Multi-Angle Reconstruction of Domain Morphology with All-Optical Diamond Magnetometry
Lucio Stefan, Anthony K. C. Tan, Baptiste Vindolet, Michael Högen, Dickson Thian, Hang Khume Tan, Loïc Rondin, Helena S. Knowles, Jean-François Roch, Anjan Soumyanarayanan, Mete Atatüre
MMulti-angle reconstruction of domain morphology with all-optical diamondmagnetometry
Lucio Stefan,
1, 2, ∗ Anthony K. C. Tan, † Baptiste Vindolet, † Michael Högen, Dickson Thian, Hang KhumeTan, Loïc Rondin, Helena S. Knowles, Jean-François Roch, Anjan Soumyanarayanan,
4, 5 and Mete Atatüre ‡ Cavendish Laboratory, University of Cambridge,J. J. Thomson Avenue, Cambridge, CB3 0HE, UK The Faraday Institution, Quad One, Becquerel Avenue, Harwell Campus, Didcot, OX11 0RA, UK Université Paris-Saclay, CNRS, ENS Paris-Saclay,CentraleSupélec, LuMIn, 91190, Gif-sur-Yvette, France Institute of Materials Research and Engineering, Agency for Science,Technology and Research (A*STAR), 138634 Singapore Physics Department, National University of Singapore (NUS), 117551 Singapore
Scanning diamond magnetometers based on the optically detected magnetic resonance of thenitrogen-vacancy centre offer very high sensitivity and non-invasive imaging capabilities when thestray fields emanating from ultrathin magnetic materials are sufficiently low ( <
10 mT ). Beyond thislow-field regime, the optical signal quenches and a quantitative measurement is challenging. Whilethe field-dependent NV photoluminescence can still provide qualitative information on magneticmorphology, this operation regime remains unexplored particularly for surface magnetisation largerthan ∼ . Here, we introduce a multi-angle reconstruction technique (MARe) that captures thefull nanoscale domain morphology in all magnetic-field regimes leading to NV photoluminescencequench. To demonstrate this, we use [Ir/Co/Pt] multilayer films with surface magnetisationan order of magnitude larger than previous reports. Our approach brings non-invasive nanoscalemagnetic field imaging capability to the study of a wider pool of magnetic materials and phenomena. I. INTRODUCTION
In the last decade, the negatively-charged nitrogen-vacancy (NV) centre in diamond has attracted great in-terest as a versatile quantum sensor for the investiga-tions of weak-field magnetism which demands high sen-sitivity, nanoscale resolution and noninvasiveness. [1–5].In the presence of a magnetic field, the Zeeman split-ting of the NV spin can be quantified by performing op-tically detected magnetic resonance (ODMR) measure-ments using laser and microwave excitation [6]. Thesingle-spin nature of the NV centre also ensures lim-ited perturbation of the measured system. Further, at-taching an NV-containing diamond platform on a scan-ning probe [2, 3, 7–9] enables scanning NV microscopy(SNVM), which allows for nanoscale noninvasive mag-netic imaging. This technique features a large operat-ing temperature range (cryogenic to room temperature)and stability in vacuum to ambient conditions [1, 6, 10].However, the ODMR measurements are restricted tomagnetic fields below
10 mT due to the field-inducedquenching of the ODMR contrast, thus preventing theoptical readout of the spin splitting [8, 11, 12]. Asa consequence, quantitative ODMR-based SNVM hasbeen demonstrated mainly on magnetic textures in thinfilms with close to zero surface magnetisation, such asantiferromagnetic or single layer ferromagnetic materi-als [4, 7, 8, 11, 13–20]. ∗ Contributed equally to this work; [email protected] † Contributed equally to this work ‡ [email protected] To extend the operational range beyond
10 mT , the NVcentre can harness the field-dependent quench of the NVphotoluminescence (PL) for magnetic imaging as demon-strated recently [11, 21–23]. Quench-based SNVM mon-itors the changes in NV PL due to the local magneticfield variation across a spin texture with the respect tothe NV quantization axis. This modality also offers re-duced acquisition time and enables microwave-free non-perturbative operation [5, 24, 25]. The interpretation ofquench-based SNVM maps can be ambiguous, becauseof the multiple parameters that influence PL quenching,such as NV-sample distance, NV axis orientation, samplemagnetization, magnetic domain size or magnetic fieldnoise [26]. Therefore, this imaging mode has been lim-ited to the mapping of magnetic domain morphology withsurface magnetisation I S (cid:46) [21–23] (equivalent to of Co ). In this report, we reveal distinct quench-based imaging regimes, dependent on the material pa-rameters, and introduce the Multi-Angle Reconstruction(MARe) protocol to interpret the domain morphologyfrom quenched SNVM maps. We demonstrate MARe on[Ir/Co/Pt] multilayer film with
12 mA out-of-plane sur-face magnetisation, an order of magnitude larger thanthe operational limit of ODMR-based SNVM. UtilisingMARe can extend the applicability of SNVM to a widerrange of materials and magnetic regimes.
II. QUENCH-BASED IMAGING INDIFFERENT REGIMES
Figure 1(a) illustrates our experimental setup consist-ing of a diamond scanning probe with an NV centre im- a r X i v : . [ c ond - m a t . m e s - h a ll ] J a n (a)(b) Field norm | B | (mT) A n g l e B ( d e g )
60 nm100 nm200 nm (c)
Histogram counts N o r m a li z e d P L
60 nm100 nm
PL PL
200 nm (d) low high
MFM contrast N o r m a li z e d P L M e a n P L ( P L )
20 120 220 320
Distance d NV (nm) P L c o n t r a s t ( P L ) (e) Figure 1.
