOMM1G) with a 2.16MHz sinusoidwaveform(StanfordResearchSystemsDS345). The coupledportof the-10dBcoupler is furtherattenuatedby6dBandcombined(Mini-CircuitsZX-10-2-42-S+)withthemixeroutputandthensentthroughasecond-10dBcoupler. Thecoupledoutput issenttoaspectrumanalyzer(AgilentE4405B)while thetransmittedoutputisamplified(Mini-CircuitsZHL-16W-43+),passedthroughanotherisolator (Teledyne Microwave T-2S73T-II), a circulator(Pasternack, PE 8401), and a high-pass filter (Mini-Circuits VHF-1200),beforedeliverytoasquare5mmx5mmlooplocated≈ 2mmabove thediamond sensor. Slowvariations in theNVODMRresonances, e.g., due to diamond temperature drift, arecompensated with≈ 0.4 Hz feedback to the MW frequency !!".TheODMR features canalsobeused to continuouslymonitor thediamondsubstratetemperatureinrealtime.

Typically 17 mW (and up to 28 mW) of LIF from the NV-diamond is collected by a 1.4 numerical aperture (NA) asphericaplanaticoilcondenser(Olympus),passedthrougha633nmlong-pass filter (Semrock LP02-633RU-25), and imaged onto a biasedphotodiode(ThorlabsDET100A).Thephotodiode(PD)ispoweredbya12VlithiumionrechargablebatteryandisterminatedintotheRF + DC port of a bias tee (Universial Microwave ComponentCorporationBT-1000-LS)withbandwidth10kHz-1GHz.ThebiasteeDCportisterminatedby50 Ωduringdatataking;duringoptical

alignmenttheportismonitoredonanoscilloscopetooptimizeLIFcollection.TheRFoutputofthebiasteeisamplifiedbyalownoiseamplifier (RF Bay LNA-545) and then sent into an LIA (StanfordResearchSystemSR850). TheLIAgainsettingis200mV,andthenominal time constant is 30 µs with a 24 dB/octave roll-off,yielding a measured 3 dB cutoff frequency of !! = 3.6 kHz and ameasuredequivalentnoisebandwidth(ENBW)of!!"#$ = 4.0kHz.The LIA voltage output is expanded by 5 times using the LIAexpandfunction,digitized(NationalInstrumentsUSB-6259)at250kHz,andthensubsequentlydividedby5.ThetemporaryLIAsignalexpansion was found to reduce the effect of read noise fromdigitization. A 3 nT magnetic field corresponds to a fractionalchangeintheNVLIFofΔ!/! ≈ 1.4 × 10!!.

Tosuppresslaserintensitynoisenear!!"#, the532nmlaserlight is sampledand focusedonaseparate, referencePD(seeFig.S4b, c). ThisPDandall electronics (bias-tee, low-noiseamplifier,LIA,inputintodataacquisitionsystem)exactlyduplicatethesetupof the signal PD and accompanying electronics. Thephase of thereference LIA is aligned with the signal LIA phase. We findsubtraction (rather than division) of the correlated noise issufficienttoreachthephotonshotnoisesensitivitysensitivitylimitintheabsenceoftheMWs,inagreementwithref.39.Thedetectedsignal isdigitallyfilteredwitha80HzFFThigh-passfilter;and1-Hz-widenotchstop filtersatall60Hzharmonics through660Hzandat30otherfrequenciesabove2kHz.Theexperimentachievessensitivity ~50% above the photon-shot-noise limit, which isdiscussedinthesensitivitysectionbelow.

Fortheintactwormstudies,severalchangesweremadetotheexperimental apparatus (see Fig. S5b). An upgraded aluminummount(largerthanthemountforexcisedaxons) isusedto fit thelarge intact specimens (see Fig. 3a). A SiC wafer with no slot isusedasaheatspreader.TheNV-diamondsensoristhereforeoffsetfromthewormexteriorbyaspacerofthickness330 µm.MWsaredelivered toa25 µm thick copper foil layerdirectlyon topof thediamond. TheOlympusoilasphericcondensor isexchangedfora0.79NAairasphericcondensor(ThorlabsACL25416U-B).Stainedtransversesections inFig.4a,bshowa typical tissue thicknessof~900 µm from the center of the axon to the worm exterior,consistent with the literature19,40, although this distance is alsonoted19tobehighlyvariableamongdifferentspecimensandalonga single organism’s length. The overall typical distance from theaxoncentertothediamondsensoris~1.2mm,consistentwiththemeasuredroughlyfour-foldmagneticsignalreductioncomparedtoexcisedworm axons,where the distance from axon center to NVdetectorlayeristypically~300 µm.

Excitation-laser-induced heating of the diamond ismeasuredvia NV ODMR frequency shifts to be 2.4 ℃/Watt. For the datashowninFig.2c,d(WormAandsquid),thediamondtemperatureis21 ± 3 ℃. As the excised axons are placed directly against thediamond, we estimate the temperature of both theWorm A andsquidaxons tobe~ 21 ℃. The live intactorganisms (WormBofFig.3bandWormsC,D,E,andFofFig.S8)areseparatedfromthediamondby the SiCheat spreader and are thus at~ 10 ℃ duringsensing.MagnetometercalibrationThe measured magnetic field !!"#$ ! is determined from theoutput voltage of the LIA, denoted !!"# ! , by therelation !!"#$ ! = !!"#!!"# ! , where !!"# is a voltage-to-magnetic-fieldconversionfactorgivenby

!!"# = ℎ!!!"#!" !!"#!!

