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Optical magnetometry of single biocompatible micromagnets for quantitative magnetogenetic and magnetomechanical assays Loïc Toraille, Koceila Aïzel, Elie Balloul, Chiara Vicario, Cornelia Monzel, Mathieu Coppey, Emilie Secret, Jean-Michel Siaugue, Joao Sampaio, Stanislas Rohart, Nicolas Vernier, Louise Bonnemay, Thierry Debuisschert, Loïc Rondin, Jean-Francois ROCH, and Maxime Dahan Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b03222 • Publication Date (Web): 01 Nov 2018 Downloaded from http://pubs.acs.org on November 1, 2018

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Optical magnetometry of single biocompatible micromagnets for quantitative magnetogenetic and magnetomechanical assays Loïc Toraille,†,4 Koceila Aïzel,‡,4 Élie Balloul,‡ Chiara Vicario,‡ Cornelia Monzel,‡,¶ Mathieu Coppey,‡ Émilie Secret,§ Jean-Michel Siaugue,§ João Sampaio,k Stanislas Rohart,k Nicolas Vernier,⊥ Louise Bonnemay,# Thierry Debuisschert,@ Loïc Rondin,† Jean-François Roch,∗,† and Maxime Dahan∗,‡ †Laboratoire Aimé Cotton, CNRS, Univ. Paris-Sud, ENS Cachan, Université Paris-Saclay, 91405 Orsay, France ‡Laboratoire Physico-Chimie, Institut Curie, CNRS UMR168, PSL Research University, Université Pierre et Marie Curie-Paris 6, 75248 Paris Cedex 05, France ¶Experimental Medical Physics, Heinrich-Heine University Düsseldorf, Universitätsstrasse 1, 40225 Düsseldorf, Germany §Physico-chimie des électrolytes et nanosystèmes interfaciaux, PHENIX, CNRS UMR 8234, Sorbonne Université, F-75005 Paris, France kLaboratoire de Physique des Solides, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France ⊥Centre de Nanosciences et de Nanotechnologies, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France #Alveole, 30 rue de Campo Formio 75013 Paris France @Thales Research & Technology, 1 avenue Augustin Fresnel, 91767 Palaiseau cedex, France 4These authors contributed equally to this work. E-mail: [email protected]; [email protected] 2


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Abstract The mechanical manipulation of magnetic nanoparticles is a powerful approach to probe and actuate biological processes in living systems. Implementing this technique in high-throughput assays can be achieved using biocompatible micomagnet arrays. Yet, the magnetic properties of these arrays are usually indirectly inferred from simulations or Stokes drag measurements, leaving unresolved questions about the actual profile of the magnetic fields at the micrometer scale and the exact magnetic forces that are applied. Here we exploit the magnetic field sensitivity of NV color centers in diamond to map the 3D stray magnetic field produced by a single soft ferromagnetic microstructure. By combining this wide-field optical magnetometry technique with magneto-optic Kerr effect microscopy, we fully analyze the properties of the micromagnets, including their magnetization saturation and their size-dependent magnetic susceptibility. We further show that the high magnetic field gradients produced by the micromagnets, greater than 104 T·m−1 under an applied magnetic field of about 100 mT, enables the manipulation of sub-10 nm magnetic nanoparticles inside living cells. This work paves the way for quantitative and parallelized experiments in magnetogenetics and magnetomechanics in cell biology.

Keywords micromagnet, NV magnetometry, Kerr microscopy, nitrogen-vacancy color center, magnetomechanics, magnetogenetics

