REVIEW OF SCIENTIFIC INSTRUMENTS 84, 065101 (2013)

A flux-coupled ac/dc magnetizing deviceD. B. Gopman,a) H. Liu, and A. D. KentDepartment of Physics, New York University, 4 Washington Place, New York, New York 10003, USA

(Received 13 December 2012; accepted 10 May 2013; published online 3 June 2013)

We report on an instrument for applying ac and dc magnetic fields by capturing the flux from arotating permanent magnet and projecting it between two adjustable pole pieces. This can be analternative to standard electromagnets for experiments with small samples or in probe stations inwhich an applied magnetic field is needed locally, with advantages that include a compact form-factor, very low power requirements and dissipation as well as fast field sweep rates. This flux captureinstrument (FLUXCAP) can produce fields from !400 to +400 mT, with field resolution less than1 mT. It generates static magnetic fields as well as ramped fields, with ramping rates as high as 10 T/s.We demonstrate the use of this apparatus for studying the magnetotransport properties of spin-valvenanopillars, a nanoscale device that exhibits giant magnetoresistance. © 2013 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4807696]

I. INTRODUCTION

The effective synthesis and control of magnetic fields isof longstanding fundamental interest for probing magnetic-field dependent phenomena. The ability to effectively magne-tize materials is also of tremendous technological importancefor testing magnetic devices, such as sensors, magnetic mem-ories and other small magnetic elements, as well as for charac-terizing a new generation of hybrid devices with semiconduct-ing and magnetic properties.1–3 This demand for magnetizingdevices has motivated the recent emergence of many differ-ent methods for generating and directing magnetic fields.4–9

From static systems involving permanent magnets to electro-magnetic systems built upon current carrying coils and super-conducting magnets, there are many options when designinga source of magnetic fields. Most designs consider: the maxi-mum desired field, the field homogeneity in the sample area,the size and access to the field region for probes (e.g., opticalor electrical), the field sweep-rate and the magnet’s linearity.In practice, the design factors are highly dependent on the re-searcher’s aim.

Standard electromagnets have several disadvantages. Thecurrent-carrying electromagnets are typically large, heavyunits that can limit the optical access to a device between thepoles, consume high power in order to drive sufficient currentthrough the coils and require water cooling in order to miti-gate the Ohmic heating.

In this paper, we introduce an ac/dc magnetizing de-vice based on the coupling of magnetic flux into two parallelsteel bars from a diametrically magnetized permanent mag-net that is mounted to a rotating stage. We denote this instru-ment flux capture instrument (FLUXCAP) for its flux cap-ture characteristics. The FLUXCAP is an alternative to stan-dard magnetizing devices for generating the fields betweentwo soft pole pieces. It has been designed for testing smallmagnetic devices, whose lateral size is much smaller than thediameter of the pole pieces. This apparatus has several ad-vantages over standard magnets: it is portable and can run

a)Electronic mail: daniel.gopman@physics.nyu.edu

entirely on battery power; most of the heating comes fromOhmic losses in the motor, for which overheating can easilybe prevented by heat-sinking; and the high speed by whichthe magnet can be rotated permits higher field ramping ratesthan many electromagnets which typically have a large induc-tance. Furthermore, the FLUXCAP permits optical access andis high vacuum compatible, permitting a wide range of testapplications.

II. PHYSICAL DESCRIPTION AND PRINCIPLESOF OPERATION

Figure 1 illustrates our implementation of a FLUXCAPmagnet. The yoke of the FLUXCAP is a Neodymium IronBoron (NIB) magnetic rod (diameter 0.5 in., length 2 in.)10

as indicated by the blue rectangle in the figure. It is magne-tized uniformly along the rod diameter. The NIB magnet isattached to a motor (brown hashed) which permits continu-ous rotation of the rod about its long axis, and consequently,continuous rotation of the magnetization in the plane perpen-dicular to the rotation axis. The magnet yoke is flanked onboth sides by soft pole pieces – two low-carbon steel bars asindicated by the black dotted regions (0.25 in.2 cross-section,length 6 in.). Two threaded holes near the termination of thebars accommodate one-quarter inch threaded steel rods, com-pleting the pole pieces. The pole gap is adjusted by threadingthe removable pole pieces (grey with black stripes) into andout of the threaded holes in the steel bars. Test devices, as in-dicated by the green solid rectangle, are inserted in the gap be-tween the pole pieces and a commercial Gaussmeter is placedat the sample location to monitor the field produced betweenthe poles. This entire apparatus is lightweight, weighing lessthan 10 kg.