!! !! cos !2 −!!"!2

.

Here!!!"#!" !!"#!!

istheslopeofthezero-crossinginV/Hz,!! isthe

electrong-factor,and !!istheBohrmagneton.Calibration of the NV-diamond magnetometer was

independently verified by applying a known test magnetic field!!"#! ! = !!"#! square 2!!!"#!! withsquarewaveamplitude!!"#!andfrequency !!"#!,andconfirmingthemagnetometerrecordsthecorrectvaluefor!

!"#$ ! .Thetestmagneticfieldisproducedbyamulti-turn circular current loop (coil)with!!"#$% = 7 and radius!!"#$ = 0.0235 m, located a distance !!"#$ = 0.103 m from thediamond chip center. The coil is connected in series with an!!"#$"! = 50 Ω resistor. The value of!!"#! is calculated using theformula

!!"#! = !!!!"#$%!!"#$!!"#$!

2 !!"#$! + !!"#$! !/!,

where!!"#$isthecurrentinthecoilgeneratedbydrivingavoltage!!"#$(!)throughthecircuit.A44mVamplitudesquarewaveyields!!"#! = 1.8 nT,withRMSvoltage!!"#!!"# = !!"#!. Whenthisvalueof!!"#! isappliedatfrequency!!"#! = 110Hz,themeasuredvalueof!(!) is consistent with the value of !!"#! to better than 5% asshown in Fig. S6a. A calibration without harmonics was alsoperformed by applying a 62 mV amplitude sine wave yielding aconsistentvalueof!!"#!!"# = !!"#!/ 2 = 1.8 nT.MagneticfieldsensitivityAmagnetometer’ssensitivity isdefinedas ! = !" !,where!" isthemagneticfieldsignalthatisaslargeasthenoise,i.e.,atSNR=1,after measurement time !41. The sensitivity of our NV-diamondmagnetometer is evaluated using threemethods. Inmethod 1, atest magnetic field !!"#! ! = !!"#! sin 2! !!"#!! is applied for!!"#$%& = 150,eachof time!!"#$% = 1 s,andthemeasuredmagneticfield!!"#$ ! isrecorded.Foreachtrial!thequantity

!! =1

!!"!"#!!"#$ ! !!"#! !

!!"#$%

!!"

iscomputed.Themethod1sensitivity!!is

!! =!!"#!!"# 2

!1

!!"#$%&!! − ! !

!!"#$%&

!!!× !!"#$% ,

where ! ≡ !!!"#$%&

!!!!"#$%&!!! , the factor of 2 accounts for in-

quadraturenoise,!!"#!!"# = !!"#!/ 2,andtypically!!"#!=250Hz. Inmethod 2, !!"#!(!) is applied for !!"#$%& = 150, each of time!!"#$% = 1 s, and !!"#$ ! is recorded. The Fourier transform of!!"#$ ! is defined to be !!"#$ ! ≡ !!" !!"#$ ! . Themethod2sensitivity!!is

!! = !!"#!!"#

1 !!"#$ − !!"#$" !!"#$ 2!" !" !!"#$

!!"#$"1Δ! !!!"# 2!" !"!!"#!!!!/!

!!"#!!!!/! !!"#$%&

× !!"#$% ,

whereΔ! = 1/!!"#$%, the expected value is taken over!!"#$%&, andtypically !!"#$" = 300 Hz, !!"#$= 600 Hz, and !!"#!= 250 Hz. Inmethod 3, no test magnetic field is applied and !!"#! ! isrecorded for !!"#$%& = 150, each of time !!"#$% = 1 s; an exampletraceisshowninFig.S6b.Thesensitivityisthencalculatedas

!! =1

!!"#$%!!"#$ ! !

!!"#$%

!!" × 1

2!!"#$,

with !!"#$ = 4.0 kHz. In all evaluations of the instrument’smagnetic field sensitivity, !! ~ !! ~ !! was found, although !!convergesmost slowly and is therefore of limited use. Over 150trials, !! ranges from 15.0 to 15.8 pT/ Hz, while !! is 15 ±1 pT/ Hz. The two values are consistent. We thus conclude theNV-diamond magnetometer sensitivity is 15 ± 1 pT/ Hz, alsoconsistent with a noise floor measurement of !!"#$ 2!" for

!!"#$% = 1 saveragedover!!"#$%& = 150,asshowninFig.S6c,d.This realized magnetic field sensitivity agrees with the

expected sensitivity for our NV CW-ESR technique limited byphotonshotnoiseandaddedMWandamplifiernoise,asestimatedherein. In the limit of low contrast ! of the ODMR feature, thephoton-shot-noise-limited sensitivity for CW-ESR magnetometryusingNV-centersisgivenby42

!!"# =43 3

ℎ!!!!

Δ!! ℛ ,

whereℛisthephotondetectionrate(awayfromresonance),Δ!isthe power-broadened full-width-half-maximum (FWHM)

resonance linewidth, and the factor!! ! comes from a Lorentzian

feature’s steepest slope. TheCW-ESRmethodemployedwith thepresentNV-diamondmagnetometerdetectsalong twoNVaxesasdescribed above, doubling the contrast while reducing themagnetic field sensitivity by the angle factor cos [!/2 − !!"!/2] =0.8165. The present instrument also uses modulation to rejectquadraturenoise,enhancingthesensitivitybyanadditional 2.Assuch, the shot-noise-limited sensitivity of our magnetometer isgivennominallyby

!!"#!"#$ = 12×

43 3

ℎ!!!!