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Article The imaging and manipulation of nanoparticles in living cells is an important tool for the investigation of bio-cellular processes, 1–3 the controlled delivery of drugs, 4 and the sensing of in-vivo forces. 5 In recent years, novel magnetogenetic and magnetomechanical approaches have been developed in which magnetic nanoparticles (MNPs) are used to actuate signalling events in cells, via biochemical or mechanical responses. 6 These experiments are based on the force induced on the MNPs by a spatially controlled magnetic field gradient that is used to direct biofunctional MNPs to targeted locations in a cell. For instance, a sharp magnetic tip is positioned close to a plated cell 7,8 in order to displace MNPs bound to the cell membrane or internalized within the cytoplasm. Depending on the MNP properties (magnetic material, size, ...) and the specific features of the tip (dimension, shape, magnetization), forces ranging between 10−15 N and 10−9 N can be achieved at the single MNP level. 7,9,10 Yet, the use of a magnetic tip has several limitations. The tips are often not well characterized, meaning that neither the amplitude nor the orientation of the magnetic field gradient at the apex of the tip are accurately known. Moreover, given that only one cell can be investigated at a time, the experimental throughput is low. Obtaining a set of statistically relevant data is then challenging. Finally, the tip has to be positioned within a few micrometers from the cell. Reaching this accuracy requires precise micromanipulation, which adds complexity and cost to the experiments. The limitations above can be overcome by using an array of soft ferromagnetic microstructures as the source of the magnetic field gradient acting on the MNPs in the cells. 11–14 The micromagnets can be deposited on a glass coverslip compatible with cell culture and remotely switched on and off by applying a control magnetic field. This approach is particularly appealing in order to parallelize the magnetic stimuli and to implement high-throughput assays that fully account for the variability associated to measurements at the single cell level. Magnetogenetic and magnetomechanical applications are often based on the manipulation of individual MNPs with a size below 50 nm to target specific biomolecules or organelles in 4


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cells. 8,9 They are thus more demanding than experiments in which large MNPs (> 100 nm) are accumulated in endosomes. 13 In particular, the micromanipulation of these small MNPs requires magnetic field gradients higher than 103 T·m−1 , with spatial properties optimized at the micrometer scale. Beside these applications, the possibility to remotely control the 3D motion of MNPs using such magnetic field gradient has a broad application range, e.g. for cell death signaling, 15 for the activation of temperature-sensitive ion channels, 16 and for the development of magnetic field controlled batteries based on ferrofluids. 17 So far, the magnetic characterization of biocompatible micromagnet arrays has been predominantly based on numerical simulations 12 or Stokes drag experiments. 13,18 Other approaches have used scanning Hall probe microscopy 19 or magnetic force microscopy. 20 Yet, we still lack a direct, non-perturbing, three-dimensional (3D) mapping of the stray magnetic field produced by the micromagnets. Here, we present an experimental approach that relies on nitrogen-vacancy (NV) wide-field optical magnetometry (figure 1). 21–24 Using this technique, we map the stray magnetic field created by soft ferromagnetic micromagnets while remotely controlling their magnetization using an external magnetic field applied by a permanent magnet. The resulting map gives both the amplitude and the orientation of the stray magnetic field, with a resolution ∼ 1 µm. From this quantitative information, we retrieve the magnetization of a single micromagnet that is spotted in an array of these fabricated microstructures. We specifically illustrate our approach on two samples in which the microstructures are rectangular cuboids with respective lateral sizes of 30 × 30 µm2 and 110 × 110 µm2 and associated thicknesses of 3.5 µm and 4 µm. The micromagnets, made of nickel and iron alloy, are deposited using conventional microfabrication techniques (see Supplementary Information). A thin copper film is first evaporated on the surface of a transparent glass coverslip. The copper film provides the electrical conductivity needed for the subsequent growth of the soft ferromagnetic material by electroplating. Thanks to a photolithographic process the shape and the dimensions of the micromagnets are precisely controlled (see inset of figure 1c). After the growth of the magnetic elements, the remain-

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ing copper layer is removed and a layer of polydimethylsiloxane (PDMS) with thickness ∼ 1 − 2 µm is spin-coated on top of the array to ensure its biocompatibility. Wide-field NV vector magnetometry is based on the spin properties of the NV center, an optically active point defect of diamond 25 that consists of a substitutional nitrogen atom (N) bounded to an adjacent vacancy (V) as shown in figure 1a. The NV center emits a bright red photoluminescence (PL) under green laser excitation, with a stable emission even at room temperature. In its negatively charged state, the NV center ground state is a spin triplet S = 1, with a spin-dependent luminescence. 26 By recording the PL intensity as a function of the applied microwave frequency, one can thus optically detect the electron spin resonance (ESR) between the ground spin level mS = 0 and the mS = ±1 levels at a resonance frequency of 2.87 GHz. Under the perturbation of an external magnetic field, the Zeeman effect splits the mS = +1 and mS = −1 levels with a frequency difference ∆ν = 2gµB BNV /h. 27 The parameter BNV is the magnetic field projection on the N–V axis of the given NV defect used for measurement, g ≈ 2 the Landé factor, µB the Bohr magneton, and h the Planck constant. When using a bulk diamond with [100] orientation containing a thin layer of NV centers, their random distribution along the orientations associated to the four [111] axes in the tetrahedral crystal structure (figure 1a) leads to a set of resonances 28 consisting in four pairs. Each pair of ESR peaks corresponds to the projection of the applied magnetic field on a given [111] orientation (figure 1b). The three components of the magnetic field vector that is applied on the set of NV centers can then be retrieved from the measurements of these four correlated projections of the magnetic field. 23 We use an ultrapure single-crystal diamond doped with a thin layer of NV centers close to the surface. This active layer, created by ion implantation 29 has a thickness of about 8 nm and a surface density of 104 NV·µm−2 . As shown in figure 1c, the diamond slab is positioned above the array of micromagnets. In order to induce their magnetization, a permanent magnet creates an external field Ba of a few mT, with an orientation in the (x, y) sample plane. The two facets and the four sides of the diamond slab are polished to respectively