The soft pole pieces capture the flux incident from theyoke and focus the field lines across the relatively short airgap between the pole pieces. As the NIB rod is rotated onits axis, the net flux captured into the pole pieces from theyoke varies periodically. This rotation translates into a nearlysinusoidally varying magnetic field between the two poles.

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065101-2 Gopman, Liu, and Kent Rev. Sci. Instrum. 84, 065101 (2013)

FIG. 1. Diagram of a flux-coupled dipolar magnet based on a permanentmagnet rod with diametric magnetization mounted to a motor. The perma-nent magnet is indicated by the blue rectangle. The motor is indicated bythe brown hashed region, and the steel bars by the black dotted regions. Thepole pieces (solid grey with black stripes) are adjustable for changing the gaplength. A test device is drawn between the two pole pieces as the green solidrectangle. The red closed curves symbolize the magnetic field lines in thesystem.

The operation of the FLUXCAP magnet depends uponthe capture of magnetic flux from a permanent magnet intotwo parallel steel bars placed on each side of the magnet.Maximal flux transfer occurs when the magnetization of thediametrically magnetized permanent magnet is directed to-ward the faces of the steel bars and minimal flux is transferredwhen the magnetization is oriented perpendicular to the facesof the bars. Thus, the permanent magnet is rotated by a motorin order to vary the flux captured by the steel bars by varyingthe angle between the magnetization direction and the steelbar faces.

We present a model for understanding the basic depen-dence of the flux in the steel rods as a function of the mag-netization direction of the permanent magnet. Equation (1)presents the field from an infinite uniformly magnetized rodwith diametric magnetization in cylindrical coordinates:

B =

!"

#

Bmax($! cos " ! $" sin "), ! < R

Bmax

%R!

&2($! cos " + $" sin "), ! > R.

(1)

Here Bmax = µ0Ms/2, where Ms is the saturation magnetiza-tion of the permanent magnet. ! and " are the radial and an-gular cylindrical coordinates. R is the radius of the permanentmagnet rod. The geometry of this arrangement is further de-picted in Fig. 2(a). While the real magnet is finite in extent, we

FIG. 2. Distortion of the magnetic field lines from a diametrically magne-tized cylinder due to the proximity of a steel bar. The red arrows in both (a)and (b) represent the radial magnetization direction. The red dashed curvesin (a) represent the magnetic field lines. The angle #0 in (b) is the angle be-tween magnetization and the steel surface normal. The red and green curvesrepresent the magnetic field lines coming out from and into the magnetic rod.

believe that this approximately captures the relevant behaviorof this system because the length of the magnetic rod is muchlarger than the distance between the rod and the steel bars(approximately one-eighth of an inch). We are ultimately in-terested in the field lines extending radially outward and intothe steel piece, which is set by Bmax, the maximum magneticfield at the surface of the magnet. This value can be directlymeasured with a magnetic field sensor placed on the surfaceof the magnet, which we have measured as 0.993 T. Havingestablished an expression for the field, we proceed to a de-scription of the flux in the steel bars.

The proximity of the two parallel steel bars have a non-negligible effect on the fields from the permanent magnet. Weassume the magnetic field on the surface of the permanentmagnet is left unchanged, but that the magnetic field lines aredistorted in such a way that field lines on the right semicircu-lar face of the magnet terminate on the right steel bar and lineson the left semicircular face terminate on the left steel bar, asdepicted graphically in Fig. 2(b). Therefore, we can estimatethe total magnetic flux into the right steel bar as the net mag-netic flux exiting the right semicircular face of the magnet.Equation (2) gives the total flux $ as a function of #0, the an-gle between the magnetization and the steel surface normal,

