A perpendicular field electromagnet with a 250mm access bore
A.P. Petrovi?, B.H.M. Smit, K.L. Fong, B. Satywali, X.Y. Tee, C. Panagopoulos
PPetrovi´c et al.
A perpendicular field electromagnet with a 250mm access bore
A.P. Petrović, a) B.H.M. Smit, b) K.L. Fong, c) B. Satywali, X.Y. Tee, and C. Panagopoulos a) Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University,21 Nanyang Link, Singapore 637371 (Dated: 7 January 2021)
We present a laboratory electromagnet capable of generating magnetic fields up to ± B , leading to an estimated uniformity of ± (cid:46) . | B | within a 28 mm zone at maximum field. The sample stage is thermally regulated and isolated from the magnet,enabling temperature control with ± I. INTRODUCTION
Many experiments in modern condensed matter physics ne-cessitate the application of a magnetic field perpendicular toa thin film sample or device. Magnetic films with perpen-dicular anisotropy (PMA) are of considerable importance forspintronic applications and provide an excellent example ofthis requirement. In such materials, the spin-orbit interactioncauses a preferential orientation of the electron spins perpen-dicular to the film plane , in contrast to the in-plane alignmentwhich would be expected from magnetostatic and exchangeeffects alone. Combining PMA with a spin-canting interactionsuch as geometric frustration or the Dzyaloshinskii-Moriyainteraction can induce the formation of chiral spin texturessuch as skyrmions , with significant potential for data stor-age, logic or neuromorphic computing .Technological applications of PMA films and/or chiral spintextures will involve the controlled reversal of out-of-planemagnetic moments. Typical examples include flipping thespin polarisation in PMA tunnel junctions , modifying the do-main structure in PMA nanodots , strips or films , andnucleating/translating/erasing individual magnetic skyrmions.Ultimately, such magnetic switching may be achieved withinmultilayer devices by applying spin torques from an out-of-plane current . However, if direct access to the exposed mag-netic layer is necessary during the research and developmentphase - as is the case for any imaging or local probe exper-iment - then an external perpendicular flux source becomesessential to manipulate the film magnetization.Integrating experimental scanning or imaging hardwarewith a perpendicular magnetic field is technically challenging.Room-temperature laboratory electromagnets generally use asplit pair of coils, each surrounding a conical pole made froma high permeability material (e.g. pure iron). These poles fo-cus the magnetic flux into the experimental area within the gapbetween them. Following this principle, a coil can be wound a) Authors to whom correspondence should be addressed:[email protected], [email protected] b) Also at Department of Applied Physics, TU Eindhoven, The Netherlands. c) Also at Department of Physics, The Hong Kong University of Science andTechnology, Hong Kong. around a C-shaped core or yoke, and the sample-holder placedin the gap between the ends of the yoke . The coil can al-ternatively be replaced by a flux-coupled permanent magnetarray , with the advantage that resistive heating is elimi-nated. Unfortunately, none of these approaches can be usedto generate a perpendicular field for room-temperature appa-ratus such as a force microscope or nanoprobe station, sincethe upper pole of the yoke would completely cover the sam-ple. A limited degree of optical access in perpendicular fieldshas been achieved using hollow magnetic poles or a “magicmangle” configuration of ferromagnetic cylinders , but boththese approaches still severely obstruct the sample surface.Previous room-temperature imaging studies of PMA filmshave circumnavigated this problem by using arrays of per-manent magnets underneath the sample to generate an out-of-plane field . Although effective, this approach has twodisadvantages: firstly, the magnetic field strength cannot becontinuously varied, thus precluding detailed studies of themagnetization evolution and reversal processes. Secondly,the field from a typical disc-shaped permanent magnet canexhibit substantial ( > ± ∼ × ± or ± . Such field strengths fall well be-low the 0.3-0.4 T required to polarise many chiral magneticfilms. Another commercial electromagnet provides perpen-dicular fields of up to 0.95 T for magneto-optical Kerr effectmicroscopy, using an annular flux yoke above