Δ!!! cos !2 −

!!"!2 ℛ

,

where Δ! = 1.5 ± 0.1 MHz is the measured linewidth; and!! = 5.3 ± 0.1% is the contrastwhen sensing along twoNV axes,which was measured in the absence of modulation whileaddressingall threehyperfine features. Thedetectedphotonrateℛ is defined in terms of the photoelectron current!ℛ = !!"#/!! ,whereq istheelementarychargeand!!"# = 400 mVisthetypicalsignal photodiode voltage after !! = 50 Ω termination. Thisidealized shot-noise-limited CW-ESR sensitivity is found to be2.9 pT/ Hz.

In practice, several factors diminish the sensitivity: first, thereferencephotodiodeaddsinquadratureanequivalentamountofshotnoise,increasingthesensitivitybyafactor!!"# = 2;second,the slope is reduced with respect to the steepest slope of aLorentizan due to the other nearby power-broadened hyperfinefeatures, resulting in a sensitivity cost of !!!"#$ = 1.19. Takingthese factors into account yields a shot–noise-limited CW-ESRsensitivityof4.9 pT/ Hz.

Furthermore, in our square-wave modulated CW-ESRimplementation, the contrast is reduced by an empirical factor!!"# ≈ 1.6,asshowninFig.S6f,duetothefinitecyclingtimeoftheNV center quantum states43,44 and the loss of signal in higherharmonics resulting from demodulationwith a sinusoidal lock-infrequencywaveform38.TheLNA-545amplifier’snoisefigureof1.8increases the noise level by !!"#$ ≈ 1.23. Application of MWsfurther increases the measured noise level by !!" ≈ 1.76, asshowninFig.S6e. Thesefactorsraisetheexpectedmagneticfieldsensitivity to ! ≈ !!"!!"#$!!"#!!"#$%!!"#!!"#$ ≈ 17 pT/ Hz,which agrees towithin 13% of themeasured15 ± 1 pT/ Hz forthedatashowninFig.S6e.

To confirm magnetometer sensitivity near the photon shotnoise limit in theabsenceofappliedMWs,wemeasured theRMSnoise in!!"# for a range of power incident on the photodiode, atboth18kHzand90kHzmodulationfrequencies,asshowninFig.S6e. Data are fit to the function ! = (! + !")!/! . For 90 kHzmodulation, fit parameters are ! = 5.4 ± 1.8 ×10!!, ! =3.0 ± 0.6 ×10!!, and ! = 1.97 ± 0.04 ×10!!, while for 18 kHzmodulation the fit parameters are ! = 1.4 ± 1.1 ×10!!, ! =4.4 ± 3.0 ×10!!, and ! = 1.90 ± 0.14 ×10!!. In both cases weobserve ! ≈ 2, as expected for a shot-noise-limitedmeasurement.Themeasurednoiseagreeswithexpectedphotoelectronshotnoise

plus LNA-545 amplifier noise for equivalent noise bandwidth!!"#$ = 4.0 kHz.

The fundamental sensitivity limit for spin-basedmagnetometers is given by the noise intrinsic to quantumprojection. Fora sampleof! electronic spinswithcharacteristicdephasingtime!!∗,thespin-projection-noise-limitedsensitivityis45

!! =ℏ

!!!!1!!!∗

.

ThesampleusedinthisworkhasatotalNVdensity~3×10!"cm!!andnopreferentialorientation46.ThedensityofNVsusedtosenseAPmagneticfieldsisreducedbyafactoroftwo,astheAPmagneticfieldprojectsalongonlytwoNVaxes. The illuminationvolumeis~ 13 µm × 200 µm × 2 mm ≈ 5 × 10!! cm!, so the number ofprobed NV spins is!~ 8 × 10!! with !!∗ ≈ 450 ns. Using thesevalues along with the electron gyromagnetic ratio ! = !!!!/ℏ =1.761×10!! s!!T!! gives a spin projectionnoise estimate for oursample of~10 fT/ Hz. At ~3000 times better than the presentnearly photon-shot-noise-limited sensitivity, there is muchpromise for significantgains inmagnetometer sensitivity throughuseofpulsedmagnetometry,optimizedNV-diamondsamples,andquantum-assistedtechniques,asdiscussedbelow.TemporalresolutionTemporalresolutionoftheNV-diamondmagnetometerwastestedby applying a testmagnetic field!!"#! ! = !!"#! square 2!!!"#!! with!!"#! ≈ 57 nT and !!"#! = 1 kHz, and measuring the 10% –90%risetimeof!!"#$ ! ,denotedby!!"/!".Using!!"# = 60kHz,!!"# = 10 µs, and 6 dB/octave roll-off (yielding a measured!!"#$ = 33 kHz), !!"/!" = 32 µs is observed as shown in Fig. S7,which displays both real-time and averaged!!"#$ ! traces thatareFFTlow-passfilteredat45kHz. AllAPdatapresentedinthispaper was acquired using !!"# = 18 kHz, !!"# = 30 µs, and 24dB/octave roll-off, which gives !!"/!" ~ 400 µs. Note that highervalues of!!"# reduceNV spin-state contrast, an effect previouslyobserved in refs. 41, 43, 44, and shown here in Fig. S6f. Whenoperating with a temporal resolution higher than 40 µs, themagneticfieldsensitivityofthepresentinstrumentisreducedbyafactorof~1.6with respect to standard running conditions. Withpulsed Ramsey-type schemes22, to be employed in a next-generationNV-diamondmagnetic imagingsystem,timeresolutionapproaching the ~200 ns NV singlet state lifetime should bepossible47. Forexample, in recentwork tobepublished,wehaveshown that pulsed Ramsey schemes allow NV-diamondmagneticfieldmeasurementson~1 µstimescales.Expected magnetic field sensitivity in next-generationinstrumentA next-generation instrument will likely employ pulsedmagneticfield sensing schemes, such as Ramsey-type sequences, which donot suffer from laser and MW power broadening of the ODMRfeaturesandthusallowforhighercontrastthanCW-ESRdoes22.ARamsey schemewith free precession time!, and optical andMWinitialization and readout times !! and !! , has a shot noisesensitivitylimitof36,48,24

