AAll-Optical and Microwave-Free Detection of Meissner Screening using Nitrogen Vacancy Centers in Diamond
All-Optical and Microwave-Free Detection of Meissner Screening usingNitrogen-Vacancy Centers in Diamond
D. Paone,
1, 2
D. Pinto,
1, 3
G. Kim, L. Feng,
1, 4
M-J. Kim,
1, 4
R. Stöhr, A. Singha, S. Kaiser,
1, 4
G. Logvenov, B. Keimer, J. Wrachtrup,
1, 2 and K. Kern
1, 3 Max Planck Institute for Solid State Research rd Institute of Physics and Institute for Integrated Quantum Science and Technology IQST,University Stuttgart Institut de Physique, École Polytechnique Fédérale de Lausanne th Institute of Physics and Research Center SCoPE, University Stuttgart (Dated: 13 January 2021)
Microscopic studies on thin film superconductors play an important role for probing non-equilibrium phase transitionsand revealing dynamics at the nanoscale. However, magnetic sensors with nanometer scale spatial and picosecond tem-poral resolution are essential for exploring these. Here, we present an all-optical, microwave-free method, that utilizesthe negatively charged nitrogen-vacancy (NV) center in diamond as a non-invasive quantum sensor and enables thespatial detection of the Meissner state in a superconducting thin film. We place an NV implanted diamond membraneon a 20 nm thick superconducting La − x Sr x CuO (LSCO) thin film with T c of 34 K. The strong B-field dependenceof the NV photoluminescence (PL) allows us to investigate the Meissner screening in LSCO under an externally ap-plied magnetic field of 4 . j c of 1 . · A / cm . Our workcan be potentially extended further with a combination of optical pump probe spectroscopy, for the local detection oftime-resolved dynamical phenomena in nanomagnetic materials. I. INTRODUCTION
Microscopic phenomena revealing complex magneticphases in two-dimensional materials are catching the centralattention in modern condensed-matter physics . Prime ex-amples are superconducting systems which are accompaniedby electronic phases , such as vortex formation in the caseof type II superconductors . Various approaches are alreadyestablished for studying superconductivity mainly based onsuperconducting quantum interference devices (SQUIDs) ,magnetic force microscopy (MFM) , scanning tunneling mi-croscopy (STM) and the investigation of magneto-opticaleffects . However, each of these techniques suffer from draw-backs such as limited temperature and magnetic field ranges,spatial resolution and complex sample preparation. A promis-ing alternative for surpassing these drawbacks is to employnegatively charged nitrogen vacancy (NV) centers in dia-mond. In fact, the NV center in diamond is a non-invasivenanoscale magnetic field sensor allowing measurements atboth, cryogenic as well as ambient conditions, with a mag-netic field sensitivity of 1 pT / √ Hz for NV ensembles and1 µ T / √ Hz in the case of single NV centers . Applications ofNV center sensing have been shown in single molecular sys-tems, investigated using nuclear magnetic resonance (NMR) and electron spin resonance (ESR) . In addition, mag-netic properties of materials have been investigated includingspin waves , ferromagnetism and superconductivity at the nanoscale with this approach. The fundamental sens-ing principle of the NV center relies on the spin dependentphotoluminescence (PL) of the defect center . Microwaveexcitations allow coherent manipulation within different spinsublevels present in the ground state. The resulting transitionfrequencies show a Zeeman effect, forming a toolset for mag-netic field sensing, known as optically detected magnetic res- onance (ODMR) technique. However, microwave excitationsare usually linked with heating effects, which could locallychange properties of the investigated sample .Here, we introduce the magnetic field dependent fluorescenceyield of an NV center ensemble which allows a reliable anddirect investigation of the spatial modulation of superconduc-tivity on a microscopic scale. Besides calibrating the changein the NV emission intensity caused by an external magneticfield with ODMR spectroscopy, our experiments rely solelyon an all-optical, non-resonant, microwave-free measurementscheme. We position an NV implanted diamond membraneat the edge of a superconducting La − x Sr x CuO (LSCO) thinfilm. We collect the NV center fluorescence at different po-sitions on the superconductor at 4 . . z -direction. Nor-malization to zero-field measurements provides us a finger-print of the Meissner screening in terms of the PL rate dropwhen the NV ensembles are in close proximity ( ≈ µ m) tothe LSCO thin film. Combining this with an analytical model,developed by E. H. Brandt , allows us to extract the criticalcurrent density j c . Furthermore, we provide a comparison ofour results with a complementary SQUID measurement. II. EXPERIMENTAL SETUP AND METHODS