the sample .However, the optical path to the sample passes through a nar-row hole in the yoke, thus preventing access to the surfaceusing bulky scanning/probing hardware. An alternative elec-tromagnet from the same supplier without any flux yoke canonly provide fields up to 0.1 T , illustrating the constraintsimposed by the requirement of unrestricted sample access.These continuity, homogeneity and field strength problemscould all be eliminated by placing the entire sample and appa-ratus into the bore of a superconducting solenoid. However,the requirement for cryogenic cooling adds considerable com-plexity to the measurement process (as well as expense duringsetup and operation). Replacing the superconducting coil witha resistive solenoid operating at room temperature yields mag- a r X i v : . [ phy s i c s . i n s - d e t ] J a n etrovi´c et al. | B | ( T ) Height above magnet core (mm)Sample position (b)(c) (d)(e) -3 -2 -1 0 1 230.62350.62400.62450.62500.62550.62600.62650.62700.6275 | B | θ Lateral position (mm) | B | ( T ) P o l a r ang l e θ ( deg r ee s ) Sample-holderFerromagneticcore Magnet coil (rectangular copper wire)
Copper heat exchanger Variable-temperature sample stage
Peltier coolers Principal mounting plateAluminium magnet bobbin (a)
Free space (for thermal isolation)
FIG. 1. (a) Cross-sectional slice through the centre of the magnet design. The 250 mm diameter zone above the sample-holder constitutes theonly spatial constraint on any experimental hardware used to analyse the thin film under test. The large area of the principal mounting plate (towhich the thermally-isolated sample-holder is fixed) provides adequate space for installing a nanoprobe station or microscope, thus minimisingany thermal drift between probe and sample. (b) Simulated flux density generated by the electromagnet driven by current I max =
28 A. Thinblack lines are flux lines, i.e. contours of the magnetic vector potential A multiplied by 2 π r (where r is the distance from the magnet centralaxis). The region occupied by the coil is delineated by blue lines and the iron core is visible as the high flux density zone at the centre of themagnet. The black scale bar measures 50 mm. (c) Zoom view of the top surface of the iron core, using the same colour scheme to illustratethe flux density as in (b). The 6 mm horizontal red line lies in the sample plane 1 mm above the core, while the 3 mm vertical red line liesalong the central axis. The white scale bar measures 2 mm. (d) Decay of the flux density moving up the vertical red line in (c): at the sampleheight, the field is decreasing at 0.064 mT µ m − . (e) Homogeneity of the absolute flux density | B | and the polar angle θ subtended by thelocal magnetic field within the sample plane (horizontal red line in (c)). etrovi´c et al. ∼
50 mm dissipating sev-eral kW in resistive heating only generates a field ∼ II. MAGNET DESIGN
Our initial approach employs a large (0.34 m outer diam-eter) solenoid coil with a “stepped” internal diameter and ahigh purity (>99.8%) iron core. A cross-section of this con-figuration is shown in Fig. 1(a), illustrating the core positiondirectly ( ≤ . In particular, the three “steps” inthe coil cross-section allow us to minimize the total resistance(and hence power dissipation) of the coil, while incorporatinga thermally-isolated sample stage and optimizing the field per-pendicularity at the sample plane. A 28 A 36 V bipolar powersupply was then selected to match the calculated resistance(1.2 Ω ) and inductance (0.11 H) of the coil.The simulated field from the solenoid (driven at the maxi-mum current, I max =
28 A) is illustrated in Fig. 1(b). Here wehave assumed an optimistic 90% coil-packing efficiency, cor-responding to 689 turns of a 2.52 mm cross-section copperwire. At the designated sample height (1 mm above the ironcore), the vertical flux density B reaches 0.624 T on the corecentral axis and the magnet is dissipating 959 W in heat due toresistive losses in the copper wire. A zoom view of the fieldin the sample zone directly above the iron core is shown inFig. 1(c), together with line cuts of the flux density verticallyabove the core centre and laterally at 1 mm above the core (thedesignated sample position). At this height, the vertical fieldis falling at 0.064 mT µ m − (Fig. 1(d)). Given that the typicalthin film heterostructures which we wish to study have thick-nesses below 100 nm, this decay is negligible. Homogene-ity within the xy plane is more difficult to achieve: althoughthe absolute flux density varies by less than ± -3 -2 -1 0 1 2 30.76250.76500.76750.77000.77250.77500.77750.78000.78250.7850 | B | θ Lateral position (mm) | B | ( T ) P o l a r ang l e θ ( deg r ee s ) Sample position | B | ( T ) Height above magnet core (mm) (a)(b)(c)
