Directional growth of iron oxide nanowires on a vicinal copper surface

Single-crystal magnetic nanostructures with well-defined shapes attract lots of interest due to their potential applications in magnetic and spintronic devices. However, development of methods allowing controlling their mutual crystallographic and geometric orientation constitutes a significant scientific challenge. One of the routes for obtaining such structures is to grow the materials epitaxially on naturally-structured supports, such as vicinal surfaces of single-crystal substrates. Iron oxides are among the most well-known magnetic materials which, depending on the phase, may exhibit ferro/ferri- or antiferromagnetic ordering. We have grown iron oxide nanowires on a Cu(410) single-crystal substrate faceted with molecular oxygen. Scanning tunneling microscopy and low energy electron diffraction revealed that the oxide grows in the [111] direction, along the step edges of the substrate and rotated by ±15° with respect to the [010] direction of copper atomic terraces (so that the the growing elongated structures are orientated parallel to each other). Notably, x-ray photoelectron spectroscopy confirmed that the nanowires represent the ferrimagnetic γ-Fe2O3 (maghemite) iron oxide phase, while micromagnetic simulations indicated that the wires are single-domain, with the easy magnetization axis orientated in-plane and along the long axis of the wire.


Introduction
Iron oxides are well-known for their electronic and magnetic properties which make them promising for spintronics Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
One of the routes for obtaining single-phase iron oxide crystals is to grow the material epitaxially on a suitable singlecrystal substrate.In the 1-2 monolayer (ML) regime (where 1 ML is defined as the amount of iron needed to form a pseudomorphic layer on the selected support), well-dispersed hexagonally-shaped mono-and bilayer FeO islands, as well as continuous films, may be grown by Fe deposition and postoxidation.Such a procedure was successfully used for growing FeO on various metal single-crystal substrates, including Pt(111) [5,6], Ru(0001) [7][8][9] and Au(111) [10].As far as the structural parameters are concerned, the stoichiometry of the islands, as well as their size and density, may be controlled by modifying the growth procedure [6,8] or applying post-growth treatments (such as exposing the islands to highly-oxidizing conditions, e.g.high pressure of molecular oxygen [11], atomic oxygen [12] or nitric oxide [13], or to reducing conditions, such as annealing in ultra-high vacuum (UHV) [14]).At higher coverages, depending on the growth conditions, islands and films representing either Fe 3 O 4 [7,15,16] or Fe 2 O 3 [15,17] phases may be formed.
The magnetic properties of materials may depend on many different factors, including the chemical composition, crystal structure, size and shape.At the nanoscale, the size and shape start to play a decisive role, especially with respect to magnetic anisotropy (i.e. the orientation of magnetic easy and hard axes [18]).Even though the theory predicts various magnetic orderings for ultrathin epitaxial FeO films [9,19], the experiments show that they are paramagnetic at RT [20,21].The situation changes for iron oxide structures representing ferrimagnetic iron oxide phases: Fe 3 O 4 and γ-Fe 2 O 3 .For instance, the group of de la Figuera has shown that Fe 3 O 4 islands grown on Ru(0001) exhibit ferrimagnetic ordering already at 1 nm thickness [22].Similar observation was made by another group for iron oxide species 2-3 nm thick grown on Pt(111) and resembling the γ-Fe 2 O 3 phase [23] (above this thickness, the oxide transforms into the α-Fe 2 O 3 phase which exhibits antiferromagnetic ordering [24]).This indicates that nanostructures representing these iron oxide phases could be potentially used for constructing low-dimensional spintronic devices operating at RT.
As far as the shape control of ferrimagnetic epitaxial iron oxide structures is concerned, Takahashi et al have shown that Fe 3 O 4 nanopyramids can be obtained on SrTiO 3 (001) via a two-step process: temperature-driven dewetting of an initial magnetite layer and further growth of Fe 3 O 4 on asprepared seed nanocrystals [25].The coercivity of the pyramids strongly depended on their size, which was attributed to the transition from mono-to polydomain state.Bennett et al, on the other hand, managed to obtain Fe 3 O 4 nanowires by depositing a metallic iron layer onto an FeO film grown on Re(0001) and inducing reactive dewetting through UHV annealing [21].The wires were characterized by high lengthto-width ratios and were growing in three 120 • -rotated orientations with respect to the underlying substrate (with occasional deviation by ±5 • ).Notably, they were shown to be ferrimagnetic and single-domain at RT. Rao and Zheng used flame vapor deposition to grow γ-Fe 2 O 3 nanowires and obtained structures growing perpendicular to the substrate (which was either an iron foil or a silicon wafer) [26].The wires were single-domain, exhibited coercivity of ∼0.02 T and saturation magnetization of 68 emu g −1 at RT. Elongated singlecrystalline structures may be also obtained through another well-established route, i.e. by growing the material on a high Miller-index (vicinal) substrate.Such substrates are characterized by the presence of narrow and regular monoatomic terraces that influence the length-to-width ratio of growing species.As an example, Ketteler and Ranke have grown elongated iron oxide islands on Pt (9 11 11) by Fe deposition at RT and post-oxidation [27].At low Fe coverages, the islands were representing the FeO phase, while at higher coverages Fe 3 O 4 crystallites with step-induced texture were starting to grow.Vicinal substrates were also successfully used for growing nanowires of other transition metal oxides.For example, the group of Netzer has grown vanadium oxide nanowires on Rh(15 15 13) and obtained exotic oxide phases not observed on flat Rh(111) [28].This behavior was assigned to stress relief at the step edges-a mechanism that does not occur on a flat surface.
We have grown iron oxide islands and films on a Cu(410) single-crystal substrate using sequential deposition of metallic Fe and post-oxidation in O 2 at elevated temperature.Copper, due to its excellent electrical properties and Earth-abundance, is widely used in electronics.The selected substrate-Cu(410)-is a vicinal Cu(001) surface.A perfect bulk-cut Cu(410) is characterized by 4-atom-wide terraces exhibiting a slightly reconstructed Cu(001) structure and separated by monoatomic steps representing the (110) plane [29].The width of each terrace is ∼7.2 Å and the step height is 1.75 Å [30,31].Under typical experimental conditions present during metal substrates cleaning, such as high temperature and UHV, Cu(410) undergoes the so-called roughening transition, in which the step atoms detach and a step-free curved surface is formed [32].Only upon exposure to molecular oxygen faceting of the surface-accompanied by the formation of an ordered structure of O atoms-takes place (the atoms build into the surface, occupying the bridge positions within the first and third atomic row of each terrace and pinning the terrace structure) [30,33].Such an O-faceted surface, denoted as Cu(410)-O, is thermodynamically more stable than clean Cu(410).Notably, it was shown that Cu(410)-O may be used as a substrate for the chemical vapor deposition growth of epitaxial graphene, with the steps of Cu inducing a 1D modulation in graphene's electronic properties [31].
To the best of our knowledge, there are no reports on the growth of iron oxides (or other transition metal oxides) on pristine or O-reconstructed Cu(410), even though there are many works related to the growth of iron oxide islands and films on a structurally-similar Cu(001) (see for example references [34][35][36][37][38]).These works indicate that iron easily oxidizes on copper, which leads to the formation of Fe 3+ -containing iron oxide phases, i.e.Fe 3 O 4 and Fe 2 O 3 .Moreover, irrespectively of the crystallographic orientation of the support, iron oxide islands preferentially grow in the [111] direction, which in the case of Cu(001) results in the appearance of two rotational domains oriented 90 • with respect to each other [34] and rotated ±15 • with respect to the underlying substrate [37].The analyses also revealed, that half of a monolayer of oxygen resides at the interface between iron oxide on copper [35].As Cu(410) is a vicinal Cu(001) surface, it could be expected that well-ordered iron oxide islands and films can be also grown on that particular substrate, with the dense step structure of the vicinal surface influencing the growth direction and the shape of the growing species.In fact, scanning tunneling microscopy (STM) and low energy electron diffraction (LEED) studies performed by our group revealed the formation of well-ordered iron oxide nanowires growing along the step edges of Cu(410)-O, with x-ray photoelectron spectroscopy (XPS) indicating that the wires represent the γ-Fe 2 O 3 iron oxide phase.Notably, micromagnetic simulations provided information on the magnetic properties of fabricated nanowires, which are predicted to be ferro-/ferrimagnetic, single-domain and highly-anisotropic, with the easy magnetization axis oriented in-plane and along the long axis of the wire.