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allow the luminescence collection and the internal beam propagation. A 100 mW laser with 532 nm wavelength (Coherent, Verdi V6) is used to excite the NV centers PL at an intensity ∼ 2 W mm-2 with a total internal reflection illumination scheme. 23,30 The PL from the layer of NV centers is collected through the diamond sample using a 10× microscope objective with a 0.25 numerical aperture. The laser excitation also induces the spin polarization into the mS = 0 state. 31 The spin resonance between mS = 0 to mS = ±1 is excited by a microwave antenna consisting of a coil of copper wire that is placed close to the diamond slab. After filtering the stray green excitation light, the PL is imaged onto a CMOS camera and each pixel is used to record an ESR spectrum, as shown in figure 1b. Note that the external magnetic field created by the permanent magnet used to remotely control the micromagnet magnetization also induces a splitting of the NV resonance frequencies. This splitting is collected in four different locations at a distance of about 100 µm from the micromagnet where the stray magnetic field produced by the micromagnet becomes negligible. It is then used to interpolate a reference splitting that is subsequently substracted from the splitting measured close to the micromagnet. In each spectrum, the four contributions can be identified with respect to a given orientation of the NV center in the crystal. Reconstructing the three components of the magnetic field vector requires to unambiguously attribute the spin resonances to a specific orientation of the NV center. This can become non trivial in the case of a ferromagnetic microstructure, such as the ones considered here, since the magnetic field orientation has strong variations close to the object of interest leading to multiple crossings in the set of spin resonance frequencies. The required identification can be achieved using dynamic control in the Fourier plane 32 or by applying frequency lock-in detection schemes. 33,34 In our case, a computer program tracks the resonance frequencies from pixel to pixel. The resulting maps of the magnetic field, obtained with an acquisition time of about 20 minutes for a field of view of 200 µm, are shown on the top line of figure 2a (see Supplementary Information for a 3D representation).

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We represent the micromagnet as a cuboid with a uniform magnetization, approximating the exact distribution of magnetic moments by an average magnetization over the whole volume. This “macrospin” model notably neglects the anisotropy of the magnetic response induced by preferred magnetization directions associated to the shape of the micromagnet 35 and the possible existence of magnetic domains inside the ferromagnetic microstructure. In the following, we assume that the magnetization is parallel to the applied magnetic field, as evidenced from the symmetry of the two-lobe structure observed in the map of the Bz component. We then compute the stray magnetic field above the micromagnet (see Supplementary Information). The fit to the experimental values of the magnetic field measured in the NV layer determines the distance d = |z1 − z2 | between the micromagnet and the NV layer (where z1 is the height of the upper facet of the micromagnet and z2 is the height of the NV layer) as well as the magnetization M induced by the applied external magnetic field Ba = µ0 Ha . Far from the saturation regime and without any hysteresis behavior, the magnetization is determined by M = χexp Ha through the experimental magnetic susceptibility χexp accounting for demagnetizing effects that are associated to the shape of the microstructure. 36 The resulting fits are shown in figure 2. We obtain d = 20 ± 3 µm, M = (8 ± 2) × 104 A·m−1 , and χexp ' 15 for the 30 µm micromagnet magnetized with Ba = 6.4 mT, and d = 32 ± 4 µm, M = (1.5 ± 0.2) × 105 A·m−1 , and χexp ' 25 for the 110 µm micromagnet magnetized with Ba = 7.5 mT. The overall good agreement of the experimental data with the macrospin model indicates that this simple description of the induced magnetization faithfully describes the magnetic field distribution created above each micromagnet. Similar results are obtained on a set of micromagnets in the same array, an essential criterion to ensure the reproducibility of parallelized experiments performed on the array. Note that the size of both the diamond-based planar sensor and the magnetic sample prevented us from controlling the distance between the NV layer and the micromagnet array. The implementation of planar scanning probe technique for NV magnetometry 37 could yield