!!"#$%& =ℏ

!!!!!! + ! + !!

!1

! ! ,

where ! ≈ ℛ!! is the number of photons collected permeasurement.Notethatthecontrast!isalsodependenton!dueto spin dephasing. For !! , !! ≲ !!∗

, the sensitivity is optimized

for ! ~ !!∗. The optimal shot-noise-limited Ramsey sensitivity isthen

!!"#$%& ∼ℏ

!!!!!! + !!∗ + !!

!!∗1

! ℛ!! .

The principal improvements from employing a Ramseyschemeare inthecontrast!andthe lackofpowerbroadeningofODMRfeatures.PulsedreadoutoftheNV-diamondsampleusedinthe present work realizes! = 9.5 ± 0.5% along a single NV axis.The CW-ESR power-broadened linewidth Δ! ≈ 1.5 MHz is alsoreplacedby thenatural linewidth

!!! =

!!!!∗

≈ 700 kHz. Note thatthereisasensitivitycostinRamseyschemesduetofinitereadouttime, which can be estimated for typical values of !! = 1 µs and!! = 400 ns, and using ! = !!∗ = 450 ns for the current diamondsample. Assuming ℛ remains the same as in the CW-ESRimplementation because of finite available laser power, a netsensitivity improvement of about a factor of 5 is expected forpulsed magnetometry with respect to optimized CW-ESR.Moreover, because Ramsey sequences allow use of higher laserintensitythaninCW-ESR,thesensitivityperilluminationvolumeisfurtherimproved. Withanexpected~50timesintensityincrease,and thus a ~50 times smaller illumination volume for the sameexcitation power, an additional ~50 times enhancement in per-volume sensitivity is expected. Improved diamond sampleswithlonger spin-dephasing times !!∗ and higher nitrogen-to-NVconversionefficiencieswill allowadditional sensitivitygains. Forthesame!!and!! ,exchangingthepresentdiamondforanequallybright diamond with !!∗ = 32 µs would further improve thesensitivity approximately 17-fold. Moreover, quantum-beatmagnetometry schemes23,49 provide common-mode rejection ofnoise due to strain and temperature inhomogeneities, promisingfurther sensitivity enhancement. Overall, through use of pulsedmagnetometryandquantum-beattechniqueswithnext-generationNV-diamondsamples,aper-volumemagnetic fieldsensitivitygainof~ 10!shouldbepossible.

SimplemagneticmodelofactionpotentialThemagneticfieldproducedbyanaxonAP,denoted!!"#$ !, !, ! ,canbederivedfromtheintracellularAPvoltageΦ(!, !, !),where!and!denotetheaxialandradialcoordinatesrespectively,usingasimplemodel thatagreeswithmorecomplexcable theory50. Theaxonismodelledasaconductingwire;hencethemagneticfieldis!!"#$ = (!!!)/(2!"), with axial current ! due to the propagatingAP.Thewire’scurrentdensityis ! = −!∇Φ(!, !, !),where!istheelectricalconductivity. Forauniformcylindricalwireofradius!!,theaxialcurrentmaybeexpressedas! = !!!!!! = −!!!!! !!(!,!,!)

!! .For constant values of conduction velocity !!, the equality!!(!,!,!)

!" = −!! !!(!,!,!)!" holds, where!! is defined to be positive50.Substitution then yields ! = !!!!!

!!!!(!,!,!)

!" . Since Φ !, !, ! ismeasuredatafixedpoint! = !!,thepartialtimederivativecanbereplacedbyafullderivative.Atdistancesclosetotheaxonsurfacewhere ! ~ !!, returncurrentsoutside theaxonareminimal50, andfringingeffectsfromthefiniteaxonlengthcanbeignored,yielding

!!"#$ !, !, ! = !!!!!!2!!!

!Φ !, !, !!" .

