Optimized cobalt nanowires for domain wall manipulation imaged by in situ Lorentz microscopy

Lorentz microscopy L. A. Rodr ıguez, C. Mag en, E. Snoeck, L. Serrano-Ram on, C. Gatel, R. C ordoba, E. Mart ınez-Vecino, L. Torres, J. M. De Teresa, and M. R. Ibarra Laboratorio de Microscop ıas Avanzadas (LMA), Instituto de Nanociencia de Arag on (INA), Universidad de Zaragoza, 50018 Zaragoza, Spain Departamento de F ısica de la Materia Condensada, Universidad de Zaragoza, 50009 Zaragoza, Spain Transpyrenean Associated Laboratory for Electron Microscopy (TALEM), CEMES-INA, CNRS-Universidad de Zaragoza, Toulouse, France CEMES-CNRS 29, rue Jeanne Marvig, B.P. 94347 F-31055, Toulouse Cedex, France Fundaci on ARAID, 50004 Zaragoza, Spain Instituto de Ciencia de Materiales de Arag on (ICMA), Universidad de Zaragoza-CSIC, 50009 Zaragoza, Spain Departamento de F ısica Aplicada, Universidad de Salamanca, 37008 Salamanca, Spain

][8][9][10][11][12] DW in magnetic nanostructures have therefore become a major topic for the research community in the field of Nanomagnetism.The specific DW configuration is the result of the balance between the magnetostatic energy, the magnetocrystalline anisotropy, and the exchange coupling.Therefore, along with the intrinsic properties of the magnetic material, it also depends on the geometry and the dimensions of the nanostructures. 13In magnetic nanowires (NWs), the possible DW configurations are either symmetric or asymmetric transverse walls (TWs) or vortex walls (VWs) and they move differently under the application of an external magnetic field or current. 14][12] Permalloy (Py) nanostructures have been extensively studied because of their low magnetocrystalline anisotropy, thus allowing the control of its magnetic properties simply adjusting its shape anisotropy.[5][6][7][8][9][10][11][12]15,16 The use of ferromagnetic materials alternative to Py and the development of advanced nanofabrication methods allowing creating magnetic nanostructures of dimensions less than 100 nm are however needed to explore their functionalities and possible applications.In the last years, focused electron beam induced deposition (FEBID) technique has demonstrated a capacity to produce high quality nanostructures based on multiple materials.FEBID uses a focused electron beam to locally decompose an organometallic gas injected in the proximity of a substrate and induces the growth of a deposit of the metal on the substrate surface. 17,18By tuning multiple growth parameters, high purity deposits can be produced.Particularly cobalt (Co) nanostructures have been obtained with purities up to 95% so these deposits present optimal properties matching those of the bulk counterpart. 19,20Furthermore, as the electron beam producing the deposition can be simply scanned upon the surface, nanostructures of various different shapes and size can be easily produced. 20The FEBID spatial resolution is also very high, down to 3 nm in the case of Pt deposits, 21 so this technique is capable of producing nanostructures with very fine details such as constrictions, needle shape tips, etc. 22 In a recent work, high purity Co NWs of lateral size down to 30 nm were produced by FEBID. 20Though the magnetic characterization of this type of systems has been carried out up to now by multiple indirect techniques, such as resistivity, magnetoresistance, Hall effect, magneto-optical Kerr effect, and electron microscopy, 19,20,[23][24][25] direct observation of the magnetic configurations and magnetization processes with high spatial a) Author to whom correspondence should be addressed.MFM can however only give qualitative information on the nature of the DW appearing in these nanostructures.More quantitative characterization of the in-plane magnetization with nanometer-range resolution can be performed using Lorentz transmission electron microscopy (LTEM) in Fresnel mode or Electron Holography.Both have demonstrated the combined possibility of very high spatial resolution with the capability of applying in-situ variation of external constraints such as temperature, 27,28 magnetic field, 6,8,12 or electric current. 15,16Furthermore, in LTEM phase retrieval by solving the transport-of-intensity equation (TIE) 29 enables the mapping of the in-plane magnetic induction of the material with the high spatial resolution.