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measurements performed with a distance between the sample and the NV layer that can be set with a precision of about a few tens of nanometers. Such control will significantly increase both the sensitivity and the accuracy of the micromagnet characterization. In our experiments, we note that χexp decreases when the size of micromagnet is reduced while keeping the same thickness. This is consistent with the fact that a microstructure with a smaller surface-to-thickness ratio is harder to magnetize. To further evaluate the importance of this effect, we perform an independent characterization of the bulk material with a SQUID magnetic sensor (Quantum Design) so as to determine the magnetic properties of a macroscopic layer of the same alloy (size of 1 cm × 1 cm and thickness of 4 µm). For an in-plane magnetic excitation, we measure a magnetic susceptibility of ∼ 120 and a saturation magnetization of 6.0 × 105 A m−1 that is reached for an applied magnetic field above 18 mT. These parameters are then used to numerically compute χexp as a function of the micromagnet size using COMSOL (see Supplementary Information), now taking into account the demagnetizing effects. The estimated values of the magnetic susceptibility χexp are 10.4 and 27.8 for micromagnet sizes of respectively 30 µm and 110 µm, in agreement with the values inferred from the experimental characterization performed using wide-field NV magnetometry. Since magnetogenetic applications require a magnetic field gradient that extends over a distance comparable to the size of a mammalian cell (∼ 50 µm), 9 we hereafter focus on the micromagnets with a size of about 100 µm. Besides their magnetic susceptibility, another key feature of these soft ferromagnetic microstructures is their magnetic saturation behavior. However, recording the magnetization saturation requires applying an external field with a magnitude that can exceed a few hundreds of mT, depending on the magnetic permittivity of the material. Yet, in practice, quantitative magnetometry with NV centers is limited to a few tens of mT for a magnetic field of arbitrary orientation, 38 meaning that the magnetization saturation can hardly be measured using this technique. We thus complement the previous magnetometry measurements with magneto-optic Kerr effect (MOKE) microscopy

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that consists in shining a linearly polarized beam and measuring the polarization change associated to the reflection on the magnetized sample (see methods in Supplementary Information). Due to the Kerr effect, the input linear polarization is rotated by an angle that is proportional to the in-plane magnetization. Using MOKE microscopy, we measure the relative magnetization of a 110 µm micromagnet as a function of the in-plane magnetic field Ba applied on the sample and generated with electromagnetic coils. In this experiment the external field is aligned along the side of the micromagnet. Since the zero magnetic field susceptibility was previously determined with NV wide-field magnetometry, the magnetization curve recorded with MOKE microscopy can be quantitatively scaled using the linear dependance between the magnetization and the applied magnetic field far from the saturation regime. The results are shown in figure 3 after a linear correction accounting for the parasitic Faraday effect of the optical components inside the microscope objective. After this scaling, we determine a saturation magnetization value Msat = 5.9 ± 0.5 × 105 A·m−1 that is reached above approximately 50 mT. Since all magnetic domains become aligned in this saturation regime, the demagnetization effect disappears and this saturation value indeed agrees with the one independently measured using the SQUID magnetometer. The images recorded with MOKE microscopy also show the shape of the magnetic domains (figure 3b). For an applied field of about 15 mT, the magnetization becomes almost uniform, corresponding to the simple macrospin model. To assert the suitability of these micromagnet arrays for biology-oriented applications, we first confirm the measurement of the generated magnetic field gradients by a Stokes drag experiment performed on 300 nm fluorescent iron-oxide MNPs (Micromod, Germany) in a liquid environment. To this end, the micromagnet array, covered with PDMS for biocompatibility, is placed in a chamber containing a dilute solution of MNPs in a viscous mixture of water and glycerol (78:22 ratio). We then bring a permanent magnet in the vicinity of the chamber such that the applied magnetic field of ' 150 mT saturates both the micromagnets and the MNPs. Individual MNP trajectories are recorded with a wide-field epifluorescence