SharpCoreSharpCore
FIG. 2. Influence of changing the core geometry on the achievablefield strength and homogeneity. (a) Simulated flux density above abroader, sharply-tapering iron core at I max =
28 A. The base and tipdiameters of the core are 23.6 mm and 8 mm respectively, comparedwith 20 mm and 12 mm for the simulations shown in Fig. 1(b-e). Thewhite scale bar measures 2 mm. Apart from the core geometry, allother simulation parameters are identical to those used in Fig. 1. (b)Decay of the flux density moving up the core axis (vertical red line in(a)): at the sample height, the field is decreasing at 0.157 mT µ m − .(c) Homogeneity of the absolute flux density | B | and the polar angle θ subtended by the field within the sample plane (horizontal red linein (a)). gle of 9.5 ◦ at the edge of the circle (Fig. 1(e)). The homogene-ity of the field amplitude and orientation are controlled by thecurvature of the top surface of the iron core: flattening thissurface would improve the orientational homogeneity, at theexpense of the amplitude homogeneity. We emphasize thatwithin the central 40 µ m × µ m region - the maximal scanarea of a typical scanning probe microscope - our core designgenerates an estimated flux density which is homogeneous towithin 0.005%, with a maximum polar offset ≤ . ◦ .Changing the geometry of the core offers a simple routeto tuning both the magnitude and homogeneity of the appliedfield. In Fig. 2(a) we show a simulation of the field profile cre-ated above an iron core with a more sharply-tapered tip, whichserves to concentrate the flux into the sample. The maximumperpendicular flux density at the sample plane increases to0.785 T (Fig. 2(b)) and we are able to optimize the tip curva-etrovi´c et al. ± ± ◦ at radius3 mm. These data demonstrate that optimal core design for aparticular experiment must balance the required field magni-tude against the sample dimensions, as well as the toleranceof the intended measurement to deviations in field orientation. III. MAGNET CONSTRUCTION
The magnet bobbin is assembled from a set of four custom-machined plates and three cylinders, all made in 6061-T6 alu-minium. This material was chosen for four reasons: it is non-magnetic, has a high thermal conductivity (to minimise ther-mal gradients across the coil), low mass and is easy to ma-chine. The plates were fastened to the cylinders using counter-sunk non-magnetic SS-316L screws and threadlocking com-pound. Helicoil thread inserts in the aluminium were avoideddue to their ferromagnetic nature. Prior to winding the coil, allinternal surfaces of the bobbin were lined with 50 µ m Kaptonfilm, which was bonded to the aluminium using a thin layer ofthermally-conductive epoxy : this eliminated the possibilityof short-circuiting the coil by scratching the wire insulationduring assembly.To maximise the current density in the coil, we used1.45 × with 110 µ m in-sulation: this was the largest cross-sectional area which couldeasily conform to the 13 mm minimum bend radius requiredby our bobbin. The coil was hand-wound using a sim-ple home-made jig which allowed the magnet bobbin and ∼
100 kg wire reel to rotate independently while keeping thewire parallel to both bobbins. From our original estimate of689 total coils (Fig. 1(b)), we anticipated winding a total of85 wire layers on the bobbin. Upon completion of each layer,a high-viscosity magnet resin was applied by brush. Thisparticular resin was selected for its rapid gelling time at roomtemperature (4 hours). At the end of the winding process,the magnet bobbin contained 622 coils: this reduction fromthe predicted value (689) can be attributed to excess resin ap-plication. After winding, the magnet was heated to 60 ◦ C inair to complete the resin curing. Electrical connections to themagnet were made using two 9 mm diameter copper weldingcables, terminated by gold-plated copper blocks clamped ontothe ends of the magnet wire. Each power terminal is isolatedfrom the magnet bobbin using a Delrin plate. An annotatedphotograph of the as-built magnet is shown in Fig. 3: its totalmass is 41 kg.