Effect of Magnetic Field Amplitude and Ori-entation on NV Luminescence. (a) Illustration of a di-amond probe scanning over a spin texture (colored cones)with magnetic field lines across the domain boundaries (redlines). The inset is a schematic of the local magnetic fieldvector B with reference to the NV quantisation axis ˆ u NV atthe tip of the diamond probe. α B indicates the angle between B and ˆ u NV . (b) Labyrinth domain morphology in Ir/Co/Ptmultilayer observed by MFM, exhibiting a zero-field period of
407 nm (scale bar: µ m ). (c) Normalized NV luminescencedefined as (PL − PL min ) / (PL max − PL min ) as a function of | B | and α B . The corresponding distributions at various d NV , ob-tained from simulated magnetic fields across (b), are overlaidon (c) (Contour lines). The 80th, 60th, and 40th percentilesare indicated with increasingly lighter contour lines. (d) Thehistograms of the simulated PL response at the three d NV val-ues,
60 nm ,
100 nm and
200 nm . PL indicates the mean PL, ∆PL marks the difference between the 90th and 10th per-centile of the PL distribution. (e) Dependence of ∆PL and PL on d NV . The peak of ∆PL marks the optimal distancefor quench-based imaging for the multilayer film of (b). Thecolored circles correspond to the three d NV values consideredin panels (c) and (d). planted close to the diamond surface at an NV-sampledistance d NV smaller than
100 nm [2, 9, 27, 28]. Theoptical ground state of the NV centre is a spin triplet,with a quantisation axis ˆ u NV along one of the four crys-tallographic axes of the diamond lattice [29, 30] and thelowest-energy state | m s = 0 (cid:105) is split from the | m s = ± (cid:105) states by .
87 GHz [31]. The local magnetic field canbe decomposed into parallel ( B (cid:107) ) and orthogonal ( B ⊥ )components with respect to ˆ u NV (Fig. 1(a) insert). The B (cid:107) splits the | m s = ± (cid:105) states which is measured bymonitoring the ODMR [32]. However, B ⊥ mixes thesespin states and modifies the branching ratio of the opti-cal transitions [12]. This results in the quenching of theNV PL and the suppression of the ODMR contrast (Sup-plemental Material A), restricting quantitative ODMR-based imaging to below ∼
10 mT [11, 12].Quench-based SNVM generates a PL intensity map,where regions with strong B ⊥ component appear darker.In the limit of modest surface magnetisation and smallNV-sample distance d NV , the domain boundaries appeardark producing faithful magnetic domain morphologymaps. Therefore, demonstrations are limited to singleor bilayer thin film systems with surface magnetisation I s (cid:46) [8, 11, 21–23]. Outside this regime, thecomplex interplay between d NV and I s , as well as themorphology lenghtscale, on the NV PL obfuscates thestraightforward correspondence of dark regions to do-main boundaries. Therefore, a systematic understandingof quench-based SNVM response is necessary to retrievethe domain morphology of a magnetic material. To dothis, we first simulate the d NV dependence of quench-based SNVM for a known magnetic structure.Our study involves [Ir( )/Co(1)/Pt(1)] magneticmultilayer, a room-temperature skyrmion platform withan out-of-plane anisotropy and I s = 12 mA (Supplemen-tal Material B) – an order of magnitude larger than sys-tems studied previously with SNVM. Further, the am-bient stability of the nanoscale spin textures [33, 34] al-lows us to correlate the quench-based SNVM images withMFM measurements [35]. Figure 1(b) presents an MFMimage of this film, exhibiting a labyrinth domain mor-phology with a zero-field period of
407 nm . Figure 1(c)presents a grey-scale map of normalised PL intensity sim-ulated as a function of field amplitude | B | and field angle α B with respect to the NV axis ˆ u NV . To understandhow the stray field distribution of the domain morphol-ogy affects the NV PL at various d NV , we simulate thevolumetric field distribution from the MFM map in Fig-ure 1(b) using the micromagnetics package mumax [36](Supplemental Material C). On Figure 1(c), we over-lay the corresponding | B | - α B distributions of the mag-netic field at three different d NV , at
60 nm (green con-tours),
100 nm (orange) and
200 nm (blue). (Supplemen-tal Material D). At d NV = 60 nm (
200 nm ), the NV PLremains uniformly quenched (unaffected) for the major-ity of the field distribution, while
100 nm d NV results instrong PL variation. Figure 1(d) clearly highlights theseNV PL variations ∆PL via the corresponding histogramsat d NV = 60 , and
200 nm . Figure 1(e) presents the ∆PL – calculated as the difference between the 90th and10th percentile of the NV PL distribution – as a functionof d NV (solid red curve) alongside the mean PL (dashedgrey curve).To assess the operational regime of quench-basedSNVM, we need to consider further the interplay be-tween I s and d NV . As shown in Figure 2(a), quench-based SNVM can be categorised into different regimes. Magnetization I s (mA) N V d i s t a n c e d N V ( n m ) (b) (c) (d) (a) Full quenchNo quench P L c o n t r a s t P L = % P L c o n t r a s t P L = % O u t li n e d i r e c t i o n a li t y (b) (c) Normalized PL (d) (e)
Figure 2.