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In this letter, we report the complete determination of the nucleation fields in L-shaped FEBID Co NWs as a function of the geometry (thickness and width) and applied magnetic field, analyzed through direct studies of the DW magnetic configurations by means of LTEM in Fresnel mode.We report the most favorable dimensions for the best DW conduit in this magnetic nanostructure.Detailed analysis of the DW configuration and magnetization orientation in these nanostructures were carried out by solving the TIE through focal series of Lorentz images and compared to micromagnetic calculations.We observed that the optimal dimension for DW propagation coincides with the crossover between the nucleation of TW and VW.
L-shaped Co NWs were grown by FEBID in a dual beam system Helios 600 Nanolab from FEI equipped with a gas injector system to inject the organometallic precursor gas Co 2 (CO) 8 inside the deposition chamber.The growth parameters to achieve high purity (>90%) Co structures have been optimized in previous works and a detailed description can be found elsewhere. 19The Co structures have been grown on electron-transparent 50-nm-thick Si 3 N 4 membranes, which are suitable for magnetic imaging in transmission experiments using electrons 20 or x-rays. 22The lengths of the two branches of the NWs were fixed for all the objects to 3.5 lm and 8.5 lm for the short and long branches, respectively.The width (w) and the thickness (t) of the Co nanostructures have been varied through the array, w ¼ 125, 250, 500, 1000 nm and t ¼ 5, 8, 10, 13, 16, 19, 22, 25, 30 nm. Figure 1(b) shows a low magnification TEM image to illustrate the morphology of the L-shaped Co NWs, in this case 500nm-wide and 30-nm-thick.LTEM experiments in Fresnel mode have been performed in a FEI Titan 60-300 Cube equipped with a Lorentz lens for TEM imaging in field-free conditions integrated in an objective lens aberration corrector (CETCOR from CEOS).Magnetic field has been applied to nucleate and manipulate DW by tilting the sample settled in a double tilt TEM specimen holder and slightly exciting the objective lens to produce an in-plane component of magnetic field. 30The value and orientation of the in-plane magnetic field have been calibrated with respect to the objective lens excitation and the tilt angles in order to automatically apply the desired value of the in-plane magnetic field compo-nent in a chosen direction in the plane of the sample.TIE analysis have been performed to retrieve the phase shift of the electron wave at the exit of the sample, 29 and then to reconstruct the in-plane magnetic induction. 31Micromagnetic simulations have been performed using the GPMagnet software package 32 to compare with the experimental data.Real physical dimensions have been used in the models.Inplane magnetic induction maps have been simulated as function of the applied magnetic field in order to determine the remanent magnetic states after DW nucleation.
A complete in-situ analysis of the nucleation field and of the configuration of the DW localized in the curved part of the NWs has been carried out as a function of the magnetic field.Propagation fields have also been measured in selected objects.To nucleate and propagate DW in the round corner of the L-shaped NW, we followed a procedure inspired in Ref. 23.The process is schematized in Figure 1(a).The magnetization is first aligned along the NW by applying a large field of approximately 400 Oe at 45 with respect to the L-shaped corner, and then the field is decreased down to zero and excited again at 90 from the previous field direction.The nucleation field (H N ) is the field value at which a DW is nucleated in the kink, and it is determined by the direct observation of the contrast changes associated with the presence of a DW in the under-focused LTEM image.The propagation field (H P ) can be determined immediately after measuring H N by decreasing the magnetic field down to zero and increasing it up at the same initial saturation direction before the nucleation process.H P is the magnetic field at which the DW moves out of the kink.In the nanostructures with intermediate dimensions (i.e., w ¼ 250 and 500 nm values), the formation of a DW is deduced from direct observation of lines of bright and dark contrast inside the NW kink.This is caused the deflection of the electron beam by the magnetic structure which depends on the relative orientation of the magnetization as seen in further Figure 4(a).In the case of very narrow objects, the DW structure is difficult to detect as the Fresnel fringes coming from the edges of the nanostructure are overlapping with the DW contrast lines.In such nanowires, H N is determined univocally by the observation of the contrast change of the Fresnel fringes along the edges of the NW.When the bright (resp.dark) lines along one side of a branch of the NW changes into dark (resp.bright), a change in the magnetization direction of the long branch has occurred and a DW has appeared.This effect is illustrated in Figures 1(c) and 1(d), in which under-focused LTEM images of a 1000nm-wide Co NW are shown in saturated state [Figure 1(c)] and in remanent state after nucleation [Figure 1(d)].A continuous bright (dark) contrast in the outer (inner) side of the whole NW is observed in the inset of Figure 1(b) because when the magnetization is saturated the electrons are deflected by the magnetization towards the same side of the NW in both branches.When the magnetization of the long branch is reversed and a head-to-head state is formed in the kink, a contrast reversal of the fringes along the long (horizontal) edges is observed because the magnetization of the two branches deflects the electrons in the opposite direction as observed in Figure 1(d).