Defining! ≡ !!!!!!!!!!

gives!!"#$ !, !, ! = ! !! !,!,!!" ,where!depends

onlyongeometricandelectrophysiologicalquantities.ForthedatashowninFig.2a-c,goodproportionalityisfoundbetween!!"#$(!)and

!!!"#$

!" with!!"#$ = 7.6 ± 1pT/(V/s).Accurate calculation of ! from first principles is nontrivial51,

since !!, !, !, and !! have substantial uncertainties. !! = 200 ±75 µm is determined from stained transverse sections of M.infundibulum (see Fig. 4), with large variations observed in axonsize (up to 50%) among otherwise similarly sized specimens, asalsonotedin19.Fortheexcisedaxonstudies,onlytheventralnervecordcontainingthegiantaxonisisolated,andthereisalsoresidual

connective tissue around the axon: hence an estimateof! = !! +100 µm ± 100 µmisused.Wetake! = 1.47 ± 0.5S/m52,giventhesignificant variation (50%) in axoplasm conductivity reported forL. pealeii51; and !! = 9 ± 4 m/s based on two-pointelectrophysiologymeasurements of!! for similar representative-sizedwormsunderposteriorstimulation.Withthesevaluesfor!!,!, !, and !! , we extract !!"#! = 13.7 ± 10 pT/(V/s), which is inagreementwiththeexperimentallyderivedvalue.

ToevaluatethefeasibilityofNV-diamondmagneticsensingofsmall mammalian neurons, a crude estimate of the AP magneticsignalsizewasmadeforPurkinjeneuronsusingoursimplemodel.We used! = .66 Ω!! !!!, an average of the values .44Ω!! !!!from ref. 53, .87 Ω!! !!! from ref. 54, and .67 Ω!! !!! fromref.55.Weused

!!!" = 339 V/s,anaverageof300V/sfromref.56,

367 V/s from ref. 57, and 350 V/s from ref. 58. We used !! = .25 m/s, anaverageof .24m/s fromref.56and .25m/s fromref59. For !! = 1 μm, 2 μm,and 3 μm, we calculate a peakmagneticfield of!axonmax = .6 nT, 1.1 nT and 1.7 nT respectively at the axonsurface.Thiscalculationisintendedforroughestimationpurposesonly. Weacknowledge that conductionvelocity is expected tobecorrelated with diameter and this is not accounted for in thiscalculation.Actionpotentialsignal-to-noiseratioTheSNRofanAPmagneticfielddatasetiscalculatedusing(i)thepeak-to-peak detected AP signal from an averaged set of !!"#measurementsand(ii)thestandarddeviationofthetimetraceinasectionofthesamedatasetinwhichnoAPispresent.Thesingle-shotSNRiscalculatedbydividingtheSNRoftheaverageddataby!!"#. For excised axon studies, ! = 0 corresponds to the

beginning of the stimulation pulse. For averaging data in intactorganismstudies, tracesarealigned in timeusingadigital triggerset on either the maximum or minimum of the extracellular APvoltage signal Φ!" ! ; this alignment compensates for specimencontractions and thus prevents smearing out of the averagedsignal.TomaximallyimprovetheSNRofaknownexpectedsignalinthepresenceofstochasticnoise,itcanbeshownthatamatchedfilter is the optimal linear filter. For a detected signal !(!)containing an expected signal and additive noise, the matchedfilteredsignal!(!)isgivenbytheconvolution

! ! = ℎ ! − !! ! !! !"′!

!,

whereℎ(!) is the time-reversed traceof theexpectedsignal. ThematchedfilterforthedatashowninFig.2cwasconstructedfromalarger set of 600 detected AP time traces all from the sameorganism.Theaverageofthe600traceswashigh-passFFTfilteredat 80 Hz to prevent non-DC values due to drift from beinginterpreted as signal. The trace was then zeroed for all timesexcept a 1.4mswindow that includes the full detectedAP signal,time-reversed, and then taken as the expected signalℎ(!) for thematchedfilter. Thisfilterwasappliedtothefourconsecutivesetsof150averagescontainedinthelargerdataset.TheSNRofeachofthese filtered traces was improved to be between 14.5 and 16,indicating that the SNR of a single AP event after filtering is1.2 ± 0.1.

SystematicchecksMultiple tests were performed, as summarized in Table S2, toverify that the observed!!"#$ ! arises solely from an axon AP(i.e., intracellular axial current): (i) observation of a non-zero!!"#$ ! signal required successful AP stimulation andpropagationasdeterminedbyelectrophysiologymeasurementsoftheextracellularactionpotentialΦ!" !, !, ! ;(ii)crosstalk(‘pickupartifacts’)duringdataacquistionbetweentherecordedΦ!" !, !, ! and !!"#(!) was ruled out by varying the recording electrodeplacementandobservingnochange in!!"#$ ! ; (iii) theoriginoftheNV-observed!!"#$ ! signalwasdemonstratedtobemagneticby switching to an LIA voltage zero-crossing with slope

!!!"#!" of

opposite sign, and observing inversion of!!"#$ ! ; (iv) similarly,inverting the phase of the LIA reference signal !!"! by 180°produced the same result, also confirming themagnetic origin ofthe signal sensed by the NV ensemble; and (v) time-varyingmagnetic fields from motional artifacts, e.g. specimen-inducedinstrumentmotioninthepresenceofagradientinthebiasfield!!,were ruled out by reversing the orientation of the permanentmagnetandobservinginversionof!!"#$ ! . DirectionaldetectionofactionpotentialsForthreespecimens,(WormsC,D,andEinFig.S8a),magneticAPsignalswererecorded forbothposteriorstimulationandanteriorstimulation, each for!!"# = 1650 trials. Themeasuredmagneticsignal!!"#$ ! wasinvertedforanteriorstimulationcomparedtoposteriorstimulation,asexpected.Inaddition,largerpeak-to-peakvaluesof!!"#$ ! wereobservedforposteriorstimulationthanforanterior stimulation for all three worms tested, by 47% ± 20%.This result did not depend on which stimulation (posterior oranterior)wastestedfirst;andwasrobustundermultipleswitchesofstimulation(e.g.,posterior,anterior,thenposterioragain).