$ = Bmax · 2R% · cos #0, (2)

where % is the length of the magnet.Finally, the magnetic flux is directed toward two pole

pieces extending into the gap between the parallel steel bars.For sufficient distances between the permanent magnet andthe pole pieces, all of the field between the pole pieces is in-directly coupled through the flux in the steel bars. The magni-tude of this field is inversely proportional to the surface areaof the pole tips. Beveling or chamfering the pole tips can fo-cus the flux captured from the steel bars into a smaller region,but this can be more susceptible to saturation and hysteresislosses than smooth, wide pole tips. The transferred flux is alsosensitive to the pole gap and distance of the pole pieces fromthe permanent magnet yoke, both of which can contribute toflux losses through leakage along the gap between the parallelbars and fringing at the poles. We present an implementationof this method of flux capture and direction that exploits apole displacement and tip surface area that gives a fraction ofa Tesla magnetic field in a "1 cm3 volume. We also adjust thepole gap in order to control the peak field applied between thepoles, as discussed below.

III. FLUXCAP OPERATION

A. Field homogeneity

The field homogeneity is a critical figure of merit for anymagnetizing device. The field at the midpoint between the twopole pieces of the FLUXCAP, for an 0.25 in pole gap, variesless than 1% over a 1 mm2 area and drops by 30% at 5 mmaway from the midline. We have simulated this scenariowith a numerical calculation of the field from two uniformlymagnetized right cylindrical tips (length 0.625 in., diameter0.5 in.). Figure 3 shows the results from our simulation as

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065101-3 Gopman, Liu, and Kent Rev. Sci. Instrum. 84, 065101 (2013)

FIG. 3. Transverse magnetic field between the pole pieces as a function ofdisplacement from the midline. The solid dots are measured with a Gauss-meter probe translated along the x axis and the solid line is a finite elementcalculation of the field from two uniformly magnetized right cylindrical tips(length 0.625 in., diameter 0.5 in.).

well as the field measured by a Gaussmeter probe translatedalong the x axis. We have qualitatively good comparison toour experimental data, although we measure a faster decay ofthe field, which can be understood due to fringing effects orthe bevel of the tips. Working with arrays of devices whoseactive area is typically around 1 mm2, we can control for fielduniformity by centering our active region between the polepieces and measuring the field directly behind our sample.

B. Variable amplitude and precision control

The gap between two steel pole pieces can be adjusted tochange the maximum applied field. This varies the peak fieldamplitude of the alternating magnetic field when the magnet isrotated continuously. Reducing the peak field amplitude maybe useful in studying devices that have multiple magnetic lay-ers, some of which are not intended to be remagnetized.

Reducing the peak field amplitude may also be useful inapplications where field precision is of most importance. Forexample, the FLUXCAP can be used to generate dc magneticfields with the magnet positioned using a stepper motor. Thefield precision is related to the minimum rotation that the mo-tor can produce and the maximum field amplitude. Each finitestep from a stepper motor (typically 0.9#) corresponds to achange in field of just over one percent of the peak amplitude.Therefore, larger pole separations may be desirable to obtainfiner control over magnetic fields.

Figure 4 demonstrates the ability to adjust the maximumfield between the poles. We adjusted the 0.25 in. diameterthreaded rods to create pole gaps in 0.125 in. increments be-tween 0.125 and 0.5 in. and operated the FLUXCAP usinga 12 V battery-powered dc motor. As the permanent mag-net was rotated continuously at a rate of 400 revolutions perminute, field measurements were made using a commercialGaussmeter and then digitized at 48 kHz. We demonstrate

FIG. 4. Magnetic field between the pole pieces as a function of time as thepermanent magnet is rotated continuously at a rate of 400 rpm. The maximumapplied field is seen to be a function of the gap spacing.

control over the peak field amplitude from 400 mT down to180 mT.

The peak amplitude Bpk at the pole gap of 0.125 in. al-lows us to estimate the efficiency by which we capture theflux from our NIB yoke into the two pole pieces. Assuming aneffective fringing area Af about 50% larger than the pole face,we compute the efficiency, e = BpkAf/$, to be approximately15%. We estimate that 85% of the flux is being lost to leakageacross the space between the steel bars. The FLUXCAP couldbe made more efficient by employing higher permeability ma-terials and through optimizing the pole piece geometry.

