Controlling Domain-Wall Nucleation in Ta/CoFeB/MgO Nanomagnets via Local Ga+ Ion Irradiation
Simon Mendisch, Fabrizio Riente, Valentin Ahrens, Luca Gnoli, Michael Haider, Matthias Opel, Martina Kiechle, Massimo Ruo Roch, Markus Becherer
CControlling Domain-Wall Nucleation in Ta/CoFeB/MgO Nanomagnets via Local Ga + IonIrradiation
Simon Mendisch, ∗ Valentin Ahrens, Michael Haider, Martina Kiechle, and Markus Becherer
Department of Electrical and Computer Engineering, Technical University of Munich, Arcisstr. 21, 80333, Munich, Germany
Fabrizio Riente, † Luca Gnoli, and Massimo Ruo Roch
Department of Electronics and Telecommunications Engineering, Politecnico di Torino, 10129, Turin, Italy.
Matthias Opel
Bavarian Academy of Sciences, Walther-Meißner-Straße 8, 85748, Garching, Germany (Dated: February 16, 2021)Comprehensive control of the domain wall nucleation process is crucial for spin-based emerging technolo-gies ranging from random-access and storage-class memories over domain-wall logic concepts to nanomagneticlogic. In this work, focused Ga + ion-irradiation is investigated as an effective means to control domain-wall nu-cleation in Ta/CoFeB/MgO nanostructures. We show that analogously to He + irradiation, it is not only possibleto reduce the perpendicular magnetic anisotropy but also to increase it significantly, enabling new, bidirectionalmanipulation schemes. First, the irradiation effects are assessed on film level, sketching an overview of thedose-dependent changes in the magnetic energy landscape. Subsequent time-domain nucleation characteristicsof irradiated nanostructures reveal substantial increases in the anisotropy fields but surprisingly small effectson the measured energy barriers, indicating shrinking nucleation volumes. Spatial control of the domain wallnucleation point is achieved by employing focused irradiation of pre-irradiated magnets, with the diameter ofthe introduced circular defect controlling the coercivity. Special attention is given to the nucleation mecha-nisms, changing from a Stoner-Wohlfarth particle’s coherent rotation to depinning from an anisotropy gradient.Dynamic micromagnetic simulations and related measurements are used in addition to model and analyze thisdepinning-dominated magnetization reversal. I. INTRODUCTION
Magnetic nanostructures based on Cobalt-Iron-Boron/Magnesium-oxide (CoFeB/MgO) thin films, withand without perpendicular magnetic anisotropy (PMA), playa vital role in many emerging technologies, from magnetictunnel-junction based sensors over non-volatile storagetechnologies, towards domain-wall and nanomagnetic logicapplications[1–5]. Especially logic applications necessitateprecise control of the magnetic energy landscape to nucleate,propagate and pin/depin domain-walls — a level of controlthat remains a significant challenge [6, 7]. As widely es-tablished semiconductor technology with unmatched spatialresolution and a wide tuning range, ion irradiation is ideallysuited to address these issues [8]. It offers a realistic perspec-tive to modify magnetic properties with nanometer precision.So far, studies on the irradiation effects on CoFeB/MgO havemainly been restricted to film level investigations and light(He + ) ions [9–11]. In this work, we investigate the usage ofheavier Ga + ions in an attempt to create artificial nucleationcenters (ANC) in Ta/CoFeB/MgO nanomagnets with PMA,employing localized ion irradiation (not implantation), thuscontrolling domain wall (DW) nucleation. Gallium ions arechosen, as they are known to reduce the anisotropy in crys-talline multilayer systems effectively [12]. Heavier atoms,furthermore, can be stopped much more effectively, reducing ∗ [email protected] † [email protected] potential damage to underlying layers. The dose-dependentirradiation effects are first evaluated on film level, probingmaterial parameter and domain configurations, before thefocus is shifted towards the irradiation of nanostructures andtime-domain measurements. We thereby explain the differenttime-dependent DW nucleation probabilities, from whichinformation regarding nucleation mechanisms (coherentrotation or depinning) and irradiation effects are derived.Unitizing this analysis, we employ irradiation at the mag-net’s centers to control the switching fields and force DWnucleation via depinning instead of coherent rotation. II. FABRICATION AND CHARACTERIZATIONA. Device Fabrication
The magnetic thin film analyzed in this work isbased on a Ta/CoFeB/MgO/Ta sandwich structure witha Co Fe B alloy target and nominal thicknesses ofTa /CoFeB /MgO /Ta (numbers given in nm). The film isdeposited at room temperature via confocal RF-magnetronsputtering (base pressure < 2 × − mbar) onto silicon (cid:104) (cid:105) substrates, topped by a thermal oxide (thickness ≈
50 nm).The individual materials are deposited at a constant workingpressure of 4 µbar ( ≈ . − for all mate-rials. Post deposition annealing ( 250 °C, N atmosphere) isused to set the effective anisotropy to the desired value of ≈ . × J m − . The stack is subsequently structured via fo-cused ion beam (FIB) lithography (using PMMA as a positive a r X i v : . [ c ond - m a t . m e s - h a ll ] F e b ion-beam resist) to realize the designed test-structures. Thelithography profile is inverted, after PMMA development, bydepositing a 5 nm thick Ti hard-mask and removing the resid-ual PMMA in a lift-off process. Finally, the non-masked areasare physically etched via Ar + ion-beam etching ( E =
350 eV).To generate ultra-short magnetic field pulses, on-chip fieldcoils are placed around the structures via conventional opti-cal contact lithography together with the deposition of a Cumetal layer ( ≈
750 nm) and a second lift-off process. TheGa + ion-irradiation, changing the magnetic properties, is car-ried out using a 50 keV focused-ion-beam (FIB) microscope(Micrion 9500ex) with a spatial resolution (beam diameter) of ≈
10 nm. For large areas, the beam is de-focused to achievehomogeneous irradiation results.