All measurements are carried out using a confocal micro-scope connected to an UHV-He bath cryostat operating at abase pressure of 3 · − mbar at 4 . . A green512 nm pulsed laser is used to excite the NV centers. Theemitted fluorescence is recorded with a photon detector de-vice. The laser spot is scanned over the sample, while record-ing the NV fluorescence, resulting in a confocal image. Fur-ther details of this experimental setup and of an additional a r X i v : . [ c ond - m a t . s up r- c on ] J a n ll-Optical and Microwave-Free Detection of Meissner Screening using Nitrogen Vacancy Centers in Diamond 2 MW (a) (b)(c) (d) N V - d i a m ond La s e r L S C O L SA O N o r m . F l uo r e sc en c e Frequency (GHz) B z = 6 mT B z = 3 mT B z = 1 mT B z = 0 mT LaserPhoton Detector
UHV-Cryostat
3D vector magnet
MWFPGA
Objec veSamplePiezo-Stage
Dichroic MirrorPiezo Mirror
Experimental Data N o r m . P L Magnetic Field B z (mT) Interpolation
FIG. 1. (a) Sketch of the experimental setup. A confocal microscopysetup is attached to a UHV-cryostat at 4 .
2K and equipped with a 3Dvector magnet for applying external magnetic fields. The microwavecircuit is only used for resonant calibration purpose and is shown inlight grey. The inset depicts the sample geometry consisting of anNV diamond membrane attached onto a superconducting LSCO thinfilm. Dimensions are not drawn to scale. (b) Energy level scheme ofthe negatively charged NV center. The ground-state spin levels canbe pumped via a green laser to the excited state. The relaxation to theground-state leads to an emission of red photons, which are measuredusing a confocal microscope. The NV center spin state can be drivenbetween the m s = | (cid:105) and the m s = |− (cid:105) , m s = | + (cid:105) states using mi-crowave excitations. The magnetic field experienced by the NVs canbe calculated using the Zeeman equation. (c) ODMR spectra of anNV ensemble in the bare diamond membrane for different magneticfields aligned in z-direction, acquired at 4 .
2K inside the UHV cryo-stat. The spectra are vertically offset for clarity. (d) Effect of increas-ing the external magnetic field on the observed NV fluorescence. Thecount rate drop is collected for different magnetic fields aligned in z-direction, estimated from the corresponding ODMR measurements.The red solid line indicates a smoothing spline interpolation. Themeasurement has been performed at ambient conditions in a sepa-rate confocal setup with a permanent magnet attached closely to thediamond membrane. setup used for NV characterization at ambient conditions canbe found in section 1 of the Supporting Information (SI). Thepulsed microwave source integrated with the setup allows usto perform magnetometry with NV centers and ODMR mea-surements which require NV spin manipulations.Magnetometry with NV centers relies on the energy-levelscheme shown in Fig. 1(b). The ground electronic state ofthe NV center is a spin triplet. The energy gap between theexcited triplet state and the ground state corresponds to a pho- ton emission of 637 nm. The NV center can be excited fromthe ground state into the phonon side band using ≈
512 nmgreen laser light. Subsequently, it relaxes to the ground stateby emitting photons in the range of 637-750 nm. The fluores-cence is highly spin state selective . In particular, the fluo-rescence rate of the m s = | − (cid:105) , | + (cid:105) states is lower than thatof the m s = | (cid:105) . In presence of an externally applied magneticfield, the | ± (cid:105) states experience a Zeeman splitting. Sub-sequently, a resonant microwave excitation enables the tran-sition between the bright m s = | (cid:105) state and one of the lessfluorescent dark | ± (cid:105) states, whenever the microwave fre-quency matches the induced energy splitting. Therefore, inabsence of an external magnetic field, the NV fluorescenceshows only a single resonance signifying the zero field split-ting of D = .