To confirm the directional dependence of the AP conductionvelocity, electrophysiology recordings were perfomedsimultaneously at twopoints separated by 6 to 10mmalong thewhole worm giant axon using two sets of bipolar measurementelectrodes. The electrodes were connected to a differentialamplifier(A-MSystemsModel1800Headstage),whichwasfurtheramplified (A-M systems Model 1800) and digizited through anoscilloscope (Tektronix TDS2004B). The delay between theinitializationofstimulationandthepeakAPsignaloneachpairofelectrodes was measured, and the conduction velocity wasdetermined from the timing difference between the detectedsignalsandthespatialseparationbetweentheelectrodepairs.ExtendeddurationactionpotentialsensingFor the long-term sensing data shown in Fig. S8b, the specimen(WormF)waspreparedandclampedtotheapparatusasdescribedabove for intact organism studies. The worm was magneticallymonitoredfor> 24 hoursinthepresenceofappliedMWsandlaserilluminationofthediamond.Followingthisduration,themagneticAPsignal!!"#$ ! wasmeasuredtohaveanamplitudeconsistentwith AP signals of specimens studied over shorter durations(Worms C, D, and E). Physical stimulus applied to the wormfurtherconfirmeditsresponsivenessandhealth.

TechnologySingle-neuron

scale

Whole-organism

scale

Labelling required

Invasive PhototoxicLong-term

measurement stability

Imaging Spatial resolution

Super-resolution

Field of view

Sensing depth

Temporal resolution

Single event

detection

Measures conduction

velocity

Measures AP propagation

direction

Traditional

intracellular

electrophysiology

YES NO NO YES NO NO5

NO n/a n/a n/a > 1 mm60 ~50 μs61

YES YES5

YES5

All-optical

electrophysiologyYES YES YES YES

62 YES

62NO

62YES

Diffraction-

limitedNO > 4 mm

62~1 mm

1 ~100 μs63YES YES

62YES

62

Calcium

imagingYES YES YES YES

64YES

65NO

65YES

Diffraction-

limitedNO 0.5 mm

66~1 mm

1100 ms

64YES NO

64NO

64

Microelectrode

arrayYES NO NO NO NO YES

67YES ~10 μm n/a 1 cm

6~1 cm

68 ~50 μs69YES YES

69YES

69

SQUID (Wikswo

technique)51

YES NO NO NO NONot

demonstratedNO n/a n/a n/a ~1 cm

70 ~50 μs51YES YES

51 Not

demonstrated

fMRI NO YES NO NO NO YES YES ~1 mm NO71

> 10 cm72

> 10 cm73

~1 s74

NO n/a n/a

MEG (uses

SQUID)75

NO YES NO NO NO YES YES ~1 mm NO > 10 cm75

> 10 cm75

~1 ms75

NO n/a n/a

Demonstrated NV-diamond

magnetic imaging

YES YES NO NO NO YES YES ~10 nm3

YES ~1 mm4

~1 mm ~30 μs NO YES YES

Projected NV-diamond

magnetic imaging

YES YES NO NO NO YES YES ~10 nm YES ~1 cm ~1 cm ~1 μs YES YES YES

Table S1 | Competing technology comparision

FigureS1|DissectedspecimenofM.infundibulum.a,PhotoofwormwithnervecordcontaininggiantaxonexposedasdiscussedinMethods.b,Close-upviewofsamespecimen.Thenervecordis~400µmacrossneartheanterior(top)end.c,Samespecimenwithmuscletissueremoved.Atthisstagethedissectionprotocol iscomplete. Allwhitescalebarscorrespondto2mm. The levelsofeachphotowereslightlyanduniformlyadjusted for improvedcontrast.d,Cartoondrawingofwormandtransversesections.MiddleandrightsectionsarereproducedfromFig.4a,b;leftmostsectionisfromnearthetipoftheposteriorendofthespecimen,furtherdemonstratingthesignificanttaperingofthegiantaxon.Allblackscalebarscorrespondto400 µm.

AxonAnterior

Posterior

a b c

d

Extended Data Figure 1

Figure S2 | Specimen orientation with respect to NV axes. a, Present specimen orientation as discussed in Methods and main text. Diagram isreproduced from Fig. 1 for comparison. b, Proposedmethod formagnetic imaging of AP dynamics from networks of smaller neuronswith arbitraryorientation. Here the sensor detects themagnetic field component normal to the diamond surface, which has opposite sign on different sides of thespecimen.