B. Magneto-Optical Imaging
The magnetic nanostructures are characterized via Wide-field Kerr-microscopy (WMOKE), both for the quasi-staticcase as well as for time-domain measurements. Static coer-civities are obtained by merely applying a stair-case field pro-file with images taken at every step. In a later data-processingstep, the coercivities of the individual magnets can be derivedfrom the respective brightness changes in the images. Reli-able time-domain measurements, however, require a more so-phisticated measurement scheme. Ultra short magnetic fieldpulses are generated via (single winding) on-chip coils, whichare bonded to pulse discharge-capacitors on the high-side,and a low-side switch. This switch is driven by a fast gate-driver and is addressed with an Agilent 81111A Pulse Gen-erator. To measure the nucleation probability p nuc of the in-dividual magnets at short timescales, the on-chip field pulsesin the ns-range are synchronized with the image acquisitionof a high dynamic-range sCMOS camera. Figure 1 depicts arough sketch of this imaging procedure. After the initial sat-uration of the magnets, a first reference image is taken. Con- Diff.-Image18 (cid:181) m Time a.u. µ H e x t a . u . Ref.-ImageOn-Chip Pulse ≈
10 ms Delay 10 ms Propagation-PulseProbing-Image
FIG. 1. Sketch of the employed measurement scheme, illustrating theprocedures in a time-line. First, a reference image of the saturatedmagnet array is taken. Subsequently, the on-chip pulse with varyingwidths of t p =
10 ns to 100 µs is triggered before a second, millisec-ond long pulse is used to propagate remaining DWs and completethe reversal process. After the propagation pulse, a second image istaken, which is subtracted from the reference image. The final dif-ference image is then used for the later analysis. This procedure isrepeated multiple times to gain statistical data for the magnets in theimage frame. secutively, the on-chip pulse is triggered to nucleate a DW. Asecond propagation pulse with a low amplitude ( ≈ III. RESULTS & DISCUSSIONA. Areal Irradiation and Static Measurements
To understand and interpret the irradiation dependentchanges in the domain wall dynamics of nanostructures, wefirst analyze the irradiation effects on film level. This al-lows probing the essential material parameter ( M s and K eff )via comparatively simple though error-prone magnetometermeasurements. The material parameters are extracted fromSQUID and VSM-magnetometer loops. K eff is thereby ap-proximated from the hard-axis loops via the area method [13].The uniaxial anisotropy constant K u , necessary for the micro-magnetic simulations, is calculated as K u = K eff + µ M .Figure 2 (a) depicts the irradiation-induced changes in M s as well as K eff with increasing ion dose. Similar to reportson the He + irradiation of Ta/CoFeB/MgO films, a decreasein saturation magnetization accompanied by an increase inanisotropy is observed. Figure 2 (b) furthermore depicts theirradiation dependent static coercivities ( H c ) of circular nano-dots ( d = ∝ K eff . The data pointsdisplay the center of the respective switching field distribu-tion (SFD), with the error bars indicating the full width athalf maximum (FWHM). Thereby, 80 magnets are probed foreach ion dose. The coercivity and thus K eff initially increasesfor low and medium doses and only starts to fall off at doseshigher ≈ . × ions / cm with the domain size droppingbelow the resolution limit at a dose of ≈ × ions / cm .The magnets cross the single-domain threshold at this point.It has to be noted that the apparent decrease in K eff above ≈ . × ions / cm could not be replicated via correspond-ing magnetometer measurements. This fact might, however,be explained by the macroscopic nature of the magnetometermeasurements, complicating the detection of small changesin the anisotropy landscape. Explaining the non-monotonicevolution of K eff is difficult without a detailed stoichiometricanalysis, and therefore no comprehensive explanation can begiven. However, as with He + irradiation [9, 14], the behav-ior might be explained by the respective atomic weights of the · . . . . · Ga + dose in ions / cm M s / A m − . . . . · K / J m − ] M s K eff K u Ta \ CoFeB \ MgO \ Ta (a) (b) Ga + dose in ions / cm µ H c / m T Ta \ CoFeB \ MgO \ Ta Irradiated nano-dots, d = 1 (cid:181) m 40 (cid:181) mDomain configurations after easy-axis demagnetization FIG. 2. The plot in (a) depicts the measured material parameter M s and K eff of the film, together with the calculated uniaxial anisotropyterm K u = K eff − µ M versus the applied ion dose. In (b), the Ga + dose-dependent coercivity evolution of circular Ta /CoFeB /MgO nano-magnets ( d = different elements inside the stack, giving the Ga + ions a muchlarger probability to interact with the heavy Ta rather than withthe comparatively light Fe, Co, or O atoms. Since Tantalumis known for its large magnetic dead