IV. MAGNETIC FIELD CALIBRATION
The magnet is operated via a LabVIEW program allow-ing real-time control and monitoring of the field as well asthe sample and magnet temperatures. This software also fa-
FIG. 3. Photograph of our as-built magnet and sample stage. The di-electric substrate has been removed from the sample-holder (expos-ing the ferromagnetic core below) and the electrical cables leading tothe sample stage have been disconnected for clarity. Labels indicate:1) coaxial cable junctions for in situ high frequency experiments; 2)principal mounting plate (featuring multiple threaded holes for in-stalling experimental hardware); 3) ferromagnetic core; 4) variable-temperature sample stage; 5) multi-pin connector for heaters, Peltiercoolers and thermometers; 6) one of four attachment points (allow-ing the entire magnet to be suspended for vibration isolation duringsensitive experiments); 7) chilled water supply lines; 8) Kapton insu-lation protecting the magnet bobbin from electrical shorts; 9) one ofnine copper heat exchangers; 10) outer diameter of the magnet coil;11) aluminium magnet bobbin. cilitates calibration of the magnet, i.e. determination of thecurrent-field conversion factor. The magnetic field is mea-sured using a factory-calibrated Hall sensor mounted on asample-holder at the same height as our experimental samples.The results are shown in Fig. 4(a): using a freshly-machined99.8% iron core with identical geometry to the simulationsin Fig. 1, a maximum field of ± .
465 T at I max =
28 A isachieved, which is lower than the expected 0.624 T. An ob-vious source of error is the reduced coil count (622 vs. 689)in our as-built magnet. However, correcting the number ofcoils and rerunning our simulations yields a maximum fieldof 0.566 T, which is still 20% higher than our measured field.This suggests that the offset originates either from the mag-netic properties of the core, or from the radial current densitywithin the magnet windings.We first consider the contribution of the core. Our simula-tion in Fig. 1(b) uses the reference permeability for pure iron µ r = ◦ C for 10 hours to improve the microstructureof our iron core, but this only increased the maximum field by1% to 0.471 T. Replacing the iron core with a high-inductionetrovi´c et al. provided another 1% increase to 0.478 T. Wetherefore believe that the principal limitation in our magnetperformance originates from a reduced coil density close tothe centre of the bobbin. The innermost coils of the mag-net were the most awkward to wind tightly due to their smallradius r , yet according to the Biot-Savart law B = µ I / r pro-vide the largest contribution to the flux density at the centre ofthe magnet. As illustrated in Fig. 2, a simple low-cost routeto improve the magnet performance would therefore be to in-crease the ferromagnetic core diameter (up to a maximum of23.6 mm imposed by the bobbin internal diameter) to capturemore flux, and sharpen the tip of the core (at the expense ofthe lateral field homogeneity at the sample). However, weemphasize that the ± ∼ .The B ( I ) curves in Fig. 4(a) appear perfectly linear, witha gradient of 0.0171 TA − for the FeCo core. However, us- - 0 . 1 0 - 0 . 0 5 0 . 0 0 0 . 0 5 0 . 1 0- 2 . 5- 2 . 0- 1 . 5- 1 . 0- 0 . 50 . 00 . 51 . 01 . 52 . 02 . 5 ( b ) Field at Sample (mT)
C u r r e n t ( A ) ( a )
Field at Sample (T)
C u r r e n t ( A )
FIG. 4. (a) Field-current calibration performed at the sample stageof the electromagnet. Data from three different ferromagnetic coresare shown: a 99.8% pure iron core immediately after fabrication,the same iron core following a 10-hour annealing process, and anannealed Fe Co V alloy. The inset highlights the small (1%) im-provement offered by the FeCo alloy compared with the annealediron. (b) Magnetic hysteresis loops for annealed iron and FeCo cores(black and green data-points, respectively) illustrating the remanentfields in each core. The stars at zero current indicate the measuredfields achieved after performing an automated demagnetization loop. ing a single linear factor to convert from magnet current tosample field becomes inaccurate at very low fields. Despiteour deliberate selection of low remanence materials for themagnet core, some hysteresis-induced error in the magneticfield experienced by the sample is inevitable. We quantifyand correct for this error by calibrating the magnetic field dur-ing a full B ( I ) hysteresis loop between ±
28 A. Figure 4(b)highlights the low-current region of the hysteresis loops ac-quired with our annealed iron and FeCo cores: a remanentfield of 1 . ± .