C. Variable frequency and field ramping

The FLUXCAP magnet can operate either as a stationaryor an alternating field magnetizing device. In the alternatingfield operation mode, a dc motor generates continuous rota-tion of the NIB yoke which drives an alternating magneticfield between the poles. By changing the frequency of rota-tion, a variation of the field sweeping rate (frequency) can beachieved. Figure 5 shows the Fast Fourier Transform spectra

FIG. 5. FFT spectra indicating the various magnet rotation rates.

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065101-4 Gopman, Liu, and Kent Rev. Sci. Instrum. 84, 065101 (2013)

FIG. 6. FLUXCAP apparatus in a testing configuration. The FLUXCAP motor and steel bars are bolted to aluminum tracks. The NIB yoke is encased inaluminum shells for coupling to the motor with a brass set screw and to two plastic ball bearings at the midpoint and the endpoint of the magnet. Adjustablepole pieces emerge from the steel bars where the test sample has been clamped to the aluminum track and a Gaussmeter probe is attached behind the sample.and sample.

of the alternating magnetic field between the poles of theFLUXCAP under different rotation speeds of the motor. Mea-surements were taken under a 0.25 in. pole gap using the samefield acquisition methods described above. We demonstratealternating magnetic fields with frequencies ranging between3 Hz and 7 Hz for voltages ranging from 7 V to 12 V placedacross the motor. Applications requiring continuous rotationof a FLUXCAP or faster rotation speeds may encounter sig-nificant heating due to eddy currents and hysteresis losses inthe low carbon steel. We would recommend using laminatedsteel in these applications in order to mitigate the eddy currentlosses.

For the lower frequencies, the FFT spectra show widesidebands due to a varying rotation rate of the permanent mag-net. We used a 12 V/84 oz-in. 37 mm dc motor,11 which uses12 W of power (1 A or 20% of its stall current) at 12 V. Atlower voltages, the maximal output torque of the motor de-creases and rotating the magnet away from the steel bars re-quires larger torque. For inputs below 7 V, this motor stalls.We use a higher torque stepper motor when slower field ramprates are needed.12

The frequency of the alternating magnetic field corre-sponds to an effective linear ramping rate over ± 85% of themaximum amplitude field. For the frequencies given here andthe 0.3 T peak amplitude for a 0.25 in. pole separation, theramping rates vary from 10 T/s down to 4 T/s for the lowestrotation frequency. These high field ramping rates make theFLUXCAP an efficient rapid magnetizing device when usedwith a continuously rotating motor. Slower variation of thefield has been achieved with the use of a high torque step-per motor, permitting field ramping rates decreasing down byseveral orders of magnitude. This could be relevant to stud-ies of thermally-activated magnetization reversal in which amagnet’s coercivity is (typically logarithmically) sensitive tothe sweeping rate.13–17

IV. APPLICATION: FAST MAGNETIZINGOF SPIN-VALVE NANOPILLARS

The FLUXCAP magnet can facilitate fast characteriza-tion of many magnetic devices such as spin-valve nanopil-lars – a two terminal magnetic device composed of two ferro-magnetic layers separated by a thin non-magnetic layer.14, 18

Typically a spin-valve device exhibits two stable resistance

states depending on the relative magnetization orientation ofthe two magnetic layers from the Giant Magnetoresistance(GMR) effect.19–22 The spin-valve state can be toggled be-tween high (antiparallel) and low (parallel) resistance by ap-plied magnetic fields. Characteristic of spin-valve nanopillarsis the use of ferromagnetic layers with different coercivities,such that one ferromagnet is typically fixed (a reference layer)while the other ferromagnet (the free layer) can be switchedrelative to the reference magnet. We can determine the relativeorientation of the layers by measuring the device resistance asa function of the applied magnetic field. More critically, us-ing the 7 Hz rotation rate of the FLUXCAP, we can rapidlyconduct MR hysteresis loops to measure the coercivity of thefree layer and the giant magnetoresistance of the spin-valve.The FLUXCAP could also be incorporated into a probe setupfor characterizing the properties of spin-valve and magnetictunnel juction (MTJ) devices.