layer in contact with fer-romagnets, we assume intermixing at the Ta/CoFeB interfaceto be the dominant cause for the decrease in M s [9, 14]. Apossible explanation for the non-monotonicity in K eff couldbe that due to this reduced interaction probability, the damageto the CoFeB/MgO interface and thus K u only becomes rel-evant at much higher doses[9, 14]. Closely related to this isthe likely accumulation of Tantalum atoms at the CoFeB/MgOinterface, also strongly affecting the anisotropy [15]. An in-teresting observation related to the anisotropy decrease is theformation of highly ordered stripe domains at high ion doses,indicating changes in more than the primary material param-eter. This is in line with reports on the increase of the interfa-cial Dzyaloshinskii-Moriya interaction upon the irradiation ofTa/CoFeB/Mg films [11]. B. Controlling the Magnetization Reversal
We have already shown that the magnets’ coercivities canbe effectively tailored by adjusting the ion dose. However,static measurements only provide limited insight into the re-versal mechanisms and are not suited to derive relevant con-clusions. Therefore, we attempt a characterization of theirradiation dependent reversal process by probing the time-dependent magnetization reversal. For this purpose, we pro-vide a sample-base of at least 40 magnets per data-point, re-ducing the effects of statistical outliers. Contrary to the dis-tribution of the demagnetizing fields, DWs in CoFeB/MgOnano-magnets usually nucleate at the nanostructures’ edgesdue to an etch-damage induced lowering of K eff [16, 17]. Tovalidate this assumption for the test structures, 20 ns longmagnetic field pulses are used to nucleate DWs in circular nano-disks with a diameter of 2 . (a)
10 15 20 25 30 35 4000 . . . . Sharrock Criteria µ H c / mT S w i t c h i n g P r o b a b ili t y Pulse width = 100 (cid:181) sPulse width = 1 (cid:181) sPulse width = 50 ns . (cid:181) m (b) FIG. 3. Plot (a) depicts the measured, field-dependent, nucleationprobabilities of a 1 µm nanomagnet for different pulse widths. Theimage in (b) depicts 1000 superimposed differential WMOKE im-ages of the nucleation events inside a 2 . The image indicates the accumulation of nucleation eventsat the edges of the disks, while an inhomogeneity in the ap-plied on-chip fields most likely explains the asymmetry to-wards the right side. Images of single nucleation events anda sanity check without nucleation can be found in the sup-plementary information (SI). The conformation of nucleationfrom the edges has severe implications. Instinctively, onewould expect the nucleation to occur at points with strongdemagnetizing fields, i.e., the center of the magnet. How-ever, the demagnetizing fields are lowest at the edges, lead-ing to the conclusion that the reduction in K eff must be sig-nificantly larger than the anisotropy variations in the mag-nets’ center. Furthermore, the question arises, whether theDW nucleation occurs via coherent rotation according to the Stoner–Wohlfarth model or by depinning from an area witheasy-plane anisotropy [18, 19]. This can be resolved by con-sidering the time evolution of both processes. The rotationfields scale over time according to the well established
Shar-rock formalism based on an Arrhenius switching model of a
Stoner–Wohlfarth particle and can be expressed by H nuc = H s0 (cid:40) − (cid:20) k B TE ln (cid:18) f t p ln ( ) (cid:19)(cid:21) (cid:41) , (1)where H s0 is the switching field at 0 K, f is the attempt fre-quency ( ≈ × Hz), and E is the energy barrier withoutapplied field [18, 20, 21]. In contrast, the time necessary fora DW to overcome the anisotropy gradient and depin can bederived from the related Néel–Brown theory and scales ac-cording to τ = f − exp (cid:20) M s V a k B T ( H d − H ) (cid:21) , (2)with V a as the activation volume and H d as the depinning fieldat 0 K [19, 22, 23]. By characterizing the switching fields overa wide range of different timescales (pulse widths) and com-paring the evolution to the models in Eq. (1) and Eq. (2), itis possible to gather detailed information about the switch-ing mechanisms. Figure 4 displays the pulse-width dependentnucleation fields of the circular nano-dots with a diameter of1 µm. The measurements cover timescales ranging from thequasi-static case down to 10 ns. The data points resemble thecenter of the distribution, with the error-bars again display-ing the FWHM. The nucleation field H nuc is furthermore de-fined according to the Sharrock formalism, as the field witha switching probability p nuc ≥
50 %. Figure 3 (a) shows aseries of exemplary nucleation probability measurements fordifferent pulse widths with the
Sharrock criteria indicated asa dashed line. The plot furthermore depicts corresponding fitsaccording to the Arrhenius switching model with the prob-ability p nuc = − exp ( − t p τ nuc ) , with τ nuc as the inverse of thenucleation rate [21].