Quench-based SNVM Imaging Regimes. (a) Different regimes of quench-based imaging as a function of NV-sample distance ( d NV ) and surface magnetisation ( I s ), based on simulated quench images. Little to no domain morphologicalinformation is captured in the No Quench (left greyed area) and
Full Quench (right greyed area) regimes where the PL mapis predominantly bright or dark, respectively. In the
Partial Quench regime (area bounded by dashed lines), field variationsare mapped to PL changes resulting in (b-d) quench images with features indicative of domain boundaries (scale bar: µ m ).Domain boundaries appear as dark isotropic PL features (low directionality) for smaller d NV and I s (b), and as directionalbright features (high directionality) at larger d NV and I s (c-d). The orientation of the directionality depends on ˆ u NV ,ϕ whichis the NV axis ˆ u NV , projected on the sample surface. The dashed lines indicate the contour lines for 5% map contrast. (e)Illustration depicting the NV axis ˆ u NV , the tilt angle ϑ NV from the normal to the sample surface, and the projection of ˆ u NV in the sample plane, ˆ u NV ,ϕ . The angle ϕ NV is the angle between ˆ u NV ,ϕ and the reference axis within the sample plane. Forpanels (a-d), ϑ NV = 54 . ◦ and ϕ NV = 0 ◦ . The combination of large d NV and small I s (small d NV and large I s ) results in predominantly bright (quenched)PL maps. In both the No Quench and the
Full Quench regimes, the lack of PL variation ∆PL implies that littleto no morphological information of the underlying spintextures is captured. In contrast, quench-based SNVMis feasible in the
Partial Quench regime (area boundedby dotted lines in Figure 2(a)) for a limited range of I s and d NV combinations. While the Partial Quench regimegives a large ∆PL , which is desirable for quench-basedSNVM, the resultant PL maps over an identical spin tex-ture can vary dramatically across this regime. To high-light this, we simulated quench-based SNVM maps of thesame area in the multilayer film using three different com-binations of I s and d NV (Fig. 2(b-d)). In general, we ob-serve an evolution from dark, isotropic features at lower I s and d NV to bright, directional features at higher I s and d NV due to competing magnetic field contributions abovedomains and domain boundaries. At lower I s and d NV (blue region in Figure 2(a)), the quench image appears asa uniform bright background with isotropic dark outlines(Fig. 2(b)). This is a result of the strong magnetic fieldlocalised at the domain boundaries which quenches the NV. The NV quench images reported to-date lie in thisregion of the parameter space [8, 21–23] (SupplementalMaterial D).For combinations of larger I s and d NV values (orangeregion in Figure 2(a)), the quench maps generate strik-ingly different images: panels (c) and (d) capture highlydirectional bright and segmented features along the do-main boundaries. In this case, strong off-axis magneticfield above domains and domain boundaries results ina predominantly dark PL map. However due to largegradients localised at domain boundaries, there are in-stances where the field is aligned closer to ˆ u NV . Thisoccurs across portions of domain boundaries orthogonalto the projection of ˆ u NV in the sample plane ( ˆ u NV ,ϕ ),resulting in directional bright features for panels (c) and(d), highly dependent on the NV equatorial angle ϕ NV (Fig. 2(e)). Notably, this directional behaviour occursover a significantly larger parameter space of the PartialQuench regime, well beyond that of panel (a), and thetrend remains valid for different domain periodicity (Sup-plemental Material D). It is worth emphasising here thatmagnetic materials with I s larger than ∼ would in-evitably constrain quench-based SNVM to the directional + ... (d)(a) = 0 (b) = 90 (c) max (deg) 0.40.60.81.0 C o v e r a g e (e) N = 2 N = 3 N = 4 N M A R e Figure 3.
Directional Quench Imaging and morphologyreconstruction. (a) Simulated quenched PL map based onspin texture in Figure 1b, with ϑ NV = 54 . ◦ , ϕ NV = 0 ◦ and(b) simulated quenched PL map in the same area but withthe NV rotated ◦ in the sample plane ( ϕ NV = 90 ◦ ). Bothmaps are simulated at a NV-sample distance d NV = 77 nm and surface magnetisation I s = 12 mA (scale bar: µ m ). (c)Reconstructed image obtained by summing (a) and (b). (d) M ulti- A ngle Re construction (MARe) illustrating the domainmorphology acquisition based on multiple N images at various ϕ NV . (e) Coverage of domain boundaries given as function of N and ϕ max . N is the number of quench images involved inthe reconstruction, and are obtained over a range of ϕ NV ( ◦ to ϕ max ) spaced by ∆ ϕ NV = ϕ max / ( N − . The reconstruc-tion with N = 4 images yields the largest coverage, whichsaturates above ϕ max (cid:39) ◦ . region of Figure 2(a). Therefore, a protocol that relatesthese images with the actual magnetic domain morphol-ogy is necessary in order to extend the operation regimeof quench-based SNVM for non-perturbative investiga-tions of such materials. III. RECONSTRUCTION OF DOMAINMORPHOLOGY - MARe
To reflect the role of ϕ NV in quench-based SNVM,we simulate two quench images for ϕ NV = 0 ◦ and ϕ NV = 90 ◦ , displayed in Figure 3(a) and 3(b), respec-tively. We set d NV =
77 nm , ϑ NV = 54 . ◦ , and ∼
12 mA surface magnetisation (Supplementary Material E) to re-flect our experimental measurements. The images forboth ϕ NV orientations show directional segments reveal-ing some features of the domain morphology, but moreimportantly these segments are complementary. There-fore, while an image at a given ϕ NV remains incomplete,images obtained at multiple ϕ NV values can collectivelygive a significantly better coverage of the underlying do-main morphology, which is the essence of the proposedimaging protocol. Multi-Angle Reconstruction protocol(MARe) harnesses the ϕ NV dependence of PL features tobuild a composite map enabling morphological imagingfurther into the Partial Quench regime, i.e. in strong-field conditions.The overlapping features in the PL maps obtained atdifferent ϕ NV , e.g. ◦ and ◦ as in panels (a) and (b)of Figure 3 allow us to perform an initial image registra-tion to compensate for the domain outline shift causedby ϑ NV (cid:54) = 0 ◦ (Supplemental Material F). Subsequently,the maps are normalised and summed to yield a MAReimage, as displayed in Figure 3(c), revealing a larger frac-tion of the domain boundaries with just two values of ϕ NV . To quantify the domain boundary coverage, weintegrate the product of the domain outlines from theMFM image (Fig. 1(b)) with the binarized MARe image.In order to maximise the fraction of domain boundariescovered by the protocol, we consider N ≥ images takenat different ϕ NV values ranging from ◦ to ϕ maxNV spacedequally by ∆ ϕ NV = ϕ maxNV / ( N − . Figure 3(d) illus-trates the MARe scheme for N = 4 and ϕ max = 120 ◦ ,which corresponds to 4 quench-based SNVM images witheach obtained at ◦ relative angle. The correspondingMARe image clearly captures an increased fraction of thedomain morphology.Figure 3(e) presents the calculated fraction of domainboundary coverage for MARe with N = 2 , and (black,blue and red curve). For N = 2 ( ) the maximum cover-age reaches ( ) at ϕ max = 80 ◦ ( ◦ ). ExtendingMARe to N = 4 further improves the coverage reachinga maximum of ∼ . This shows that even for N ≤ ,the MARe protocol is capable of recovering the domainmorphology with near-unity coverage.Figure 4 presents our experimental demonstrationof domain morphology mapping using MARe on the[Ir/Co/Pt] multilayer. To obtain quench-based SNVMimages we use a (100) diamond probe containing a singleNV centre with ϑ NV = 60 ± ◦ and d NV = 77 ± (Supplementary Material E). The combination of the d NV (
77 nm ) value and I s (12 mA) of the [Ir/Co/Pt] multilayer yields directional quench images according toFigure 2(a). Figures 4(a) and 4(b) show experimental = (a) = (b) (c) MFM domain outline (d)
Normalized PL + Figure 4.