87 GHz. For a non zero magnetic field, thissplits into two resonances corresponding to the | (cid:105) → | − (cid:105) and | (cid:105) → | + (cid:105) transitions. The unique combination of theseproperties of the NV center, allows us to calibrate the mag-netic field, by observing field dependent ODMR spectra, asshown in Fig. 1(c). For all measurements, the magnetic fieldis applied along the z direction ( (cid:126) B = ( , , B z ) ), normal to the(100) surface. Therefore, all four possible NV orientations ex-perience the same Zeeman splitting ∆ f given by ∆ f = γ B z √ . γ is the gyromagnetic ratio, which is 28 MHz / mT for the NVelectronic spin. The observed frequency splitting is propor-tional to the applied magnetic field following this equation.However, this method requires the application of a resonantmicrowave driving frequency. Microwave applications are of-ten accompanied by local heating effects, which could causeundesired changes in the properties of the investigated system,especially in case of a superconducting sample.This can be circumvented by utilizing a non-resonant mea-surement scheme without microwave excitations. The fluores-cence yield detected from the NV center strongly depends onthe applied off-axis magnetic field. In particular, it decreaseswith increasing the B z -field. This can be explained by the spinmixing of the sublevels when the magnetic field is misalignedwith respect to the NV axis. The mixing of the spin sublevelsleads to an inefficient spin-dependent PL rate by enhancingthe probablity of the non-radiative inter system crossing to themetastable state. The resulting PL drop can be used for a qual-itative investigation of the magnetic fields . Fig. 1(d) showsthis behavior of the NV emission for different magnetic fields B z at ambient conditions. A significant decrease of the de-tected PL up to 25 % is observed for the highest applied mag-netic field of 22 . z -direction. This approachstill relies on ODMR spectra for the quantitative calibrationof the magnetic fields on the NV axis. However, besides thisthe direct all-optical record of the NV emission relies on anon-resonant, microwave-free method. Measurements of fieldvariations and qualitative observations of magnetic properties,which are often required for supercondcting systems, are stillviable using the direct emission of the NV centers. There-fore, the magnetic field dependent PL can be a sensitive toolfor detecting non-equilibrium phase transitions and dynamicalphenomena with a high spatial resolution.ll-Optical and Microwave-Free Detection of Meissner Screening using Nitrogen Vacancy Centers in Diamond 3 (a)(b) T c M agne t i c M o m en t ( * e m u ) Magnetic Field (mT) -8 -6 -4 -2 0 2 4 6 8-8-4048 M agne t i c M o m en t ( * e m u ) Magnetic Field (T)
25 30 35 40 4504812 M u t ua l I ndu c t an c e ( a r b . un i t s ) Temperature (K) M u t ua l I ndu c t an c e ( a r b . un i t s ) Temperature (K) H c1 FIG. 2. (a) Real part of the mutual inductance versus the tempera-ture. The mutual inductance is measured as the magnetic interactionbetween two coils. Within these, the LSCO sample is positioned andthe temperature is swept from 300K to 5K. The inset shows a signif-icant drop of the inductance at 34 K indicating a critical temperatureof T c = −
7T to 7 T. The inset shows the behavior of the magnetic mo-ment for weak magnetic fields between 0 and 5mT. The inflectionpoint of the curve indicates the first critical field H c , being at around2mT. III. RESULTS AND DISCUSSIONA. Investigated LSCO Sample
In order to demonstrate this, we characterized the Meissnerscreening caused by a type II cuprate superconducting LSCOsample. LSCO is among the most studied high T c super-conductors in recent years . Furthermore, it has attractedmuch interest since Cooper pair formation, diamagnetism and vortex mechanisms have been measured above T c .Therefore, LSCO is not only an ideal sample to benchmarkour technique with existing quantities and models, but alsoforms a system with interesting superconducting propertieswhich could be investigated with our method in future ex-periments. The studied sample consists of a single crys-talline LSCO thin film epitaxially grown on a (001) LaSrAlO (LSAO) substrate and exhibits a critical temperature of T c =