05 mT persists at I = . ± .
05 mT. Measurements in true zero field canbe achieved by performing an automated demagnetization se-quence, in which a series of n currents I i = I max × ( − A ) i is ap-plied to the solenoid. Here A ∼ . I ∼
20 A, i = n and the sequence terminates when I n fallsbelow a user-configurable threshold ∼ ≈ V. VARIABLE-TEMPERATURE SAMPLE STAGE
A major limitation of any laboratory electromagnet is theheat dissipated by the resistive coil. Since the magnetic prop-erties of thin film materials can vary strongly with temperature(especially their anisotropy), it is essential to manage this heatflow and hence maintain a known, constant temperature at thesample/device under analysis. Our solution to this problem isshown in Fig. 5: we place the sample on a massive (0.2 kg)copper block suspended from the principal mounting plate bystiff Delrin arms, thus thermally decoupling the sample envi-ronment from the magnet body. The copper block houses two50 Ω cartridge heaters (wired in parallel for redundancy) anda platinum resistive thermometer , which are connected toa PID temperature controller . On each side of the block,a 10.4 W Peltier cooler is mounted using thermally con-ductive silver epoxy . The hot side of each Peltier chip isheatsunk to the magnet body using flexible copper braid. Anadditional 5.1 W Peltier cooler is positioned under the ferro-magnetic core, below a threaded mount which facilitates corereplacement. The maximum current rating for each Peltierchip is 2.2 A. All three coolers are wired in series and poweredby a programmable 0-2.5 A current source , which in turn ismanually adjusted using an analog output from the tempera-ture controller. A further platinum thermometer is mountedon the magnet body for monitoring purposes.The centre of the copper thermal block is hollow, allowingit to encircle the ferromagnetic core. Our sample-holders arecomposed of a 25 × × , with aground plane deposited on the underside. This substrate canbe patterned with electrical contacts or waveguides to allow insitu excitations and measurements from dc to 40 GHz. Sam-ples are affixed directly on top of the substrate, using diluteGE varnish for electrical isolation if appropriate. For ease ofhandling and insertion, the substrate is glued into a U-shapedbronze frame using thermally conductive epoxy . This as-etrovi´c et al. (a) (b)
5W Peltier coolerScrew mount for core replacement
FIG. 5. Variable-temperature sample stage viewed from (a) above and (b) the side, along the direction indicated by the blue arrow in (a).The Delrin arms provide a stiff, low thermal conductivity interface to the principal mounting plate on the magnet body. Samples are loadedusing a removable sample-holder plate, which slides horizontally into position parallel to the viewing arrow in (a). Each sample-holder incor-porates two SMP end-launch coaxial connectors which mate with female SMP jacks in the PEEK connector block, thus firmly securing thesample-holder. Up to six further electrical contacts to the substrate can be made using a series of 0.1 mm copper beryllium leaf springs, posi-tioned between the two SMP jacks. Beneath the copper thermal block, the ferromagnetic core screws into a threaded mount, thus facilitatingreplacement of the core for tuning the field magnitude and homogeneity. sembly slides into position on top of the sample stage, guidedby two copper rails to mate with a set of six electrical and twomicrowave connectors housed in an insulating PEEK frame.After inserting the sample-holder into this connector block,the separation between the substrate ground plane and theshaped core below is 200 µ m. The sample is hence electri-cally and thermally isolated from the magnet bobbin.In addition to regulating the temperature of the samplestage, it is also important to prevent the magnet from over-heating. During operation, heat is removed from the magnetby nine water-cooled copper heat exchangers . Five of theseare fixed to the underside of the magnet bobbin using brassscrews and thermal paste, while the other four are attachedto aluminium wedges embedded within the coil. All heat ex-changers can be replaced if they develop leaks during use. A0.6 kW recirculating chiller pumps water through all nineheat exchangers in parallel, at a maximum rate of 15 l min − .We find that a temperature setpoint of 10 ◦ C provides the opti-mal balance between maximal cooling power at high currentsand minimal condensation on the magnet bobbin in zero field.While current is flowing through the magnet, a thermal gra-dient develops between the upper and lower surfaces of thebobbin. This gradient is not detrimental to the thermal sta-bility of our sample stage, which only contacts the magnetbobbin at the principal mounting plate. However, the magnetcooling efficiency could certainly be improved by mountingadditional heat exchangers on the top surface of the bobbin.We have chosen not to implement this step in our magnet, tomaximise the free space available for installing experimentalhardware.