Following this strategy, the DW nucleation takes places by a monodomain-type switching of the magnetization in the long branches.In our method, a domain wall is created in the tip of the longer branch and propagates almost instantaneously (after a small increase of the magnetic field) to the curved kink of the NW for H applied ¼ H N .The results of this study are plotted as a function of the width in Figure 2(a).The different experimental points are obtained by averaging the nucleation fields measured in several (up to 5) cycles.The error bars are calculated as the standard deviation of the measured values, and they are due to small hysteretic effects of the objective lens pole pieces and/or small variations in the assessment of the magnetic field value at which the DW is created and propagates.Most NWs present a clear decreasing dependency of H N as a function of the width, which qualitatively matches the theoretical dependence with the inverse of the width.However, those with the most reduced dimensions, for instance all those with w ¼ 125 nm and for w ¼ 250 nm for t < 13 nm, do not obey the theoretical prediction, presenting significantly diminished H N values.This can be explained in terms of a nucleation process dominated by extrinsic factors, such as the dominancy of the surface effects on the DW dynamics of the NW with reduced dimensions.As the surface-to-volume ratio increases, the role of surface roughness in the nucleation/propagation processes becomes more and more important, eventually causing a sudden drop of the H N values.These data are plotted differently in Figure 2(b), as a function of the thickness for the different sets of widths.In the NWs of largest and smallest width (1000 nm-and 125 nm-wide), H N hardly depends on the thickness (t), being constant around 50 Oe in the case of the 1000 nm-wide NWs and approximately 100 Oe for w ¼ 125 nm.A progressive increase of H N with thickness is observed in the 250 nm-wide NWs from 115 Oe for t ¼ 5 nm up to close to 285 Oe for t ¼ 30 nm.More interestingly, the 500 nm-wide NWs present a maximum of H N ¼ 196 Oe for t ¼ 13 nm, whereas in the thinnest NWs (t ¼ 5 nm) DW nucleates at 86 Oe, and at 155 Oe in the thickest ones (t ¼ 30 nm).