34 K which is depicted in the mutual inductance measure-ment shown in Fig 2(a). The mutual inductance has beenmeasured by placing the LSCO sample within two pick-up
NV-Diamond512 nm ya
LSAO Magne c fieldLSCO20 nm
LSCO sampleNV-Diamond y
100 µm (a)(b)
Inside (y
Outside (y>a) (c) 140 MHz 0. The confocal scans are obtainedwith a resolution of 100 x 100 pixels, where each pixel has beenrecorded for 0 . y > a and y < a at 4 . y > a (bluecurve), the ODMR splitting is about 2 times larger compared to thecase of y < a (red curve). coils (see section 7 of the SI). By applying a weak mag-netic field through one of the coils, the magnetic interactionthrough the superconducting sample can be investigated. Wealso recorded the magnetic moment m as a function of themagnetic field at 4 K for gaining more information about themagnetic phase diagram including the lower critical field H c (see Fig. 2(b)). This indicates a first magnetic penetration atabout 2 mT, where magnetic fluxes start to enter the supercon-ducting sample.ll-Optical and Microwave-Free Detection of Meissner Screening using Nitrogen Vacancy Centers in Diamond 4 B. Detection of Meissner State with the NV Center PL Drop To study the spatial distribution of the Meissner screeningcaused by the LSCO thin film at 4 . ( y < a ) , as well as background measurement without havingLSCO on top ( y > a ) . Note that all PL measurements arenormalized with respect to a corresponding zero field confo-cal scan for estimating the effective fluorescence rate drop.Fig. 3(b) shows a confocal scan of the NV ensemble obtainedfrom regions y < a (left panel) and y > a (right panel) respec-tively, for an applied field of 4 . y > a is signif-icantly brighter compared to the case of y < a . We choosethe central area (depicted as white square) of the confocal im-ages for evaluation, since the center of the image shows theleast distortion (see section 2 of the SI). For y < a , the nor-malization with respect to a zero field measurement revealsan average fluorescence drop of 2 . y > a the fluorescence count rate drop amountsto 5 . . leading to varying magnetic fields ex-perienced over the whole diamond membrane. NV centers inthe area of y < a experience a reduced magnetic field strengthand therefore show a significantly decreased PL drop com-pared to the y > a region. For y > a , which is outside thesuperconductor, no Meissner screening is present. Therefore,the NV center ensemble measures the unscreened applied fieldof 4 . . µ W, measured in front of the UHV chamber glasswith a powermeter. With such low laserpower we can ensure,that the laser spot is not changing the superconducting prop-erties of our sample .In order to quantify the strength of the magnetic field that pen-etrates through the LSCO thin film, we first verify the Meiss-ner effect using a resonant process, i.e. ODMR spectroscopy.We obtained ODMR spectra on the NV ensembles for bothregions, y < a and y > a . The corresponding spectra are de-picted in Fig. 3(c). The red curve on the left panel shows theresonance peaks of the NV ensemble inside the LSCO thinfilm with a frequency splitting of ∆ f = 60 MHz. This corre-sponds to a z -aligned magnetic field of ≈ . y > a , exhibits asplitting ∆ f of ≈ 140 MHz corresponding to a magnetic fieldstrength of ≈ . z -direction. This is in an excel-lent agreement with the fact, that the NV ensemble in y > a does not experience any Meissner screening. Therefore, themagnetic field strength calculated from the ODMR spectrummatches the applied, unscreened magnetic field value. Con-sequently, these results corroborate a magnetic field screeningof ≈ 56 %. Note that, the magnetic field in the region of y < a is not vanishing. This can be attributed to the relatively large (a) (b) ya ya a M agne t i c F i e l d B z ( m T ) Position y (µm)3500 4000 4500 5000 55000510152025 with SC without SC P L D r op ( % ) Position y (µm) Magne c Field Calibra on Experimental Data Brandt Model M agne t i c F i e l d B z ( m T ) Position y (µm) Experimental Data Brandt Model M agne t i c F i e l d B z ( m T ) Position y (µm) FIG. 4. (a) Spatial variation in the PL drop measured by laser rasterscan at 4 . 