VI. MAGNET THERMAL STABILITY
We define two conditions to assess the thermal performanceof our electromagnet: short-term temperature stability in re-sponse to rapidly-changing fields, and long-term stability inconstant fields.An important feature of our control software is a “Pulse”function which ramps the magnet current momentarily to a(high) setpoint, then returns immediately to a lower constantfield. This is useful for quickly polarizing a magnetic filmwhile avoiding any thermal instability in the magnet or sam-ple. Our power supply has a high bandwidth (>800 Hz) andhence the ramp-rate limiting factor is its 36 V maximum out-put voltage, since the potential across the coil has both re-sistive IR and inductive LdI / dT components during mag-net charging/discharging. We find that a minimum rate of20 As − ( ∼ . − ) can be achieved even close to maximumfield, which is consistent with the measured magnet resistance1.22 Ω and calculated inductance (0.083 H for 622 coils).We demonstrate the thermal stability of the magnet during a2 second pulse to maximum field in Fig. 6(a). Before applyingthe pulse, the magnet is cooled to ∼
286 K by the 10 ◦ C chilledwater circuit. The sample stage is stabilised at 298 K by regu-lating the heater output from the temperature controller whilepassing a constant 0.7 A current through the Peltier coolers.Following the pulse, the magnet body temperature only risesby 0 . et al. ( a ) M a g n e t S a m p l e
T i m e ( s e c o n d s )
Magnet Temperature (K)
Sample Temperature (K)
T i m e ( m i n u t e s )
Magnet Temperature (K) ( b )
Sample Temperature (K)
01 02 03 0
Current (A)
01 02 03 0
Current (A)
FIG. 6. (a) Thermal stability of the magnet and sample stage duringmagnet pulsing to maximum field. The slow drift to lower temper-atures is due to the cooling from the 10 ◦ C chilled water supply. (b)Long-term (1 hour) thermal stability of the magnet and sample ata constant field of 0.3 T. The data acquisition frequency is 1 Hz;the sample temperature only fluctuated above the ± tended imaging experiments at high fields) is illustrated inFig. 6(b). We pass a constant 17.6 A current through themagnet (corresponding to a 0.3 T field at the sample), whilecontinuously monitoring the magnet and sample temperaturesfor 1 hour. Although the magnet temperature rises by 16 Kduring this period, the sample stage is maintained at 298 Kwith the same ± ≈
318 K. At such high temperatures, the principal limitingfactor in our sample stage design is the heatsinking of the twoPeltier coolers on the copper sample block. If we attempt torecover thermal stability by increasing the Peltier current (and hence raising the cooling power), the waste heat at the hotside of the Peltier chips cannot dissipate sufficiently quicklyinto the magnet body and the sample stage is thermally over-loaded.The thermal decoupling between sample stage and magnetbody also enables experiments to be performed above roomtemperature. In its present configuration, our apparatus is lim-ited to operation below 90 ◦ C, since the solder joints in thePeltier coolers risk failure through thermal fatigue above thistemperature. The Delrin arms on the sample stage are notexpected to deform until at least 120 ◦ C, while the insulationmaterials used to assemble the magnet are rated for use up to180 ◦ C. We therefore anticipate that by substituting the Del-rin with a carbon fiber matrix (or a similar heat-tolerant, lowthermal conductivity material), and replacing the Peltier cool-ers with versions adapted for high temperature use, measure-ments could be performed up to at least 180 ◦ C. At this tem-perature, we estimate that the magnet body would experiencea heat load ≈ VII. CONCLUSIONS
We have designed and built a ± ± VIII. DATA AVAILABILITY
The data which support the findings of this study are avail-able from the corresponding authors upon reasonable request.