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microscope, at a distance of 7 µm above the surface of the micromagnet array (figure 4a). Since inertial effects can be neglected, the velocity v of each MNP is related to the magnetic force F through the Stokes law F = 6πηrv, where η is the viscosity of the medium and r the particle radius. The inferred Fx and Fy components of the drag force are shown in figure 4b. Note that the MNPs accumulate close to the micromagnet, and their fluorescence prevents us from resolving individual trajectories and measuring the drag force in this region. The magnetic saturation of the MNPs ensures that the magnetic field gradient ∇B is related to the magnetic force through F = msat Vp ∇B, where msat = 1.6 × 105 A·m−1 is the MNP magnetization and Vp their volume. From this formula, we compute the magnetic gradient generated by the micromagnet (figure 4c). The result inferred from the Stokes measurements is consistent with the evaluation of the magnetic field based on the macrospin model, consisting in a uniformly magnetized cuboid. Yet, we note some discrepancies that we attribute to inhomogeneities in the MNP properties (size, shape, magnetization) and imprecision in the determination of their 3D trajectories. This comparison underlines the superior accuracy and resolution provided by the quantitative 3D mapping of the stray magnetic field using optical magnetometry methods. Finally, we evaluate the efficiency of the micromagnet array in the context of in vivo magnetic manipulation by performing an experiment on the intracellular manipulation of MNPs in living cells cultured on a patterned substrate. The setup is depicted in figure 5a. To fully benefit from the well-characterized magnetic field gradient, the cells are micropatterned at a controlled distance from the micromagnets. This patterning is achieved by incubating the array covered with PDMS, first with a solution of polylysine (Sigma-Aldrich, USA), and next with a solution of PEG-SVA (Laysan Bio, USA). This polymer layer passivates the surface and efficiently prevents cell adhesion. The coverslip, incubated with a solution of photo-initiators, is then illuminated with UV light (365 nm wavelength) at specific locations close to the micromagnet using PRIMO photopatterning system (Alveole, France). 39 We also use a protocole adapted from 40,41 using a quartz mask and deep UV illumination to

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pattern passivated surfaces. The main difference in our protocol is the use of PAcrAm-g(PEG, Amine, Silane) instead of PLL-g-PEG (see Supplementary Information for a detailed description of the protocol). After rinsing, the coverslip is incubated with fibronectin that attaches on the illuminated regions (figure 5b). HeLa cells plated in DMEM (Dulbecco’s Modified Eagle Medium) on the coverslip specifically adhere on the patterns within 2 hours (figure 5c). We use silica core shell MNPs (Si-MNPs), 42 consisting of a maghemite core of 9 nm in diameter which is surrounded by a silica shell. The full size of the Si-MNPs ranges from 40 to 50 nm in diameter. Once injected into the cytoplasm of targeted cells, the intracellular localization and dynamics of the Si-MNPs are recorded via their fluorescence. For this particular array, the micromagnets have a size of 100 µm and a thickness of 10 µm. In the absence of the external control magnetic field, we observe no evidence of attraction and the Si-MNPs remain dispersed in the cytoplasm. This result shows that the micromagnet has a negligeable intrinsic magnetization, in agreement with the previous characterizations. Conversely, when applying an external magnetic field of 100 mT, the micromagnet reaches its saturation magnetization. It then generates a stray magnetic field gradient of about 104 T·m−1 at a distance of 10 µm from its edges. This amplitude of the magnetic field gradient corresponds to an attractive force of about 5 fN on a single Si-MNP. This attractive force then leads within a few seconds to the accumulation of the Si-MNPs on the side of the cell close to the micromagnet, as shown in figure 5d. The Si-MNPs diffuse back into the cytoplasm when switching off the external magnetic field. In an experiment realized without the micromagnets, we checked that the external magnetic field that allows us to control the micromagnet magnetization is too weak to have any influence on the MNPs motion (see Supplementary Information). Additional experiments performed using ferritin-MNPs instead of Si-MNPs have also been performed, with consistent results (see Supplementary Information).