1. Nucleation by Coherent Rotation
We first consider the pristine magnets and compare thedata to the aforementioned nucleation and depinning domi-nated models. The nucleation fields show good agreementwith the numerical fits according to the
Sharrock equation,displayed as black lines; the fitting parameters converge to H s0 = ( . ± . ) mT and E k B T = ( . ± . ) . Addi-tionally, we attempt to fit equation Eq. (2) analytically byminimizing its cumulative error-function utilizing a linearizedleast-squares problem [24]. However, an acceptable solution (displayed as a dotted line) is only obtained excluding pulsewidths < >
10 µs) depinningfrom the nucleation sites, could very well be the limiting fac-tor, thus explaining the apparent underestimation of the
Shar-rock fits at quasi-static fields. The question now arises whether − − − − − − − − − t p / s µ H nu c / m T PristineDose ≈ . × ions / cm Dose ≈ . × ions / cm Sharrock-FitsDepinning-Fit E k B T = 30 . ± . H s0 = (36 . ± . E k B T = 27 . ± . H s0 = (76 . ± . E k B T = 34 . ± . H s0 = (87 . ± . FIG. 4. Calculated nucleation fields ( H nuc ) depending on the ap-plied pulse width. The individual data points display the center of theSFDs with the error bars displaying the FWHM. The corresponding Sharrock fits are illustrated as black lines. A fit, assuming depin-ning mediated nucleation according to equation (2) for the pristinemagnets is illustrated in red. Ga + irradiation not only increases the effective anisotropy ofthe disk’s core but whether its effect on the pre-damaged edgesis different. Therefore, Fig. 4 also displays the time evolu-tion of nano-disks homogeneously irradiated with a dose of3 . × ions / cm and 4 . × ions / cm . The doses arechosen to probe the peak of the static coercivity increase aswell as a position within the downward slope. For better il-lustration, the doses are marked, in their respective colors, asdashed lines in Fig. 2 (b). The slopes, again, indicate nucle-ation by coherent rotation as the dominant mechanism. Fromthe corresponding Sharrock fits, we derive the energy barri-ers to be E k B T = ( . ± . ) and E k B T = ( . ± . ) , re-spectively. The fields at which these barriers become zeroare determined to be H s0 = ( . ± . ) mT and H s0 =( . ± . ) mT. The energy barrier can be roughly mod-eled as E ≈ K eff V nuc with V nuc as the nucleation volume (notto be confused with the activation volume V a )[20]. The nucle-ation field at 0 K, on the other hand, is equal to the anisotropyfield H anis ≈ K eff M s [18, 20]. Comparing the derived parame-ters of the pristine magnets with those irradiated, two distinctobservations become apparent. The intrinsic switching field H s0 scales in accordance with the increase in anisotropy andthe reduction of M s . The energy barrier E k B T , however, in-creases (if at all) only marginally, despite the increase in K eff .Of course, the conducted measurements are limited in scopeand only allow for a cautious interpretation of this unexpectedresult. Irradiation induced reductions in the nucleation vol-umes V nuc could compensate for or even surpass the increasein anisotropy. However, this would conflict with the current,simplistic picture of a homogeneous change in the material pa-rameter of an effective medium. The analyzed doses translateto one Ga + ion roughly every 2 nm if applied homogeneously.The focused ion beam is, thereby, scanned horizontally (line-wise) across the magnets with a constant speed. While thehorizontal and vertical ion spacings are assumed to be reason-ably constant, they are not expected to be the same, as thehorizontal lines must be stitched together vertically. This ar-tificial lattice could account for the reduced nucleation vol-umes. However, additional studies are needed to give a moredetailed answer. Attempts to determine the local nucleationprobability as for the pristine magnets were unsuccessful, asthe high nucleation fields result in very high DW velocities,leading to complete reversals already within a fiew ns.