Experimental verification of Multi-angle Reconstruction of Domain Morphology.
Experimental quenchingmap of the same area of Figure 3(a, b) with ϑ NV = 60 ± ◦ and (a) with ϕ = 0 ◦ and (b) with ϕ = 90 ◦ . The two images arecombined to give (c) the reconstructed domain morphological map with N = 2 . (scale bar: µ m ). (d) Binarized and magnifiedimage of Figure 1(b) covering the same area in (a, b and c), with domain boundaries marked in red. quench images acquired at ϕ NV = 0 ◦ and ϕ NV = 90 ◦ ,respectively, on the same area used for simulating Fig-ure 3(a) and 3(b) (Supplemental Material B). Thedomain boundary coverage of each of these images is +13 − % , in line with the simulations and there is goodagreement between the simulated and the measured im-ages for both orientations (Supplemental Material G).Figure 4(c) is the corresponding N = 2 MARe imageshowing matching bright features with the highlighteddomain boundaries of the binarised MFM image dis-played in Figure 4(d). The experimentally achieved do-main boundary coverage is improved to +12 − % – an en-hancement beyond the single frame coverage of ∼ .The deviation from the simulated coverage is due to thenonlinearity of the experimental map, as well as im-age thresholding and registration operations (see Sup-plementary Material H). Another reason for this de-viation might be due to perturbations of the domainmorphology induced by MFM scanning. As the exper-imental protocol includes MFM scans performed beforeand after each quench-based SNVM map, we do observelocal perturbations due to MFM that could potentiallylead to deviations from the unperturbed images capturedby quench-based SNVM (see Supplemental Material I).Nonetheless, the experimental demonstration of MAReextends the operational range of non-invasive quench-based SNVM into the Partial Quench regime.
IV. OUTLOOK
Our work methodically evaluates quench-based SNVMin terms of characteristic NV and magnetic materialproperties. We establish a predictive scheme involvingMFM, micromagnetics and NV photodynamics simula-tions, which yields images in excellent agreement withexperimentally acquired data. We find two regimes of quench imaging where morphological information is cap-tured. The first regime corresponds to mostly brightPL maps with dark outlines tracing the domain bound-aries, which corresponds to materials of low magnetisa-tion ( I s < ). The second regime, which has not beenreported to-date, results in PL maps with directionalsegmented features with strong ˆ u NV ,ϕ dependence. Weestablished a multi-angle reconstruction scheme, hereinnamed as MARe, to enable domain morphology mappingwith near-unity coverage for the second regime. The ex-perimentally validated MARe protocol extends quench-based SNVM imaging of out-of-plane spin textures tomagnetic systems with I s > . Furthermore, thescheme to identify the imaging regimes can be generalizedto complex magnetic textures, thus enabling the forecastof the attainable SNVM modes. We anticipate that theseinsights, alongside tools developed for prediction, inter-pretation and reconstruction, will stimulate the adoptionof quench-based SNVM as a non-perturbative nanoscalemagnetometry to a wider pool of materials, thereby fur-thering the development of quantitative quench-basedSNVM imaging. V. ACKNOWLEDGEMENTS
This work was performed at the Cambridge NanoscaleSensing and Imaging Suite (CANSIS), part of theCambridge Henry Royce Institute, EPSRC grantEP/P024947/1. We further acknowledge funding fromEPSRC QUES2T (EP/N015118/1) and from the Bettyand Gordon Moore Foundation. This work was alsosupported by the Faraday Institution (FIRG01) and bythe SpOT-LITE programme (Grant Nos. A1818g0042,A18A6b0057), funded by Singapore’s RIE2020 Initia-tives. A. K. C. Tan acknowledges funding from A*STAR,Singapore. B. Vindolet acknowledges support by a PhDesearch Grant of Délégation Générale de l’Armement.J.-F. Roch thanks Churchill College and the French Em-bassy in the UK for supporting his stay at the CavendishLaboratory.
Appendix A: Simulation of the NV photodynamics
To capture the photodynamics of the NV centre, we use of a seven-state model which includes the ground-state andexcited-state fine structure of the NV centre (Fig. S5). The strain splitting is E gs = E es ≈ , where the subscripts gsand es indicate the optical ground state and the optical excited state, respectively. At zero-field, the levels | i (cid:105) with i = 0 , , are split by D gs = 2 .
87 GHz in the optical ground state while the levels of the excited state | i (cid:105) , i = 3 , , ,are split by the excited state zero-field splitting D es = 1 .