Diamond

NV axes

4 mm

APmagneticfield

Diamond

Sensingregion

Specimen

Specimen

532 nmlight

NV axes

Top view

Side view

Axial view

Specimen

NV layer

NV layer

a

AP

Axon

Top view

Diamond

Specimen

NV axes

APmagneticfield

Diamond

Axial view

NV layer

NV axes

Soma

APmagneticfield

b

Extended Data Figure 2

FigureS3 | Illustrationofmagnetometry technique. Left columnshowsschematicdiagrams illustratingnumberofODMR features,numberofMWfrequenciesapplied,andnumberofNVaxesusedforsensing;middlecolumnshowscalculatedODMRfluorescenceprofilesinunitsofthenaturallinewidthΓ,intheabsenceofpowerbroadening;andrightcolumnshowsassociateddispersion-typelock-inamplifier(LIA)signals.FluorescenceandLIAsignalsaregiven in arbitrary units. SeeMethods for discussion of the lock-in scheme. a, Diagram, fluorescence signal, and LIA signal for a singleODMR featureaddressedbyasingle(modulated)MWfrequency,sensedalongasingleNVaxis.b,Diagram,fluorescencesignal,andLIAsignalforthreeODMRfeaturesaddressedbyasingle(modulated)MWfrequency,sensedalongasingleNVaxis.c,Diagram,fluorescencesignal,andLIAsignalforthreeODMRfeaturesaddressed by three (modulated)MW frequencieswith equivalent spacing, sensed along a singleNV axis. The central feature corresponds to all threeappliedfrequenciesresonantlyaddressingODMRfeatures,asdescribedinMethods.d,Diagram,fluorescencesignal,andLIAsignalforsamescenarioasin(c)butwith!!orientedtohaveequalprojectionalongtwoNVaxes,overlappingtheirODMRfeatures,asdiscussedinMethods.

Resonancefeatures

Microwavefrequencies

NVorientations

111

Resonancesfeatures

Microwavefrequencies

NVorientations

113

Resonancefeatures

Microwavefrequencies

NVorientations

133

Resonancefeatures

Microwavefrequencies

NVorientations

233

a

b

c

d

a

Extended Data Figure 3

FigureS4|Microwave,laser,andlightcollectionsetup.a,MWgeneration,modulation,anddeliverysetupasdescribedinMethods.b,LasersetupasdescribedinMethods.c,Signalphotodiode,referencephotodiode,anddownstreamelectronicsandLIAsasdescribedinMethods.

Microwave generatorAgilentE8257D

Mini-CircuitsZHL-16W-43+

IsolatorTeledyne Microwave

T-2S73T-II

CirculatorPasternackPE 8401

16 watt amplifier

10 watt50 terminator

Frequency sourceRigol DG1022U

FMinput 2

RFoutput

IsolatorTeledyne Microwave

T-2S73T-II

To microwave deliveryat diamond

Frequency sourceStanford Reserach Systems

DS345

MixerRELCOM M1G

2.158 MHzsinusoid

~2.89 GHz

Spectrum analyzerHP E4405B

~ 0.4 Hz feedback onmicrowave frequency

High-pass filterMini-CircuitsVHF-1200

-10 dBcoupler

Power combinerMini-CircuitsZX-10-2-42-S+

-10 dBcoupler

6dBattenuator

FMinput 1

Data acquistionNational Instruments

USB-6259

18 kHz square-wavemodulation

1

2

3

Frequency sourceStanford Reserach Systems

DS345

MixerRELCOM M1G

2.158 MHzsinusoid

-10 dBcoupler

6dBattenuator

a

F=200 mm lens(tilted)

Mirror

To diamond

Pick-offTo referencephotodiode

532nmlaser

CoherentVerdiV-5

b

AmplifierRF BayLNA-545

A

DCRF+DCRF

Bias teeUMMC

BT-1000-LS

12 Volt2300 mAhrechargablebattery

50

1.8 dB NF45 dB gain

Lock-in amplifierStanford Research Systems

SR850

A

DCRF+DCRF

50

18 kHz square-wave modulation

Ref.

Ref.

Both SR850 settings:30 s time constant24 dB rolloff200 mV gain setting

To oscilloscope

To oscilloscope

Signalphotodiode

Referencephotodiode

ThorlabsDET100A

ThorlabsDET100A

Lock-in amplifierStanford Research Systems

SR850

Bias teeUMMC

BT-1000-LS

AmplifierRF BayLNA-545

1.8 dB NF45 dB gain

Data aquisitionNational Instruments

USB-6259

c

Extended Data Figure 4

FigureS5|Diamondmounting.a,DiamondmountingforexcisedaxonexperimentsasdescribedinMethodsandmaintext. b,DiamondmountingforwholelivewormexperimentsasdescribedinMethodsandmaintext.MWsareappliedthroughthe25µmthickcopperlayer.

Side view

Top view

Microwaveloop

Acrylicclamping

Lightcoupler

DiamondNVlayer

Side view

Top view

Diamond

Siliconcarbide

Siliconcarbide

Immersionoil

Lightcollection

Lightcollection

Axon

Worm body

Acrylicclamping

Silicon carbide (330 m)Copper (25 m)NV layer (13 m)

Diamond (500 m)

NVlayer

Siliconcarbide

Aluminum (13 m)NV layer (13 m)

Diamond (500 m)

Inset

Axon

Immersion oil

Inset

Worm body

NV layer anddiamond (undersilicon carbide)