2. Nucleation by Depinning
Controlling the position of DW nucleation with high spatialaccuracy is an essential requirement for prospective DW ap-plications. By targeted irradiation, the anisotropy can, in prin-ciple, be lowered locally, creating so-called artificial nucle-ation centers (ANC) [25]. However, the known occurrence ofsignificant anisotropy lowering (with unknown distribution)towards the edges severely impedes efforts to create the nu-cleation volume with the lowest PMA reliably. Nucleation byDW depinning from a fixed anisotropy gradient (e.g., an areawith strongly reduced or easy-plane (negative) anisotropy),however, offers an interesting alternative. Here, the anisotropycan be lowered by much larger extents, provided that the de-pinning fields fall below the intrinsic nucleation fields (viacoherent rotation) [12]. Furthermore, the depinning processis governed by different time dynamics, leading to potentiallylower switching fields upon approaching timescales close to τ , which are, of course, most interesting for applications. Forthis purpose, ANCs with an anisotropy close to zero are placed
400 nm (a) d = 2 . (cid:181) m ~M ≈ . K u A ex = 2 × − Jm − K u ≈ . × Jm − α = 0 . M s = 6 . × Am − (b) d = 1 (cid:181) m
400 nm (c) K u d = 1 (cid:181) m FIG. 5. Image (a) depicts a differential WMOKE image of aTa/CoFeB/MgO nano-disk with a diameter of 2 . ≈ K u inside the ANC area. Image (c) depicts the grain structure of oneof the simulated samples, with the colors representing the respec-tive anisotropies. ANC and magnet are separated by a 30nm broadtransition region (illustrated in green) with a linear anisotropy gradi-ent. The simulated dots’ grain and mesh sizes are set to ≈ . × . in the nanomagnets’ center ( d = . × ions / cm is used to increase K eff beyond its peak (at ≈ . × ions / cm ). The effectiveanisotropy is subsequently reduced by a second, target irra-diation in the center, with an additional 3 . × ions / cm leading to a cumulative total dose of ≈ × ions / cm for the ANC. For this dose, Fig. 2 (b) shows a coercivity of ≈ . d ≈
400 nm) at the center of the circular mag-net, which matches the irradiated ANC area’s size, indicatesa change in the magnetization direction. However, it is notclear whether the magnetization of the ANC points in-planeor whether it is being aligned anti-parallel by the demagne-tizing fields of the host magnet. Complementary to the ex-periments, a simulation model was developed to better ana-lyze and understand the magnetization reversal in this geom-etry. The model parameters are chosen to best approximatethe characterized magnets. A detailed representation is de-picted in Fig. 5 (b,c) (see SI for more additional information).The depinning from the ANC can be verified by analyzingthe time dependence of the switching fields. This is done fora series of magnets with centered circular ANCs (diametersranging from d =
100 nm to d =
400 nm). The cumulativeion dose of all ANCs is 8 × ions / cm (keeping in mindthe background dose of 4 . × ions / cm ). Fig. 6 depictsthe measured nucleation fields with their corresponding fitsaccording to equation (2). The measured nucleation fieldsappear to agree well with the depinning model down to lowµs timescales. From this point onward, H nuc seemingly in-creases drastically, reaching levels close to those of the irradi-ated magnets in Fig. 4. However, a doubling of the nucleationfields within one order of magnitude (time) is hardly explain-able by any reasonable depinning or rotation model. To ex-plain the observed increase in H nuc , it is necessary to considerthe measurement procedure discussed in section II B. After the − − − − − − − − t p / s µ H nu c / m T ANC d = 400nmANC d = 300nmANC d = 200nmANC d = 100nm t p ≈ τ = τ exp h M s V a k B T ( H d − H ) i , τ ≈ Background Dose ≈ . × ions / cm Cumulative ANC Dose ≈ × ions / cm H c without ANC = (13 . ± . H d e p i n = . m T V a ≈ . × − m V a ≈ . × − m V a ≈ . × − m H d e p i n = . m T H d e p i n = . m T FIG. 6. Measured nucleation fields of double-irradiated nano-disks( d = t p . The disks fea-ture circular, different sized ANCs at their centers with the respectivediameter given in the legend. initial (ns-long) nucleation pulse, a secondary (ms-long) lowfield pulse is used to propagate the DW and ensure a completemagnetization reversal. However, the time between these twopulses allows the magnetization to relax back into the nearestlocal energy minimum. For a significant portion of the rever-sal process, this means to flip back into the initial state. Weattempt to explain this phenomenon by a simplified but vividmodel and underline it via micro-magnetic simulations andrelated measurements. After the initial depinning from theANC, the domain expansion can, in first approximation, bemodeled as the expansion of a circular bubble from the pointof depinning (engulfing half of the ANC area to reduce its DWlength). During this process, the system gains exchange andanisotropy energy as the DW length grows with the circum-ference ( ∝ π r domain ) until reaching the magnet’s edge, whereit splits into two DWs with lengths ∝ r magent . The reducingdemagnetizing fields do not compensate for this energy gain,as the magnet features a single-domain ground state. With-out an