2K with (blue dots) and without (red dots) superconduct-ing sample (left panel). At each position, the PL drop of the NVensemble is recorded. Estimates of the magnetic fields (right panel)come from a calibration with ODMR spectra. In presence of theLSCO thin film, for y > a , the external magnetic field asymptoticallyreaches 4 . y < a it is strongly screened due to the su-perconducting properties of LSCO. The sharp increase of the mag-netic field at the edge indicates high magnetic flux densities. Such aspatial dependence is not observed in absence of the LSCO thin film.Each data point corresponds to the normalized averaged PL drop atthe center of the confocal scan of about 4 µ m . (b) Fitting of the ex-perimental data by using Brandt’s model. The solid lines representthe fit. Both fit functions (inside and outside) reveal a critical currentdensity j c of 1 . · A / cm . NV to superconductor distance ( ≈ µ m) (see section 6 of theSI). Also the formation of magnetic vortices in type II super-conductors could result in a non vanishing magnetic field inthe LSCO sample .This approach can be extended further to gain insights aboutthe Meissner screening and for characterizing the LSCO thinfilm to a greater detail. This is achieved by raster sweeping thelaser focal spot over the diamond membrane along the y direc-tion. The corresponding spatial variation of the PL drop underan applied magnetic field of B z = . y < a and y > a respectively. Inside the super-ll-Optical and Microwave-Free Detection of Meissner Screening using Nitrogen Vacancy Centers in Diamond 5conductor, we measure a relatively homogeneous PL drop ofabout 2 %, which slowly increases towards the boundary, i.e. y = a . Note that, the conversion from PL drop to an effectivemagnetic field is achieved using the calibration data presentedin Fig. 1(d). The latter reveals a magnetic field strength rang-ing between 1 . . ≈ . ≈ y = a , implyingan equivalent increase of the effective magnetic flux density,which penetrates through the LSCO thin film. While the ma-jority of the LSCO thin film expels the magnetic field, near theboundaries the field is enhanced to almost 16 mT. The mag-netic field flux is screened to the edge of the LSCO sampledue to the diamagnetic properties of the superconducting com-pound. This leads to an enhanced magnetic flux density at theboundary of the superconducting LSCO sample. Note that, inabsence of the LSCO sample, such a spatial dependence of thePL drop is not observed in the bare NV membrane (red dotsin Fig. 4(a)). C. Application of Brandt’s Model The magnetic field profile in a superconducting thin filmcan be analytically evaluated by Brandt’s model . The spa-tial dependence along the y -direction, of the magnetic fieldapplied perpendicular to the superconducting thin film is: H ( y ) = J c π arctanh (cid:113) ( y − b ) c | y | y < a J c π arctanh c | y | (cid:113) ( y − b ) y > a (1) J c stands for the critical sheet current in units of A / m and theparameters b and c can be represented as b = a / cosh π H a J c c = tanh π H a J c , where a corresponds to the halfed sample length. The parame-ter b can be interpreted as a lateral penetration depth of the ex-ternally applied magnetic field H a , indicating how far H a pen-etrates from the sides into the sample. We fit our experimentaldata using this model in order to quantify the critical currentdensity j c = J c / d , in which the flux lines start to move underthe action of Lorentz force. Note that, similar to the obser-vation in Fig. 3, the magnetic field is not vanishing inside thesuperconductor. Therefore, we restrict our fit within the limitwhere the magnetic field is reduced to 18% of