Due to the anomalous H N dependence observed, H P have been determined for the 500 nm-wide NWs, the result is plotted together with the H N values in Fig. 3.In sharp contrast with the H N thickness dependence, the propagation field presents a nearly constant value varying from 55 to 65 Oe in the thickness range from 8 to 22 nm.As a result, the optimal thickness (t ¼ 13 nm) that leads to a maximum nucleation field (H N ¼ 196 Oe) gives rise to the largest difference between the nucleation H N and the propagation H P fields (DH) of 142 Oe.Such a large DH is important to optimally manipulate the DW for information storage or processing, as it facilitates their independent nucleation and propagation at largely different fields.This is a crucial point to minimize the writing/reading errors due to random thermal DW depinning.Furthermore, the set of 500-nm-wide NWs lies on the range of dimensions that still obeys the theoretical prediction for H N for intrinsic nucleation processes determined by the exchange and magnetostatic energy.It also increases the tolerance of the magnetic device to small local variations of H N and H P that may occur during fabrication such as roughness, composition, inhomogeneities, etc.As 500 nmwide NWs exhibit this anomalous H N evolution as function of thickness with the appearance of an optimal DH value, we focus our studies on the analysis of the DW configurations in these particular NWs.DW have then been analyzed using the TIE analysis of focal series of LTEM images.Figure 4(a) displays a series of defocused LTEM images obtained in the 500 nm-wide NWs for different thickness, which already indicates the formation of two types of domains as a function of thickness, a TW for t < t max and a VW (or multi-VW) for t > t max .TIE reconstructions have been carried out to corroborate this fact and provide more detailed information on the magnetic structure nucleated at the kink.This is displayed in Figures 4(b)-4(e), where the color-and arrow-coded TIE reconstruction of the in-plane magnetic induction obtained from LTEM images is reported for "thin" and "thick" NWs, i.e., Fig. 4(b): t ¼ 10 nm, Fig. 4(c): t ¼ 13 nm; Fig. 4(d): t ¼ 19 nm; Fig. 4(e): t ¼ 30 nm.It is clearly seen that a TW is formed at t ¼ 10 and 13 nm, a VW structure is observed for t ¼ 19 nm, and a multi-VW configuration is determined at t ¼ 30 nm.Micromagnetic simulations of the Co nanowires with the same width and thickness have been performed to support our experimental observations.A defect-free model of the nanowires with squared profiles and bulk-like magnetic parameters was used.Simulations were carried out following the same experimental procedure and are depicted in Figs.4(f)-4(i), the magnetic configuration shown in the images being the remanent state after nucleating the DW.Despite the small differences in the positions of the DW, most likely due to morphological differences between the real and the simulated defect-free nanostructures (roughness, irregularities, small thickness variations), the micromagnetic simulations are in very good agreement with the TIE reconstructions.They demonstrate that the DW nucleated in the curved corner is a TW in the case of thin nanowires (for t t max ), whereas in thick NWs VW or multi-VW structures are pinned close to the corner.These results indicate that the width and thickness of the NW which present the most valuable H N , H P , and DH fields for application (w ¼ 500 nm and t 13 nm) are also the dimension where a crossover between TW and VW states occurs. 14o summarize, nucleation fields (H N ) and propagation fields (H P ) of domain wall in L-shaped FEBID Co nanostructures have been studied by in situ Lorentz TEM.We evidenced an optimal Co NW dimension of w max ¼ 500 nm width and t max ¼ 13 nm for which the nucleation field is maximal (197 6 4 Oe) and the difference between H N and H P is also maximized, DH ¼ 146 Oe.Such large difference between H N and H P is required for technological applications to guarantee safe and independent nucleation and propagation of DW.This optimal physical dimension coincides to a thickness where the DW switches from a transverse wall configuration (for t < t max ) to a vortex wall type for thicker NW.

FIG. 1 .
FIG. 1.(a) Schematic representation of the procedure to determine H N and H P by magnetic field dependent LTEM (from left to right).(b) Low magnification TEM image of a 500-nm-wide L-shaped FEBID Co nanowire.Insets: Underfocused Lorentz images of the kink when (c) the magnetization is saturated (H > H sat ), and (d) the DW is nucleated (H H N ), where the Fresnel contrast is reversed.

FIG. 2 .
FIG. 2. Dependence of the nucleation fields as a function of (a) the width and (b) the thickness of the nanowires.In (a), some thicknesses are not plotted for the sake of clarity.

FIG. 4 .
FIG. 4. (a) Sequence of out-of-focus Lorentz images of L-shaped nanowires as a function of the thickness in 500 nm-wide Co NWs.(b)-(e) TIE-reconstructed inplane magnetic induction of a Co NW in the TW regime (t ¼ 10 and 13 nm), in the VW regime (t ¼ 30 nm), with an intermediate state between TW and VW (w ¼ 19 nm).(f)-(i) Micromagnetic simulations of the NWs reconstructed by TIE.The inset in (b) shows the color code used for the different orientations in all the figures.