Figure 6 demonstrates a testing configuration for this ap-paratus. A spin-valve nanopillar device is wire bonded to acoplanar waveguide board, which is in turn has been sol-dered to end-launch coaxial jacks. The waveguide is mountedrigidly to the outer aluminum rail of the apparatus such thatthe device is centered between the two pole pieces. A com-mercial Gaussmeter probe is also mounted on the aluminumrail and is attached to one of the pole pieces. A small ac

FIG. 7. GMR signal versus field for 130 hysteresis loops obtained in 20 s.

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065101-5 Gopman, Liu, and Kent Rev. Sci. Instrum. 84, 065101 (2013)

FIG. 8. Averaged magnetic hysteresis loop of a spin-valve device.

excitation current probes the differential resistance acrossthe 300 $ 50 nm2 spin-valve nanopillar, whose physicalproperties have been described in detail elsewhere.18 TheFLUXCAP is configured with a one-quarter inch pole gap and12 V power to run the motor at 7 Hz.

Figure 7 shows over 100 hysteresis loops recorded from20 s of operating the FLUXCAP. Sharp changes in the differ-ential resistance RAC indicate toggling of the magnetizationof the free layer from “up” (anti-parallel) to “down” (parallel)relative to the reference layer. As mentioned previously, thereference layer has a coercivity over 1 T, and is kept fixedduring these measurements. Due to the thermally activatednature of magnetization reversal, a characteristic distribu-tion of switching fields is apparent in this ensemble of hys-teresis loops. It is therefore effective to consider an aver-aged hysteresis loop, such as the one depicted in Fig. 8.From this figure, we estimate a coercivity of 150 mT and aGMR ratio (&R/R) of 0.2%, which is consistent with similardevices.14, 23, 24

V. CONCLUSIONS

We have demonstrated the operation of the FLUXCAP, acompact magnetizing device based upon the capture and fo-cusing of flux from a rotating permanent magnet. This devicecan perform most of the same tasks as conventional electro-magnet based magnetizing devices in that it can synthesizestatic and dynamic magnetic fields over a broad range of fieldvalues. Yet the FLUXCAP immediately presents itself as anelegant alternative: it operates as an ac magnetizing devicerequiring only a 12 V battery and a dc motor; its power con-sumption is marginal (12 W), and it does not require watercooling. The pole pieces are modular – it is straightforwardto change the maximum field applied by varying the pole gapor even substituting a threaded rod with a different bevel orchamfer. This permits easy modifications to the magnitudeand homogeneity of the applied field with minor changes inthe FLUXCAP design. Furthermore, large field ramp ratesare possible with FLUXCAP and have been demonstratedfor studying spin-valve nanopillar devices. This enables sta-

tistical studies of thermally activated magnetization reversal,quick resetting of magnetic devices and testing the dynamicresponse of magnetic field sensors.

FLUXCAP magnets are versatile enough to function wellin a variety of other applications. The setup could be madeUHV compatible – in fact, the permanent magnet and mo-tor could be placed outside of the UHV chamber and the fluxcoupled into the chamber with the soft steel core. FLUXCAPmagnets can clearly be used for electronic transport measure-ments and could be integrated into probe stations. For exam-ple, it could be used to add magnetic capabilities to a semicon-ductor tester. By designing the shape of pole pieces and theposition to place the sample, one can achieve different fielddirections using the FLUXCAP. Finally, it is easy to imag-ine combining two or three such magnets to generate a two-dimensional or even three-dimensional vector field for sophis-ticated measurements.

ACKNOWLEDGMENTS

We appreciate Dr. Stéphane Mangin of Nancy Univer-sité and Dr. Eric E. Fullerton of the University of California,San Diego for providing the spin-valve samples used in thecharacterization of magnetic properties used in this study.We would also like to acknowledge Dr. James Rantschler ofXavier University of Louisiana for fruitful discussions lead-ing to the design of FLUXCAP. This research was supportedby NSF Grant Nos. DMR-1006575 and DMR-1309202.

1L. Hueso and V. A. Dediu, Nature Mater. 8, 707 (2009).2J. B. Yi, C. C. Lim, G. Z. Xing, H. M. Fan, L. H. Van, S. L. Huang,K. S. Yang, X. L. Huang, X. B. Qin, B. Y. Wang et al., Phys. Rev. Lett.104, 137201 (2010).