external field, the bubble provided it has not reachedthe edge tends to collapse (it snaps back to the starting point)as the DW tries to lose energy by reducing its length. Thiseffective force on the DW is also described as a Laplace-likepressure, reported in circular domain-structures, with a r de-pendence [17, 26, 27]. Figure 7 illustrates the evolution ofthe total energy (without Zeeman terms) and respective snap-shots of the domain structure throughout the reversal process.Data and images are derived from MuMax3 micromagneticsimulations of a 1 µm nanomagnet with a centered ANC ac-cording to Fig. 5 (b,c) [28]. The simulation parameters (listedin the plot) are thereby chosen to resemble the characterizedmagnets best. As described in the model above, the total en-ergy initially increases significantly as the bubble domain ex-pands towards the edge, where it reaches a tipping point be-fore falling off, as the DW splits, reducing its length. Afterovercoming this energy barrier, the domain configuration canbe described as quasi-stable until the propagation pulse com-pletes the reversal process. In other words, Fig. 6 displays thefields necessary to form a quasi-stable domain rather than todepin a DW. In addition to dynamic simulations, it is possi-ble to test the model implicitly by measuring certain depen-dencies. Assuming correctness of the model, larger magnetswould require stronger fields to propagate the DW to the edgewithin the pulse duration. Figure 8 compares the nucleationfields of two different magnet sizes with diameters of 1 µmand 2 . t p <
200 ns, the measured nu-cleation fields start to diverge, with the larger magnets requir-ing significantly higher field strengths for the DWs to form thenecessary quasi-stable multi-domain state. However, it has tobe noted that data for the 2 . . . . . . . . . . . · − − . − . − . · − Time / s E t o t a l − E Z ee m a n / J E total − E Zeeman H z H pu l s e / m T (cid:181) m A ex = 2 × − J m − K u ≈ . × J m − M s = 6 . × A m − K ANCu ≈ . × J m − α = 0 . FIG. 7. Plot of the simulated magnetization reversal process, depict-ing a 1 µm circular nanomagnet with centered ANC ( d = Zeeman term) in combination with snapshots of the domain structureat relevant points. The assumed material parameters are listed in theplot. Further information about the simulations can be found in thesupplementary information. cleation fields, it is possible to derive upper and lower boundsfor the collapse times. In case the domain collapses within thetime between pulses, the switching fields should be indepen-dent of the number of pulses (at least in first approximation,not considering the higher attempt count per measurement).Starting at ≈ <
50 ns, comparable nucleation fields are ob-served. All these observations and simulations let us assumethat the depinning fields scale according to equation (2) evenbelow µs pulse widths.Upon analyzing the ANC size-dependent depinning fields − − − − − − − − t p / s µ H nu c / m T . (cid:181) m disk, ANC 400nm1 (cid:181) m disk, ANC 400nm2 . (cid:181) m disk, ANC 400nm, varying pulse period − − − − − − − Pulse period P pulse / s Pulse width = 50 nsBurst
Time A m p li t ud e Period Pulse width
FIG. 8. Combined plot, showing on the lower x -axis the nucleationfields over different pulse widths, 1 µm (orange) and 2 . x -axis (blue) displaysa sweep of the pulse period P pulse and its effects on the measured nu-cleation fields. The cumulative pulse-width is thereby kept constantat 1 µs (Burst = ) . d / (cid:181) m − µ H d e p i n / m T H depin V active . . . · − V a c t i v e / m H intdepin = (13 . ± .
1) mT
FIG. 9. A Plot of the depinning fields H depin at 0 K (on the left) com-bined with the activation volume V a (right) for the depinning from acircular ANC, depending on the ANC curvature d ANC . Both exhibita linear d dependence, however, with complementary slopes. Thedashed lines depict the best linear fits. in Fig. 6 and Fig. 9 , it becomes evident that the depinningprocess from the circular sources scales ∝ d ANC (the curvatureof the circle) and thus similar to DW depinning from a notch[29–31]. Figure 9 depicts both the effective activation vol-umes ( V a ) and the depinning fields at 0 K versus d ANC . V a iscalculated from equation (2) assuming M s ≈ × A m − .The intrinsic depinning field H intdepin of the anisotropy gradi-ent can be derived from the zero-intercept of the linear fitto be H intdepin = ( . ± . ) mT [29]. Analyzing the evolu-tion of the activation volume is more complicated. First ofall, it is necessary to point out that the calculated absolutevalues strongly depend on the value of M s , which is not pre-cisely known. The sizes for V a , although showing a linear d ANC dependence, shrink only marginally compared to thephysical dimensions of the respective ANCs. To better illus-trate this, we translate the activation volume into an effectiveANC diameter d effANC , assuming a cylindrical shaped volume( d effANC = (cid:112) V a / ( π t film ) ). This yields effective diameters from ≈
140 nm to 160 nm, indicating that, especially for the largerANCs, only a small portion takes part in the depinning pro-cess. This complies with the depinning models, predictingdepinning at the grain with the lowest anisotropy gradient.