In conclusion, we demonstrate that the magnetic properties (susceptibility and satura-

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tion magnetization) of a soft ferromagnetic micromagnet can be quantitatively measured by combining the informations obtained with NV wide-field magnetometry, which maps the stray magnetic field produced by the micromagnet, and MOKE microscopy which reveals the sample magnetization. In the future, these two complementary methods can be easily integrated in a single setup. Furthermore, we show that the response of the micromagnet to a magnetizing external field can be described using a simple macrospin model. For microstructures of size ∼ 100 µm, the large gradients (> 104 T·m-1 ) generated close to the micromagnet enable the manipulation of small MNPs (magnetic core < 10 nm) inside living cells. Overall, these tools will enable the implementation of quantitative experiments in many biological and biophysical contexts, including magnetogenetics and force sensing in realistic bio-environments.

Acknowledgement The authors thank F. Treussart for suggesting to use wide-field NV magnetometry to characterize the micromagnets, M. Lesik, S. Pezzagna and J. Meijer for the fabrication and characterization of the NV-doped diamond sample, and A. Thiaville for helpful discussions. M.D. acknowledges funding from French National Research Agency (ANR) Paris-ScienceLettres Program (No. ANR-10-IDEX-0001-02 PSL), from Labex CelTisPhyBio (No. ANR10-LBX-0038). K.A. acknowledges support from Institut Pierre Gilles de Gennes. This project has received funding from the European Union Horizon 2020 Research and Innovation Programme under the project MAGNEURON (grant agreement No 686841) and from the European Union Seventh Framework Programme (FP7/2007-2013) under the project DIADEMS (grant agreement No.611143).

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Supporting Information Methods: macrospin model, MOKE measurement, COMSOL simulations. Application to the manipulation of MNPs in living cells: fabrication of the micromagnet array, chemical engineering of magnetic nanoparticles, patterning PDMS with PAA-g-pMOXA, cell culture and plating on the micromagnet array, micro-injection of the MNPs inside the cells, record and analysis of the images of the Stokes drag experiments, force calibration of the Stokes drag experiments, additional images of the MNPs manipulation. Supplementary movies: 3D representations of the stray magnetic field created by the micromagnet and measured with NV magnetometry (respective size 30 µm and 110 µm), video record of the f-MNPs trajectories controlled by the micromagnet magnetization.

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(21) Steinert, S.; Dolde, F.; Neumann, P.; Aird, A.; Naydenov, B.; Balasubramanian, G.; Jelezko, F.; Wrachtrup, J. Rev. Sci. Instrum. 2010, 81, 043705. (22) Pham, L. M.; Le Sage, D.; Stanwix, P. L.; Yeung, T. K.; Glenn, D.; Trifonov, A.; Cappellaro, P.; Hemmer, P. R.; Lukin, M. D.; Park, H.; Yacoby, A.; Walsworth, R. L. New J. Phys. 2011, 13, 045021. (23) Chipaux, M.; Tallaire, A.; Achard, J.; Pezzagna, S.; Meijer, J.; Jacques, V.; Roch, J.-F.; Debuisschert, T. European Physical Journal D 2015, 69, 166. (24) Tetienne, J.-P.; Dontschuk, N.; Broadway, D. A.; Stacey, A.; Simpson, D. A.; Hollenberg, L. C. L. Science Advances 2017, 3, e1602429. (25) Zaitsev, A. Optical Properties of Diamond, 1st ed.; Springer-Verlag Berlin Heidelberg, 2001. (26) Schirhagl, R.; Chang, K.; Loretz, M.; Degen, C. Annual Review of Physical Chemistry 2014, 65, 83–105. (27) Rondin, L.; Tetienne, J.-P.; Hingant, T.; Roch, J.-F.; Maletinsky, P.; Jacques, V. Rep. Prog. Phys. 2014, 77, 056503. (28) Lai, N. D.; Zheng, D.; Jelezko, F.; Treussart, F.; Roch, J.-F. Appl. Phys. Lett. 2009, 95, 133101. (29) Pezzagna, S.; Naydenov, B.; Jelezko, F.; Wrachtrup, J.; Meijer, J. New J. Phys. 2010, 12, 065017. (30) Le Sage, D.; Arai, K.; Glenn, D.; DeVience, S.; Pham, L.; Rahn-Lee, L.; Lukin, M.; Yacoby, A.; Komeili, A.; Walsworth, R. Nature 2013, 496, 486–489. (31) Doherty, M. W.; Manson, N. B.; Delaney, P.; Jelezko, F.; Wrachtrup, J.; Hollenberg, L. C. Phys. Rep. 2013, 528, 1 – 45. 16