42 GHz . The transition rates from level | i (cid:105) to the level | j (cid:105) aredenoted as γ ij . The decay rates are defined as in the work by Tetienne et al. [12]: we assume γ = γ = γ = γ r , γ = γ , and γ = γ . The spin non-conserving transitions from the excited state are assumed to be forbidden.Optical excitation pumps the ground state populations to the excited state but stimulated emission is neglected, thelaser being off-resonant and the vibrational relaxation decay time being short. The values used for the numericalsimulations are taken from the works by Robledo et al. and Tetienne et al. [12, 37] (Tab. S1). Within the assumptionof Markovian noise: d ρ ( t )d t = − i (cid:126) [ H , ρ ] − m (cid:88) k =0 (cid:16) L † k L k ρ + ρL † k L k (cid:17) + m (cid:88) k =0 L k ρL † k (A1)where H is the magnetic-field dependent Hamiltonian describing the seven-state system, ρ is the density operatorand L k are the Kraus operators which describe the m photon emission or absorption processes. We work in theapproximation of microwave excitation rate weaker than the laser pumping, hence T ∗ dephasing is neglected. Thelaser pump is described as an incoherent absorption process. The Kraus operators then can either take the form: L absk = √ γ ji | i (cid:105)(cid:104) j | , i = (3 , , , j = (0 , , (A2)or L emk = √ γ ij | j (cid:105)(cid:104) i | , i = (3 , , , , j = (0 , , . (A3)Extra Kraus operators can be added if incoherent microwave driving is included in the model: L mwk = (cid:113) γ mwij | i (cid:105)(cid:104) j | , i, j = (0 , , , i (cid:54) = j . (A4)The steady-state PL rate is proportional to the sum of the steady-state populations in the excited state: Γ PL ∝ (cid:88) i =3 ρ ii . (A5)Decay rate (MHz) γ r γ γ = γ γ γ = γ Table S1.
Photodynamics parameters.
The previ-ously reported [12, 37] decay rates used in the 7-statemodel for the NV magnetic field-dependent photody-namics. Figure S5.
Schematics of the NV seven-level system.
Seven-level system used to capture the NV photodynamics, foran arbitrary magnetic field. In general, off-axis magnetic fieldscouple the zero-field eigenstates and allow for spin-flip transi-tions which modify the zero-field photodynamics. Green linesrepresent laser excitation, red lines optical decay and purplelines non-radiative decay.
B (mT) N o r m a li z e d p o p u l a t i o n (a) |0| 1 | + 1Singlet B (mT) N o r m a li z e d P L (b) E S R c o n t r a s t ( % ) Figure S6.
Magnetic field-dependent NV photodynamics. (a) Changes in steady state population under continuousgreen excitation of the triplet ground state and singlet state of an NV as a function of a magnetic field, B ⊥ , orthogonal to theNV axis ˆ u NV . (b) The corresponding quench response of the NV PL (blue curve) with increasing B ⊥ due to larger shelving statepopulation (shown in (a)). ODMR contrast (red curve) is also reduced due to the decrease in population difference between | (cid:105) and |± (cid:105) (shown in (a)). Magnetic field components orthogonal to ˆ u NV (off-axis) couple the different spin states, modifying the branchingratio of the transitions [12] and altering the steady-state populations of the levels (Fig. S6(a)). On one hand, thisleads to a reduction of the ESR contrast (Fig. S6c), because of the reduced population difference between the | (cid:105) and |± (cid:105) levels (Fig. S6(b)). On the other hand, this leads to the quenching of the PL [8, 12, 38], due to a largerpopulation getting trapped in the singlet state (Fig. S6(b)). This effect leads to a trade-off between magnetic fieldamplitude ( ∝ /d NV ) and spatial resolution ( ∝ d NV ) when imaging small spin textures. Appendix B: Material Properties and Preparations
The multilayer stack of [Ir( )/ Co(1)/ Pt(1)] were deposited on thermally oxidised Si wafers by DC magnetronsputtering. Additional fabrication information is found in previous studies [34]. Relevant properties of the Ir/Co/Ptstack are shown in Table S2. The surface magnetisation I s is given by M s · t eff , where t eff is the effective magneticthickness which is the number of repetition multiplied by the thickness of the magnetic layer. In this case, t eff =14 nm,and hence I s =12.3 mA (Table. S3). The I s of various systems studied with quenched SNVM is given in Table S3 forcomparison. The zero-field magnetic domains are stabilised by demagnetising the sample. This results in labyrinthmorphology with a period, P =407 nm (Fig. S9(a)).The sample is marked with a wirebonder (Fig. S7) which allows us to image the same area of interest (yellow boxin Fig. S7) using two techniques (SNVM and MFM) on separate platforms. MFM is always carried out before andafter quenched SNVM, to ensure that the morphology of the probed area remains identifiable and the features arelargely unchanged. MarkerArea of Interest40 m
Figure S7.
Marked Sample.
Microscopic image of a marked area of the sample surface with a MFM probe in view. Themarking is achieved using a wirebonding tip, and the area of interest probed by quenched SNVM, micromagnetics and MFMin the main text is highlighted in yellow. M s (MA / m) K eff (MJ / m ) D (mJ / m ) Table S2.
Material Properties.
The saturationmagnetisation M s , effective anisotropy K eff and DMIstrength D of [Ir/Co/Pt] film. Material System I s (mA)14 × Ir/Co/Pt . Pt/CFA/MgO/Ta [22]
CFA: Co FeAl
FM: Ni/Co/Ni
Table S3.
Material Systems.
The surface magnetisa-tion I s of various systems studied with quenched SNVMcompared to [Ir/Co/Pt] . (a) B x ( m T ) (b) B y ( m T ) (c) B z ( m T ) Figure S8.
Simulated Magnetic Field. (a-c) Magnetic field components B x , B y , B z , at d NV = 77 nm above the samplesurface, simulated based on the magnetisation distribution in Figure S9(b). (Scale bar: µ m ) (a) lowhigh M F M c o n t r a s t (b) Figure S9.