IV. CONCLUSION
Ta/CoFeB/MgO films and nanostructures were irradiatedwith Ga + ions to globally and locally modify the magneticenergy landscape, aiming to effectively control the posi-tion of DW nucleation. It has been shown that K eff ini-tially increases up to doses of 3 . × ions / cm followedby a steep decline, crossing the easy-plane threshold at ≈ × ions / cm . The time-dependent nucleation field anal-ysis of irradiated magnets revealed shrinking nucleation vol-umes, despite increases in the anisotropy field and K eff . Con-trol over nucleation points and fields is achieved, employinga second focused irradiation, creating artificial regions witheasy-plane magnetization, from which a DW can depin. Thefields needed to depin a DW from this anisotropy gradientscale ∝ d ANC . ACKNOWLEDGMENTS
The authors would like to thank Michael Wack for thesupport in VSM measurements. Furthermore, we would liketo thank the IGSSE for its financial support. We gratefullyacknowledge the support of the NVIDIA Corporation withthe donation of a Titan XP GPU, which was used for thisresearch. Finally, we would like to acknowledge the supportof the Central Electronics and Information TechnologyLaboratory – ZEIT lab . [1] K. Garello, F. Yasin, S. Couet, L. Souriau, J. Swerts, S. Rao,S. Van Beek, W. Kim, E. Liu, S. Kundu, et al. , SOT-MRAM300mm integration for low power and ultrafast embedded mem-ories, in (IEEE, 2018)pp. 81–82.[2] F. Riente, S. Mendisch, L. Gnoli, V. Ahrens, M. R. Roch, andM. Becherer, Ta/CoFeB/MgO analysis for low power nanomag-netic devices, AIP Advances , 125229 (2020).[3] K. Garello, F. Yasin, H. Hody, S. Couet, L. Souriau, S. Sharifi,J. Swerts, R. Carpenter, S. Rao, W. Kim, et al. , Manufacturable300mm platform solution for field-free switching SOT-MRAM,in (IEEE, 2019) pp. T194–T195.[4] S. Sakhare, M. Perumkunnil, T. H. Bao, S. Rao, W. Kim,D. Crotti, F. Yasin, S. Couet, J. Swerts, S. Kundu, et al. , En-ablement of STT-MRAM as last level cache for the high per-formance computing domain at the 5nm node, in (IEEE, 2018)pp. 18–3.[5] F. Xie, R. Weiss, and R. Weigel, Hysteresis compensation basedon controlled current pulses for magnetoresistive sensors, IEEETransactions on Industrial Electronics , 7804 (2015). [6] M. Manfrini, A. Vaysset, D. Wan, E. Raymenants, J. Swerts,S. Rao, O. Zografos, L. Souriau, K. B. Gavan, N. Rassoul, et al. ,Interconnected magnetic tunnel junctions for spin-logic appli-cations, AIP Advances , 055921 (2018).[7] S. Mendisch, V. Ahrens, M. Kiechle, A. Papp, and M. Becherer,Perpendicular nanomagnetic logic based on low anisotropyCo/Ni multilayer, Journal of Magnetism and Magnetic Mate-rials , 166626 (2020).[8] J. Fassbender and J. McCord, Magnetic patterning by meansof ion irradiation and implantation, Journal of Magnetism andMagnetic Materials , 579 (2008).[9] T. Devolder, I. Barisic, S. Eimer, K. Garcia, J.-P. Adam, B. Ock-ert, and D. Ravelosona, Irradiation-induced tailoring of themagnetism of CoFeB/MgO ultrathin films, Journal of AppliedPhysics , 203912 (2013).[10] L. Herrera Diez, F. García-Sánchez, J.-P. Adam, T. Devolder,S. Eimer, M. El Hadri, A. Lamperti, R. Mantovan, B. Ocker,and D. Ravelosona, Controlling magnetic domain wall motionin the creep regime in He+-irradiated CoFeB/MgO films withperpendicular anisotropy, Applied Physics Letters , 032401(2015). [11] L. H. Diez, M. Voto, A. Casiraghi, M. Belmeguenai, Y. Rous-signé, G. Durin, A. Lamperti, R. Mantovan, V. Sluka, V. Jeudy, et al. , Enhancement of the Dzyaloshinskii-Moriya interactionand domain wall velocity through interface intermixing inTa/CoFeB/MgO, Physical Review B , 054431 (2019).