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(32) Backlund, M. P.; Kehayias, P.; Walsworth, R. L. Phys. Rev. Applied 2017, 8, 054003. (33) Clevenson, H.; Pham, L. M.; Teale, C.; Johnson, K.; Englund, D.; Braje, D. Applied Physics Letters 2018, 112, 252406. (34) Schloss, J. M.; Barry, J. F.; Turner, M. J.; Walsworth, R. L. arXiv e-prints 2018, arXiv:1803.03718 [quant-ph]. (35) Cowburn, R. Journal of Physics D: Applied Physics 1999, 33, R1–R16. (36) Blundell, S. Magnetism in Condensed Matter, 1st ed.; Oxford University Press: Oxford, 2001. (37) Ernst, S.; Irber, D.; Waeber, A.; Braunbeck, G.; Reinhard, F. arXiv e-prints 2018, arXiv:1805.03199 [physics.ins-det]. (38) Tetienne, J.-P.; Rondin, L.; Spinicelli, P.; Chipaux, M.; Debuisschert, T.; Roch, J.-F.; Jacques, V. New Journal of Physics 2012, 14, 103033. (39) Strale, P.-O.; Azioune, A.; Bugnicourt, G.; Lecomte, Y.; Chahid, M.; Studer, V. Advanced Materials 2016, 28, 2024–2029. (40) Azioune, A.; Carpi, N.; Fink, J.; Chehimi, M. M.; Cuvelier, D.; Piel, M. Langmuir 2011, 27, 7349–7352. (41) Carpi, N.; Piel, M. J Vis Exp 2014, 83, 51193. (42) Makrygenni, O.; Secret, E.; Michel, A.; Brouri, D.; Dupuis, V.; Proust, A.; Siaugue, J.M.; Villanneau, R. Journal of Colloid and Interface Science 2018, 514, 49 – 58.

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Nano Letters

a

z 𝑩 𝒂

y

x

b normalized PL

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1.00

0.99 0.98 2.70 2.75 2.80 2.85 2.90 2.95 3.00 3.05 frequency (GHz)

c

CMOS camera

z x

y

lens

bandpass filter

magnetic micromagnets objective

laser excitation

MW antenna

(100) diamond crystal S N

NV layer

d magnetic micromagnets

permanent magnet

Figure 1: (a) NV color center in diamond (black circle: carbon atom; blue circle: nitrogen atom; white circle: vacancy) used as an atomic-like magnetic sensor. Each NV center has an intrinsic quantization axis defined by the vector from the nitrogen impurity to the vacancy. This NV axis has then four possible directions in a diamond crystal with (100) orientation along the z vertical axis. (b) Optically detected spin resonance signal measured with an ensemble of NV centers. The four pairs of peaks, repre~a sented by the set of colors, are linked to the projections of the applied magnetic field B (Ba,x = −1.4 mT ; Ba,y = −6.2 mT ; Ba,z = −0.5 mT ) on the different orientations of the NV axis that are shown in (a). (c) Setup for wide-field NV magnetometry. An external permanent magnet is used to remotely control the micromagnet magnetization. Inset: optical microscopy image showing part of the micromagnet array. The length of the square shaped micromagnets is 110 µm.

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Bx (mT) z

x

By (mT)

b

Bz (mT)

0.6

1.5

-0.6 0.6

-1.5 1.5

-0.6

-1.5

Bx (mT)

By (mT)

Bz (mT)

1.5

2

2

-1.5 1.5

-2 2

-2 2

-1.5

-2

-2

3.5

y

𝑩𝒂

model

experiment

a

c 0

𝑩𝒂

-3.5 3.5

100 μm

d

linecuts

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

0.3 0.0 -0.3 50 100 y (μm)

0

1.5 1.0 0.0 -0.5 0 40 80 120 x (μm)

1.0

1.0

0.0

-1.0

-1.0 40 80 120 x (μm)

-3.0 0 50 100 150 200 250 x (μm)

0

50 100 150 y (μm)

2.0 1.0 0.0 -1.0 -2.0

3.0 1.0

-1.0 0 50 100 150 200 250 x (μm)

Figure 2: (a) Vector components of the stray magnetic field produced by the micromagnets, measured using wide-field NV magnetometry. The orientation of the applied in-plane magnetic field is represented by the arrow. The squares in dotted line indicate the micromagnet location. The experimental results shown on top are compared to the macrospin model of the induced magnetization shown below, after optimization of the two free parameters of the model. The left (resp. right) part of the figure displays the x, y and z components of the magnetic field produced by the 30 µm (resp. 110 µm) micromagnet, after substraction of the applied magnetic field which is calibrated using the measurement of the NV resonances far from the micromagnets. (b) Examples of cross-cut comparisons between the data and the macrospin model along the dashed lines indicated above.