the maximumobserved field. This model agrees very well with our data forboth y < a (Fig. 4(b), left panel) and for y > a (Fig. 4(b), rightpanel). The corresponding fitting paramaters for fixed values of H a = . a = µ m are, b = ± . µ m, c = . ± . J c = ± / m. Knowing J c and the sample thickness d = 20 nm we have extracted the crit-ical current density as j c = . · A / cm . This value is invery good agreement with recently reported values for LSCOnanowires indicating the NV fluorescence drop as reliablequantity for characterizing thin film superconductors. Alsonote, that the corresponding j c value agrees very well with acalculation based on our SQUID measurement in Fig. 2. Themagnetic moment m can be obtained using Brandt’s analyticalmodel and the corresponding J c with m = J c a tanh π H a J c . (2)resulting into a magnetic moment of m ≈ . 012 emu. Thisis comparable with our SQUID measurement in Fig. 2(b),in which the magnetic moment ranges from 0 . . m can be explained bythe performed calibration measurement. The PL drop to mag-netic field strength conversion in Fig. 1(d) assumes a magneticfield applied in z-direction ( B z ). This is a fair assumption forthe region y < a and y > a (far inside and outside of the super-conductor). However, in close proximity of the LSCO edge( y = a ) the magnetic field is forced to curl around the edge ofthe superconductor. Therefore, it is expected, that the off-axiscomponent of the magnetic field is not pointing only in thez-direction. Instead, a strong in-plane component has to beassumed. This fact can explain the overestimation of j c . IV. CONCLUSION In conclusion, we have presented a microwave-free NVcenter based method for characterizing relative magnetic fieldchanges. In order to demonstrate this, we investigated a su-perconducting LSCO thin film. So far, the NV center hasmainly been used as magnetic field sensor in a resonant mea-surement scheme utilizing microwave excitations. Here weextend its application by employing the magnetic field depen-dent PL of an NV center ensemble in a microwave-free man-ner providing a direct manifestation of the Meissner screen-ing in our LSCO sample. To the best of our knowledge, thisis the first demonstration of NV center magnetometry on asuperconducting sample that does not require resonant mi-crowave pulse schemes, apart from calibrating the absolutemagnetic field. The PL calibration can either over-or under-estimate the magnetic field strength to a certain extent. How-ever, this is not important for measurements relying on rel-ative strength changes of the magnetic field such as in thecase of the Meissner state in superconductors. The presentedmethod enables a fast and precise measurement of such rela-tive magnetic changes excluding heating effects on the sam-ple. Furthermore, the magnetic field dependent NV emissionused in this work can be extended further by combining opti-cal pump probe spectroscopy, thereby enabling access to dy-namical systems with fast timescales. With the NV center asnanoscale magnetic field sensor, this opens up a promisingll-Optical and Microwave-Free Detection of Meissner Screening using Nitrogen Vacancy Centers in Diamond 6avenue for exploring a multitude of problems in condensed-matter physics such as non-equilibrium collective phenomenaincluding the vortex formation and motion in type II super-conductors. ACKNOWLEDGMENTS We acknowledge financial support for this work providedby the European Research Council (ERC) under the EuropeanUnion’s Horizon 2020 research and innovation programme(grant agreement No. 742610), EU via project ASTERIQS,Max Planck Society and DFG via FOR 2724. DATA AVAILABILITY The data that support the findings of this study are availablefrom the corresponding author upon reasonable request. REFERENCES Bandyopadhyay, A.; Frey, N. C.; Jariwala, D.; Shenoy, V. B. Nano Lett. , 19, 7793-7800. Wu, M. K.; Ashburn, J. R.; Torng, C. J.; Hor, P. H.; Meng, R. L.; Gao,L.; Huang, Z. J.; Wang, Y. O.; Chu, C. W. 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