ACKNOWLEDGMENTS
We acknowledge support from the Singapore NationalResearch Foundation (NRF) NRF-Investigatorship (No.NRFNRFI2015-04), Singapore MOE Academic ResearchFund Tier 3 Grant MOE2018-T3-1-002 and Tier 1 GrantM4012006. We are grateful to Alex Rajan and ChandraboseRajagopal from Ebenezer Exel Engineering for technical as-sistance. S. N. Piramanayagam, “Perpendicular recording media for hard diskdrives,” Journal of Applied Physics , 011301 (2007). etrovi´c et al. S. Ikeda, K. Miura, H. Yamamoto, K. Mizunuma, H. D. Gan, M. Endo,S. Kanai, J. Hayakawa, F. Matsukura, and H. Ohno, “A perpendicular-anisotropy CoFeB-MgO magnetic tunnel junction,” Nature Materials , 721(2010). F. Hellman, A. Hoffmann, Y. Tserkovnyak, G. S. D. Beach, E. E. Fuller-ton, C. Leighton, A. H. MacDonald, D. C. Ralph, D. A. Arena, H. A.Dürr, P. Fischer, J. Grollier, J. P. Heremans, T. Jungwirth, A. V. Kimel,B. Koopmans, I. N. Krivorotov, S. J. May, A. K. Petford-Long, J. M.Rondinelli, N. Samarth, I. K. Schuller, A. N. Slavin, M. D. Stiles, O. Tch-ernyshyov, A. Thiaville, and B. L. Zink, “Interface-Induced Phenomena inMagnetism,” Reviews of Modern Physics , 025006 (2017). C. Moreau-Luchaire, C. Moutafis, N. Reyren, J. Sampaio, C. A. F. Vaz,N. Van Horne, K. Bouzehouane, K. Garcia, C. Deranlot, P. Warnicke,P. Wohlhüter, J.-M. George, M. Weigand, J. Raabe, V. Cros, and A. Fert,“Additive interfacial chiral interaction in multilayers for stabilization ofsmall individual skyrmions at room temperature,” Nature Nanotechnology , 444 (2016). A. Soumyanarayanan, M. Raju, A. L. Gonzalez Oyarce, A. K. C. Tan, M. Y.Im, A. P. Petrovi´c, P. Ho, K. H. Khoo, M. Tran, C. K. Gan, F. Ernult,and C. Panagopoulos, “Tunable room-temperature magnetic skyrmions inIr/Fe/Co/Pt multilayers,” Nature Materials , 898–904 (2017). A. Fert, V. Cros, and J. Sampaio, “Skyrmions on the track,” Nature Nan-otechnology , 152–156 (2013). K. M. Song, J. S. Jeong, B. Pan, X. Zhang, J. Xia, S. Cha, T. E. Park,K. Kim, S. Finizio, J. Raabe, J. Chang, Y. Zhou, W. Zhao, W. Kang, H. Ju,and S. Woo, “Skyrmion-based artificial synapses for neuromorphic com-puting,” Nature Electronics , 148–155 (2020). J. Igarashi, J. Llandro, H. Sato, F. Matsukura, and H. Ohno, “Magnetic-field-angle dependence of coercivity in CoFeB/MgO magnetic tunnel junc-tions with perpendicular easy axis,” Applied Physics Letters , 132407(2017). C. Moutafis, S. Komineas, C. A. Vaz, J. A. Bland, T. Shima, T. Seki,and K. Takanashi, “Magnetic bubbles in FePt nanodots with perpendicu-lar anisotropy,” Physical Review B , 104426 (2007). R. Lavrijsen, J. H. Franken, J. T. Kohlhepp, H. J. Swagten, and B. Koop-mans, “Controlled domain-wall injection in perpendicularly magnetizedstrips,” Applied Physics Letters , 222502 (2010). A. Talapatra and J. Mohanty, “Laser induced local modification of magneticdomain in Co/Pt multilayer,” Journal of Magnetism and Magnetic Materials , 224–230 (2016). P. M. Shepley, H. Tunnicliffe, K. Shahbazi, G. Burnell, and