[12] J. H. Franken, M. Hoeijmakers, R. Lavrijsen, and H. J. Swagten,Domain-wall pinning by local control of anisotropy in Pt/Co/Ptstrips, Journal of Physics: Condensed Matter , 024216(2011).[13] M. Johnson, P. Bloemen, F. Den Broeder, and J. De Vries, Mag-netic anisotropy in metallic multilayers, Reports on Progress inPhysics , 1409 (1996).[14] H. T. Nembach, E. Jué, K. Poetzger, J. Fassbender, T. J. Silva,and J. M. Shaw, Tuning of the dzyaloshinskii-moriya interac-tion by He + ion irradiation, arXiv:2008.06762 (2020).[15] N. Miyakawa, D. Worledge, and K. Kita, Impact of ta diffusionon the perpendicular magnetic anisotropy of Ta/CoFeB/MgO,IEEE Magnetics Letters , 1000104 (2013).[16] X. Zhang, N. Vernier, W. Zhao, L. Vila, and D. Ravelosona,Extrinsic pinning of magnetic domain walls in CoFeB-MgOnanowires with perpendicular anisotropy, AIP Advances ,056307 (2018).[17] Y. Zhang, X. Zhang, N. Vernier, Z. Zhang, G. Agnus, J.-R.Coudevylle, X. Lin, Y. Zhang, Y.-G. Zhang, W. Zhao, et al. ,Domain-wall motion driven by Laplace pressure in Co- Fe-B/MgO nanodots with perpendicular anisotropy, Physical Re-view Applied , 064027 (2018).[18] E. C. Stoner and E. Wohlfarth, A mechanism of magnetic hys-teresis in heterogeneous alloys, Philosophical Transactions ofthe Royal Society of London. Series A, Mathematical and Phys-ical Sciences , 599 (1948).[19] S.-B. Choe, D.-H. Kim, K.-S. Ryu, H.-S. Lee, and S.-C. Shin,Direct observation of Barkhausen effect in strip-patterned fer-romagnetic Co/ Pd multilayer films, Journal of applied physics , 103902 (2006).[20] M. P. Sharrock, Measurement and interpretation of magnetictime effects in recording media, IEEE Transactions on Magnet-ics , 4414 (1999).[21] W. Wernsdorfer, E. B. Orozco, K. Hasselbach, A. Benoit,B. Barbara, N. Demoncy, A. Loiseau, H. Pascard, and D. Mailly, Experimental evidence of the Néel-Brown modelof magnetization reversal, Physical Review Letters , 1791(1997).[22] W. F. Brown Jr, Thermal fluctuations of a single-domain parti-cle, Physical Review , 1677 (1963).[23] L. Néel, Théorie du traînage magnétique des ferromagnétiquesen grains fins avec applications aux terres cuites, Ann. géophys. , 99 (1949).[24] See supplemental material, .[25] S. Breitkreutz, J. Kiermaier, S. Vijay Karthik, G. Csaba,D. Schmitt-Landsiedel, and M. Becherer, Controlled reversalof Co/Pt dots for nanomagnetic logic applications, Journal ofApplied Physics , 07A715 (2012).[26] K.-W. Moon, J.-C. Lee, S.-G. Je, K.-S. Lee, K.-H. Shin, and S.-B. Choe, Long-range domain wall tension in Pt/Co/Pt films withperpendicular magnetic anisotropy, Applied Physics Express ,043004 (2011).[27] X. Zhang, N. Vernier, W. Zhao, H. Yu, L. Vila, Y. Zhang, andD. Ravelosona, Direct observation of domain-wall surface ten-sion by deflating or inflating a magnetic bubble, Physical Re-view Applied , 024032 (2018).[28] A. Vansteenkiste, J. Leliaert, M. Dvornik, M. Helsen, F. Garcia-Sanchez, and B. Van Waeyenberge, The design and verificationof MuMax3, AIP Advances , 107133 (2014).[29] K.-J. Kim, G.-H. Gim, J.-C. Lee, S.-M. Ahn, K.-S. Lee, Y. J.Cho, C.-W. Lee, S. Seo, K.-H. Shin, and S.-B. Choe, Depinningfield at notches of ferromagnetic nanowires with perpendicularmagnetic anisotropy, IEEE Transactions on Magnetics , 4056(2009).[30] K.-J. Kim and S.-B. Choe, Analytic theory of wall configura-tion and depinning mechanism in magnetic nanostructure withperpendicular magnetic anisotropy, Journal of Magnetism andMagnetic Materials , 2197 (2009).[31] J. J. Goertz, G. Ziemys, I. Eichwald, M. Becherer, H. J.Swagten, and S. Breitkreutz-v. Gamm, Domain wall depin-ning from notches using combined in-and out-of-plane mag-netic fields, AIP Advances6