3F. Wang, F. Macia, M. Wohlgenannt, A. D. Kent, and M. E. Flatte, Phys.Rev. X 2, 021013 (2012).

4W.-H. Chang, J.-H. Chen, and L.-P. Hwang, Magn. Reson. Imaging 28, 129(2010).

5D. A. Arena, Y. Ding, E. Vescovo, S. Zohar, Y. Guan, and W. E. Bailey,Rev. Sci. Instrum. 80, 083903 (2009).

6M. Gilbert, H. C. Mertins, M. Tesch, O. Berges, H. Feilbach, and C. M.Schneider, Rev. Sci. Instrum. 83, 025109 (2012).

7F. Heigl, O. Krupin, G. Kaindl, and K. Starke, Rev. Sci. Instrum. 73, 369(2002).

8J. Li, E. Jin, H. Son, A. Tan, W. N. Cao, C. Hwang, and Z. Q. Qiu, Rev. Sci.Instrum. 83, 033906 (2012).

9D. Nolle, M. Weigand, P. Audehm, E. Goering, U. Wiesemann, C. Wolter,E. Nolle, and G. Schuetz, Rev. Sci. Instrum. 83, 046112 (2012).

10This study used Neodymium Iron Boron (NIB) magnets purchased fromK & J Magnetics, see http://www.kjmagnetics.com.

11This study used a 12 V 19:1 Metal DC Gearmotor (37 mm Shaft) with 84oz-in torque and 500 rpm. The motor is from Pololu Metal Gearmotors, seehttp://www.pololu.com.

12For slower field sweeping, we use a High Torque (175 oz-in) Stepper Mo-tor. It can be found under model number 5709M from Lin Engineering, seehttp://www.linengineering.com.

13W. Wernsdorfer, E. B. Orozco, K. Hasselbach, A. Benoit, B. Barbara, N.Demoncy, A. Loiseau, H. Pascard, and D. Mailly, Phys. Rev. Lett. 78, 1791(1997).

14D. B. Gopman, D. Bedau, S. Mangin, C. H. Lambert, E. E. Fullerton, J. A.Katine, and A. D. Kent, Appl. Phys. Lett. 100, 062404 (2012).

15Y. Jiang, S. Abe, T. Nozaki, N. Tezuka, and K. Inomata, Phys. Rev. B 68,224426 (2003).

16J. Z. Sun, L. Chen, Y. Suzuki, S. S. P. Parkin, and R. H. Koch, J. Magn.Magn. Mater. 247, 237 (2002).

17J. Z. Sun, J. C. Slonczewski, P. L. Trouilloud, D. Abraham, I. Bacchus, S.S. P. Parkin, and R. H. Koch, Appl. Phys. Lett. 78, 4004 (2001).

Downloaded 19 Jun 2013 to 128.122.53.108. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://rsi.aip.org/about/rights_and_permissions

065101-6 Gopman, Liu, and Kent Rev. Sci. Instrum. 84, 065101 (2013)

18S. Mangin, D. Ravelosona, J. A. Katine, M. J. Carey, B. D. Terris, andE. E. Fullerton, Nature Mater. 5, 210 (2006).

19M. N. Baibich, J. M. Broto, A. Fert, F. N. Van Dau, F. Petroff, P.Etienne, G. Creuzet, A. Friederich, and J. Chazelas, Phys. Rev. Lett. 61,2472 (1988).

20G. Binasch, P. Grunberg, F. Saurenbach, and W. Zinn, Phys. Rev. B 39,4828 (1989).

21T. Valet and A. Fert, Phys. Rev. B 48, 7099 (1993).22W. P. Pratt, S. F. Lee, J. M. Slaughter, R. Loloee, P. A. Schroeder, and J.

Bass, Phys. Rev. Lett. 66, 3060 (1991).23D. Bedau, H. Liu, J. Z. Sun, J. A. Katine, E. E. Fullerton, S. Mangin, and

A. D. Kent, Appl. Phys. Lett. 97, 262502 (2010).24D. Bedau, H. Liu, J. J. Bouzaglou, A. D. Kent, J. Z. Sun, J. A. Katine, E.

E. Fullerton, and S. Mangin, Appl. Phys. Lett. 96, 022514 (2010).

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