T. A. Moore,“Magnetic properties, domain-wall creep motion, and the Dzyaloshinskii-Moriya interaction in Pt/Co/Ir thin films,” Physical Review B , 134417(2018). S. Mangin, D. Ravelosona, J. A. Katine, M. J. Carey, B. D. Terris, and E. E.Fullerton, “Current-induced magnetization reversal in nanopillars with per-pendicular anisotropy,” Nature Materials , 210–215 (2006). E. M. Williams, “The Dorf Effect: Magnetization Ripple In Particulate Me-dia,” IEEE Transactions on Magnetics
MAG-18 , 1086 (1982). R. Proksch, E. Runge, P. K. Hansma, S. Foss, and B. Walsh, “High fieldmagnetic force microscopy,” Journal of Applied Physics , 3303–3307(1995). R. D. Gomez, E. R. Burke, and I. D. Mayergoyz, “Magnetic imaging in thepresence of external fields: Technique and applications (invited),” Journalof Applied Physics , 6441 (1996). J. Mohanty, R. Engel-Herbert, and T. Hesjedal, “Variable magnetic fieldand temperature magnetic force microscopy,” Applied Physics A , 1359(2005). T. A. Harroun, C. M. Desrochers, M. P. Nieh, M. J. Watson, and J. Kat-saras, “0.9 T static magnetic field and temperature-controlled specimen en-vironment for use with general-purpose optical microscopes,” Review ofScientific Instruments , 014102 (2006). R. Oldenbourg and W. C. Phillips, “Small permanent magnet for fields upto 2.6 T,” Review of Scientific Instruments , 2362–2365 (1986). O. Cugat, P. Hansson, and J. M. D. Coey, “Permanent Magnet Variable FluxSources,” IEEE Transactions on Magnetics , 4602–4604 (1994). N. K. Duong, M. Raju, A. P. Petrovi´c, R. Tomasello, G. Finocchio, andC. Panagopoulos, “Stabilizing zero-field skyrmions in Ir/Fe/Co/Pt thin filmmultilayers by magnetic history control,” Appl. Phys. Lett. , 072401(2019). Model VFM4, Asylum Research, Oxford Instruments, Goleta, CA. Vertical field option, NTEGRA nanolaboratory, NT-MDT Spectrum Instru-ments, Moscow, Russia. Perpendicular Electromagnet, Evico Magnetics GmbH, Dresden, Germany. Perpendicular Coil, Evico Magnetics GmbH, Dresden, Germany. D. Meeker, “Finite Element Method Magnetics,” . Model BOP 36-28GL, Kepco Inc., Flushing, NY. EP21TCHT-1 single-component epoxy, Master Bond Inc., Hackensack, NJ. .060”x.175” Heavy GP/MR-200 rectangular MW 36 copper magnet wire,Superior Essex Inc., Atlanta, GA. MC4236 / W4236 two component epoxy potting compound, ElantasMalaysia Sdn. Bhd., Selangor Darul Ehsan, Malaysia. Model XHGT-9060, Lake Shore Cryotronics Inc., Westerville, OH. Vacoflux 50, Vacuumschmelze GmbH, Hanau, Germany. Model PT-103, Lake Shore Cryotronics Inc., Westerville, OH. Model 325, Lake Shore Cryotronics Inc., Westerville, OH. Adaptive Models ET-063-08-15 and ET-031-08-15-RS, European Thermo-dynamics Ltd., Kibworth, United Kingdom. Epo-Tek E4110, Epoxy Technology Inc., Billerica, MA. Model PTR21-2.5, Kepco Inc., Flushing, NY. Rogers Corporation RO3003, Chandler, AZ. Epo-Tek H70E-2, Epoxy Technology Inc., Billerica, MA. Models LI-102 and LI-301, Thermo Electric Devices, Draycott, UnitedKingdom.41