Image Thresholding. (a) MFM image of sample surface (highlighted in Figure S7) showing labyrinth domains atzero field. (b) Corresponding binary image after thresholding process, yielding up/down magnetisation used for simulations inFigure S8. (Scale bar: µ m ) Appendix C: Micromagnetic simulations
The magnetic field above the spin texture was obtained via Mumax3 simulations. For the study of quenched imagingin various regimes (Fig. 2 in main text), The multilayer film is modelled using the effective medium method [39] so as toreduce computation resources. The simulation grid consists of × × cells spanning µ m × µ m ×
384 nm (cell size: ≈
39 nm ×
39 nm × ). The first 14 layers are modelled with an effective saturation magnetisation M eff = M s / and the volume above as non-magnetic spacers. The simulation is further refined for comparison withexperiments (Fig. 3 and 4 in main text) with each cell layer corresponding to of Ir, Co, or Pt. Maintaining thesame grid size, this reduces the total simulated height to
128 nm . Similarly, the Pt, Ir layer and the volume above themultilayer film are modelled as non-magnetic spacers. Differing from the effective medium model, the Co layer has theexperimentally obtained magnetisation M s . In both cases, the simulated non-magnetic volume above the multilayerfilm allows us to retrieve the magnetostatic field environment above the spin texture (Fig. S8) via Mumax3. Themagnetisation distribution used in the simulation is based on segmenting a MFM image into up and down domainsby image thresholding (Fig. S9).1 (a) (b)
300 0 300
Displacement (nm) (c)
300 0 300
Displacement (nm) (d) N o r m a li z e d P L A u t o c o rr e l a t i o n Figure S10.
Quenched image autocorrelation and directionality. (a) Quenched images at d NV = 12 nm and I s = 1 . and (b) at d NV = 78 nm and I s = 10 . . (Scale bar: µ m ) (c, d) Autocorrelation maps of panels a, b, respectively. Quenchedmaps with low directionality display a a cross-correlation peak with circular simmetry. When the directionality increases, thepeak becomes elliptic. Appendix D: Analysis of Quenched Imaging Regimes
The diagram in Figure 2 of the main text is constructed based on the directionality of the observed PL featuresand the contrast of quenched images with different combinations of surface magnetisation I s and NV-sample distance d NV . The directionality of the PL features is determined from the auto-correlation of the quenched image (Fig. S10).The directionality is defined as − r min /r max , where r min and r max are respectively the minor and the major axisof an elliptical Gaussian fit to the cross-correlation peak. A directionality equal to zero indicates isotropic features(Fig. S11(a)), and a value increasing to unity implies increasing anisotropy. The PL contrast is given as − P /P ,where P x is the x th percentile of the PL distribution of each quenched image (Fig. S11(b)).Apart from the films magnetisation and d NV , we expect the magnetic field distribution be heavily influenced bythe domain periodicity. We show here that the quench imaging regimes put forward in the main paper remain validat different P, with appropriate scaling of d NV and M. We define the scaled d NV as d NV (cid:48) = d NV × ( P/P ) S d , andscaled M as I (cid:48) s = I s /I s, × ( P/P ) S i where P = 407 nm and I s, = 12 . correspond to the value for our sample[Ir( )/ Co(1)/ Pt(1)] . Scaling factor S d and S i are empirically determined to be − and − . ∼ (cid:112) / . Theanalytical derivation is however beyond the scope of the paper. The scaled directionality maps at varying P are givenin Figure S12. We also include films studied by Gross et al. [21] and Rana et al. [23] in this framework (Fig. S13).The framework is in good agreement with the work of Gross et al. which observed isotropic PL features. In the studyof Rana et al., we are unable to resolve the directionality of the features observed. However, we expect the quenchedimaging regime to deviate from our framework as our simulation model does not include exchange bias present intheir film.2 Magnetisation I s (mA) D i s t a n c e d N V ( n m ) (a) D i r e c t i o n a li t y Magnetisation I s (mA) D i s t a n c e d N V ( n m ) (b) P L C o n t r a s t ( % ) Figure S11.
Details on Quenched Imaging Regimes . (a) The directionality of PL features and (b) the PL contrast of aquenched image given as a function of d NV and I s . S c a l e d d n v ( d n v ) P = 200 nm (a) P = 400 nm (b) P = 600 nm (c) P = 800 nm (d) D i r e c t i o n a li t y Scaled I s ( I s ) Figure S12.
Scaled Quenched Imaging Regimes at Varying Domain Periodicity . The directionality of PL features asa function of scaled I s ( I (cid:48) s ) and scaled d NV ( d NV (cid:48) ) at domain periodicity, (a) P = 200 nm , (b) P = 400 nm , (c) P = 600 nm and(d) P = 800 nm . The similar directionality picture indicates that the quench imaging regimes remain valid across different P with appropriate scaling to I s and d NV . Scaled I s ( I s ) S c a l e d d n v ( d n v ) Rana, K. et al.(ArXiv 2019)Gross, I. et al.(Phy. Rev. Mat. 2018)[Ir/Fe/Co/Pt]×14 D i r e c t i o n a li t y Figure S13.
Overview of Quenched Imaging on Thin Films . Previous studies involving quenched imaging of thin filmsare plotted on the scaled directionality map. The position on the map is based on the d NV , I s , and P in each study. (a) Microwave Frequency (GHz)2.84 2.87 2.90 P L I n t e n s i t y ϑ (deg)10 60 110 1605203550 ϑ NV = 60 ± 2°(b) φ (deg)10 60 110 1605203550 O D M R S p li tt i n g ( M H z ) FitData φ NV = 93 ± 2° Figure S14.
Axis measurements of the NV probe. (a) ODMR spectrum obtained under an external magnetic field. Wecan observe the splitting of the | m s = +1 (cid:105) and | m s = − (cid:105) due to the Zeeman effect. We measure a splitting of
54 MHz whichcorresponds to a field felt by the NV of about . (b) Measurement of ϕ NV . We fix ϑ and ϕ is varying. When the ODMRsplitting is maximum, ϕ = ϕ NV . (c) Measurement of ϑ NV . We fix ϕ and ϑ is varying. ϑ = ϑ NV when the ODMR splittingreaches its maximum value. Applied Field (mT) M O K E S i g n a l ( a . u . ) (a) (b) H e i g h t ( n m ) Figure S15.