Siliconcarbide

Lightcoupler

Axon

Axon, acrylic clamp,aluminum strip,

and microwave loopare not shown

Worm and acrylicclamp are not shown

Excised axon diamond mounting Whole live worm diamond mounting

Air

a b

Extended Data Figure 5

5

FigureS6|Magnetometercalibrationandsensitivity.a,CalibrationverificationasdescribedindetailinMethods.A110Hzsquarewavewith1.8nTamplitude(calculatedfromcoilgeometry,coildistancetodiamondsensor,andcurrentthroughcoilonly)isaveragedfor!!"# = 1000trials.Themeasuredmagneticfield,calibratedonlyfromthevalueof!!"#andthelock-inamplifiervoltagetimetrace!!"# ! ,isconsistentwitha1.8nTamplitudesquarewavetobetterthan5%.Graydashedlinesdepict-1.8nTand+1.8nTlevels.Theslightroundingofthesquarewave’scornersresultsfromcoilnon-idealitiesratherthanthemagnetometer.b,Real-timetraceofmeasuredmagneticfield!!"#$(!)withnoexternaltime-varyingmagneticfieldapplied.c,Fouriertransform(blackpoints)of!!"# = 150tracesof(b)issmoothed(redline)forclarityandisconsistentwithanoverallsensitivityof15pT/ Hz.d,Reproductionof(c)withlinearscaleoverapproximateneuronsignalbandwidth(80Hzto2kHz).Alldataaretakenforstandardconditions(!!"# = 18kHz,nominal!!"# = 30 µs,with24dB/octaveroll-off).e,MeasuredandcalculatedRMSnoiseon!!"# ! versusPDsignalvoltage.Datashowninblue(red)weretakenwithoutappliedMWsat!!"# = 18(90)kHz.Blueandredcurvesarefitstotherespectivedatasets,(discussedinMethods),demonstratingthesquare-rootdependenceofthemeasurednoise.PurplestarmarksthemeasurednoiseduringtypicaloperatingconditionsinthepresenceofappliedMWs.Blackcurvesindicatecalculatedtheoreticalnoiseforshotnoisefromasinglechannel(dotted),shotnoiseincludingboththesignalandreferencechannels(dashed),andexpectednoiselevelincludingshotnoisefrombothchannelsandtheLNA-545amplifiernoisefigureof1.8(dot-dashed).f,Measuredslopeofthezero-crossing

!!!"#!" !!"#!!

withmodulationfrequency!!"#.Bluelinedenotes!!"# = 18kHz.Theopencirclemarkstheslopeintheabsenceofmodulation,calculatedfromthemeasuredDCphotodiodesignalandtheLNA-545amplifierandLIAgains.

a

c

e

b

d

f

Extended Data Figure 6

6

FigureS7|Temporalresolution.a,Real-timetraceof1kHzsquarewavewith57nTamplitudeasdescribedinMethods.b,Sameexperimentalsetupas(a),buthighlyaveraged (!!"# ~ 10!). Dataanalysis indicatesa10%-90%rise timeof!!"/!" = 32µs. For thisdataonly,!!"# = 60 kHz,!!"# = 10 µsnominally,anda6dB/octaveroll-offisused,yieldingameasured!!"#$ = 33 kHz.DataareFFTlow-passfilteredat45kHz.

a

b

Extended Data Figure 7

7

TableS2|Systematicchecks

Reversal Result Systematic ruled out

Axon firing ! Axon not firing Bmeas

(t) ! 0

Any non-AP signal, including stimulation

artifacts

�

ex

(z1

, ⇢1

, t) ! �

ex

(z2

, ⇢2

, t) Bmeas

(t) ! Bmeas

(t) Cross-talk of Bmeas

(t) with �

ex

(z, ⇢, t)

sgn[

dVLIAdf

] = 1 ! sgn[

dVLIAdf

] = �1 Bmeas

(t) ! �Bmeas

(t)Any non-magnetic artifact including cross-

talk of Bmeas

(t) with �

ex

(z, ⇢, t)�LIA

! �LIA

+ 180

� Bmeas

(t) ! �Bmeas

(t) Cross-talk of Bmeas

(t) with �

ex

(z, ⇢, t)

B0

! �B0

Bmeas

(t) ! �Bmeas

(t)Magnetic artifact from motional coupling

to small

@B0@x

across diamond

Extended Data Table 2 | Systematic checks

FigureS8 |Directional sensing for threespecimensandextendeddurationsensing. a,Measured time traceofAPmagnetic field!!"#$(!) forM.infundibulumgiantaxonswith!!"# = 1650. DataareshownforWormsC,D,andEforbothposteriorstimulation(leftcolumn)andanteriorstimulation(rightcolumn).ForthesampleconsistingofWormsC,D,andE,thepeak-to-peakvalueof!!"#$(!)islargerby47% ± 20%forposteriorstimulationthanforanteriorstimulation. b,MeasuredtimetraceofAPmagneticfield!!"#$(!)forM.infundibulumgiantaxon(WormF)with!!"# = 1200. WormFwascontinuouslymagneticallymonitoredwithfulllaserandMWpowerfor24hourspriortostimulationandmeasurementoftheAPmagneticfield!!"#$ ! .Thepeak-to-peakvalueof!!"#$(!) forwormF isnotstatisticallydifferent fromthepeak-to-peakvalueof!!"#$(!) forwormsC,D,orEwithposteriorstimulation.Theseresultsindicatelittleifanynegativeeffectsfromthissensingmethodoverlongtimeperiods.

Posterior stimulation Anterior stimulation

Worm C

Worm D

Worm E

Worm F

Extended Data Figure 8

9

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