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-3.5

Nano Letters

a magnetization (105 A/m)

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applied magnetic field (mT) -150 6

-100

-50

0

50

100

150

4 2 0

-2 -4 -6

b

Ba= -15.1 mT

Ba= -5.1 mT

Ba= 4.9 mT

Figure 3: (a) Magnetization curve of a 110 µm micromagnet recorded with MOKE microscopy (black circles). The red curve is a saturation fit to the MOKE data. The magnetization axis associated to the MOKE measurement is calibrated using the linear dependance of M with Ba in the regime where NV magnetometry gives an absolute quantitative determination of the stray magnetic field produced by the induced magnetization in the micromagnet.(b) MOKE images showing the evolution of the magnetic domains in the micromagnet as it is progressively magnetized by increasing the applied magnetic field amplitude Ba . .

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a

b

external magnet

Fx

c

Fy

0

0

2.0

2000

7 µm

Gly/H2O micromagnet

PDMS z 𝑩 𝒂 y glass coverslide x objective

40

x (µm)

measurement region

80

120

40 80

120

0 20 40 60 80 y (µm)

gradient (kT/m)

2000 2000

x (µm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

experimental results macrospin simulation

1.5

1500 1500

1500

1.0

1000 1000

1000

0.5

500 500

0 20 40 6010 80 0 0 y (µm)

0

0

0

10

500

20 20

0

0 10 20 30 40 50 60 30 40 50 60 distance to edge along y (µm) 0

30

10

40

20

30

50

60

40

50

-7 -3.5 0 3.5 7 (pN)

Figure 4: (a) Setup of the Stokes drag experiment. MNPs of 300 nm size, suspended within a mix of water and glycerol, are submitted to the magnetic field gradient created by a micromagnet of 110 µm size. An applied field aligned along the y-axis saturates the magnetization. The MNPs trajectories are monitored in a measurement plane located at a distance of 7 µm from the micromagnet. For clarity, the luminescence excitation and collection are not depicted. (b) x (top) and y (bottom) components of the magnetic forces applied on the MNPs by the saturated micromagnet. The wide arrows indicate the orientation of its induced magnetization. Note that when the MNPs accumulate close to the micromagnet, their fluorescence prevents us from resolving individual trajectories and measuring the drag force in this region. (c) Amplitude of the magnetic field gradient applied on the MNPs along the dashed lines of figure (b). The experimentally obtained data (red dots) are compared with the calculation based on the macrospin model using the micromagnet magnetization determined by combining NV and MOKE microscopies (dashed line).

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Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

a

b

Injection needle

z

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c

x

y magnet z 𝑩𝒂 x

y

PDMS

glass coverslide

fibronectin (adhesive pattern) repellant molecules (PEG)

d

200 μm

e

50 μm

g

f

Ba = 0 mT

t=0s

Ba = 100 mT

t = 20 s

Ba = 0 mT

t = 70 s

Figure 5: (a) Setup for the magnetic manipulation of Si-MNPs in a living cell. For clarity, the external magnet, the luminescence excitation and the collection objective are not depicted. (b) Optical microscopy image of the array of micromagnets (dark squares). The bright spots correspond to fluorescent fibronectin binding to the coverslip in the regions determined by UV photopatterning. (c) Specific adhesion of fluorescent HeLa cells on the micropatterns defined near the micromagnets. (d) Zoom on a micromagnet, with a cell patterned near its edge. The dotted line show the limit size of the micromagnet. (e) Luminescence image recorded without any external magnetic field. The Si-MNPs are not specifically located inside the cell. (f ) Due to the magnetization (indicated by the wide arrow) induced by switching on the external magnetic field Ba , the micromagnet creates a local magnetic field gradient that attracts the Si-MNPs. The luminescence emitted by the Si-MNPs is observed inside the cell near the micromagnet edge. (g) When the external magnetic field is switched off, the Si-MNPs diffuse back into the cytoplasm.

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Nano Letters

Graphical TOC Entry Bx (mT) z

By (mT) x

Bz (mT) micromagnet OFF

y 100 μm 25 μm

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micromagnet ON

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