Calibration Strip Characterisation. (a) Intensity of polar MOKE signal of a [Ta/CoFeB/MgO] strip as afunction of an out-of-plane magnetic field. (b) Topography image of [Ta/CoFeB/MgO] calibration strip (scale bar: µ m ) Appendix E: NV Sensor Characterisation
We use a 3-axis Helmholtz coil to apply an external magnetic field B at varying ϕ and ϑ , with a fixed fieldstrength | B | = 1 mT . We obtain the ODMR spectra by recording the integrated PL intensity of the NV centre as wesweep the microwave (MW) frequency. In the presence of magnetic field, the ODMR spectrum displays a splittingof the | m s = +1 (cid:105) and | m s = − (cid:105) states due to the Zeeman effect (Fig. S14(a)). This splitting is proportional to theprojection of the magnetic field on the NV axis ˆ u NV . The ODMR spectrum is first obtained as a function of ϕ whilefixing ϑ = 90 ◦ (Fig. S14(b)). The Zeeman splitting is maximum when ϕ = ϕ NV which in our case is ϕ NV = 93 ± ◦ .Next, we vary ϑ while fixing ϕ = ϕ NV (Fig. S14(c)). Similarly, the maximum splitting occurs when ϑ = ϑ NV whichwe obtain to be ϑ NV = 60 ± ◦ .We determine the NV-sample distance d NV by measuring with our diamond tip the stray field emitted across theedge of a [Ta/CoFeB/MgO] strip. The out-of-plane magnetic hysteresis is characterised by a MagVision Magneto-Optical Kerr Effect (MOKE) microscope (Vertisis Technology) in the polar sensitivity mode and shows that themagnetisation remains saturated at remanence (Fig. S15). The Zeeman shift of the ODMR spectrum across the edgeat remanence is given in Figure S16(a) (blue dashed curve) and is fitted (red curve) following the procedure devised byHingant et al. [40] to retrieve the d NV . We repeat the measurement numerous times along the edge at
50 nm spacing,and the extracted values are averaged (Fig. S16(b)). The diamond tip used in this work has a d NV = 77 . ± .4 Position ( μ m)0 21 Z ee m a n s h i f t ( m T ) H e i g h t ( n m ) O cc u r e n c e s d NV (nm)(a) (b) Figure S16.
Calibration of the NV probe. (a) We represent on this plot the topography of the edge of a CoFeB magneticstripe (in brown) and the measured Zeeman shift of the NV ODMR spectrum (in blue) due to the magnetic field emitted atthe edge of the stripe. We deduce the value of d NV from the fit (in red) of the Zeeman shift experimentally measured. (b)Histogram distribution of all the NV-sample distances we measured. The average value is d NV = 77 . and the standarddeviation is σ d NV (cid:39) . Appendix F: Quenched Imaging with [111] NV Centre
The discussion in the main text focuses on NV centres found in commercially available (100) diamond tips. Quenchedmaps obtained with NVs with ϑ NV = 54 . ◦ on samples with out-of-plane magnetic anisotropy give rise to differentimaging regimes, as explained in the main text. Notably, there is a range of d NV and I s where the quenched mapsdirectionally highlight the domain boundaries. The directionality is due to the non-zero angle between the NV axisand the magnetic anisotropy. Hence, this effect is not present when using NV centres pointing along the [111] axis (i.e. ϑ NV = 0 ◦ ), hosted in (111)-oriented diamond tips, which have been recently reported [41]. The simulations shown inFigure S17(a-c), which have been taken at the same d NV and I s of Figure 2(b-d) of the main text, respectively. At lowmagnetisation (Fig. S17(a)), the NV PL is quenched along the domain boundaries (cross-correlation in Fig. S17(d)),resulting in a bright image with dark outlines. At higher magnetisation (Fig. S17(b)) the quenching still traces thedomain boundaries (cross-correlation in Fig. S17(e)), but also expands further within the domain area. The thinbright lines correspond to the innermost areas of the domains, where the magnetic field is mainly orthogonal to thesample surface and thus aligned with the NV axis. In Figure S17(c), the combination of large magnetisation and high d NV gives an image similar to Figure S17(b), but with lower resolution. (a) (b) (c) N o r m . P L
300 0 300
Displacement (nm) (d)
300 0 300
Displacement (nm) (e)
300 0 300
Displacement (nm) (f) C r o ss - c o rr . Figure S17.
Quenching with [111] NV centres . Quenching maps obtained with NVs with ϑ NV = 0 ◦ on the same area asFigure 2 in the main text (scale bar: µ m ). The different maps correspond to (a) I s = 3 . , d NV = 30 nm , (b) I s = 9 . , d NV = 84 nm , and (c) I s = 15 . , d NV = 162 nm , which correspond to the parameters of Figure 2(b-d) of the main text. (d-f)2D cross-correlation maps of the images in (a-c) with the domain boundaries. The negative correlation at zero displacementindicates a low PL at the boundary. If the displacement increases, the correlation is positive, corresponding to the bright PLobserved within the domains. (b) (c) (d)(e) (f) (g)(a) N o r m . P L B i n a r i z e d P L Figure S18.
Estimation of the domain coverage. (a) Portion of the binarised MFM scan (background) and domain edges(red pixels) obtained via Canny edge detection (scale bar: µ m ). Quenched maps of the same area, where (b) is the map takenwith an NV with ϑ NV = 54 . ◦ and ϕ NV = 0 ◦ , (c) is the reconstructed image with N = 4 at ϕ max = 180 ◦ (see main text), and(d) is acquired with an NV with ϑ NV = 0 ◦ . (e-g) are the images obtained by binarising (b-d), respectively. Appendix G: Domain Coverage Estimation
In order to estimate the percentage of domain boundaries covered by the simulated quenched maps, we first binarizethe selected MFM images with Otsu thresholding [42] (a portion is shown Fig. S18(a)) and detect the boundaries withthe Canny algorithm. The quenched maps are simulated from the stray fields obtained with Mumax3, as explainedabove. We first simulate the quenched maps with NVs at ϑ NV = 54 . ◦ and different ϕ NV (Fig. S18(b) for ϕ NV = 0 ◦ ).The single images are then registered to the domain boundaries with the ECC image alignment algorithm [43], inorder to compensate for the small shift from the domain boundaries induced by the non-zero angle between themagnetic anisotropy and ϑ NV . The images are then combined as explained in the main text (Fig. S18(c) for N = 4 and ϕ max = 180 ◦ ). Additionally, we simulate a quenched map with an NV at ϑ NV = 0 ◦ , which exhibits no shift andno ϕ NV -dependence (Fig. S18(d)). The images are then binarized using local gaussian thresholding (Fig. S18(e-g)).The binarized images are multiplied to the domain boundaries and integrated to yield the coverage. For experimentalquenched maps, the above estimation protocol includes additional thinning and dilation of the binarized images beforemultiplication. The thinning and dilation process ensures that local deviations between the binarized experimentalquenched maps obtained via SNVM and the domain outline retrieved from MFM images are accounted in the coverageestimation. These local deviations are largely due to experimental map nonlinearity, suboptimal image threshold andregistration conditions, and MFM perturbation. To estimate the experimental coverage error, we use the 3 smalleststructuring element – a 3 pixel wide diamond, 3 pixel wide square and 5 pixel wide diamond – for binary dilation.The coverage value is given by the estimation protocol using a 3 pixel wide square dilation structuring element whilethe coverage bounds are given by the diamond structuring elements.7 = 0 = 90 max = 180 , N = 10
300 0 300 (d)
300 0 300
Displacement (nm) (e)
300 0 300 (f)
Max. angle max (deg) C o v e r a g e ( a r b . un i t s ) (g) N o r m . P L C r o ss c o rr . C o m b i n e d i m a g e s ( N ) Figure S19.
Directionality and image reconstruction (a,b) Simulated quenched maps with ϕ NV = 0 ◦ and ϕ NV = 90 ◦ and (c) MARe image with N = 10 and ϕ max = 180 ◦ . (Scale bar: µ m ). (d-f) 2-dimensional cross-correlations between thequenched images in (a-c) and the domain boundaries. For single images (d,e), the cross-correlation shows a positive correlationshifted from the origin in the direction opposite to ˆ u NV ,ϕ , the projection of ˆ u NV in the sample plane. This indicates that thebright outlines are highly directional and do not occur exactly on top of the domain boundaries. On the contrary, the cross-correlation of the MARe map (f) is isotropic, indicating that most of the boundaries are uniformly covered. (g) Simulations ofdomain boundary coverage to include N beyond N = 4 . Appendix H: Directionality, image reconstruction and boundary coverage
We can further analyze the properties of quenched maps by studying the 2-dimensional cross-correlation betweenthe maps and the domain boundaries. We do this by simulating the quenched maps starting from the MFM image(Fig. S9(a-b)), as described above and in the main text. We then calculate the cross-correlation between the maps andthe domain boundaries obtained from the MFM map with the Canny edge detection algorithm. The cross-correlationplots (Fig. S19(d-e)) show a non-uniform positive correlation peak which is shifted from the origin. The shift isopposite to the direction of the direction of ˆ u NV ,ϕ . This indicates that the directional features on average do notoccur on top of the domain boundaries. The shift originates from the non-zero tilt of ˆ u NV from the normal to thesample plane. This has important consequences for the MARe scheme, since the shift needs to be compensated withimage registration algorithms before combining the images (Sec. G). In Figure S19(c) we show a MARe image with N = 10 and ϕ max = 180 ◦ . The corresponding 2D cross-correlation (Fig. S19(f)) displays a circularly symmetric peak,indicating that the reconstructed map is non-directional.We also study the option of using more than four images ( N > ) to reconstruct the domain morphology. We showthe result of the simulations in Figure S19(g). As presented in the main text, N = 4 achieves a peak coverage ofabout . at ϕ max ≈ ◦ . The maximum coverage for N = 5 is ≈ . at ϕ max ≈ ◦ . For N > , the coveragereaches a peak value of ≈ .8 ce Quenched SNVM MFM Simulation
Scan 2
Scan 1
Scan 2Scan 1 highlow
MFM contrast high low
PL contrast highlow
PL contrast (a) (b) (d) (e) (c)
Figure S20.
Evidence of non-perturbative imaging.
Sequential study of the domain morphology by (a,b) consecutivequenched SNVM imaging, followed by (c,d) consecutive MFM. Areas of perturbation due to consecutive MFM imaging arecircled (c, d), while no visible changes are observed in the corresponding areas in the consecutive quenched images (a, b). (e)Simulated quenched image based on second MFM scan 2 (d) shows dissimilar PL features in the circled vicinity as comparedto experiments (a, b). (Scale bar: 500 nm)
Appendix I: Imaging with Minimal Perturbation
As explained in the main text and in previous studies [21–23], quenched SNVM enables perturbation-free imagingof spin textures. We present here a comparison of repeated quenched SNVM and MFM scans over the same area,which highlight the non-perturbative advantage of quenched SNVM. We first obtain two consecutive quenched imagesover an area on the sample (Fig. S20(a,b)), and thereafter another two consecutive MFM images over the same area(Fig. S20(c, d)). By comparing the quenched and MFM images, we observed areas (circled in Fig. S20(a-e)) showingnon-perturbative consecutive quenched imaging (Fig. S20(a,b)), but were subsequently perturbed by consecutive MFMscans (Fig. S20(c,d)). 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