Materials and methods
The experiments were performed in a multiprobe UHV chamber (base pressure: 5 × 10 −10 mbar; from Omicron) equipped with facilities necessary for single crystals cleaning and iron oxides growth, i.e.Ar + (purity 99.999%; Linde) sputter gun, Fe electron beam evaporator (EFM 3; Focus GmbH) and an O 2 (99.999%;Linde) line, as well as structural analysis tools, including low-temperature STM (CreaTec), LEED and XPS (both from Omicron).
The cylindrical-shaped Cu(410) single crystal (99.999%; from SPL; 8 mm in diameter, 1 mm in thickness, with side mounting slits) was cleaned by repeated cycles of 0.6-1.0keV Ar + ion sputtering at RT, annealing in UHV at 850 K for 15 min (to smoothen the surface, leaving it in an unreconstructed state) and in 1 × 10 −6 mbar O 2 at the same temperature (to remove carbon and promote surface faceting).Iron oxides were grown by depositing Fe (purity 99.995%; Alfa Aesar) from a 2-mm rod onto an O-facetted substrate held at RT and oxidizing it under the same conditions as those used for carbon removal and surface faceting.Also, an Fe/Cu(410) reference sample was prepared by depositing Fe onto a clean and unreconstructed Cu(410) surface at RT.
The structure of the studied systems was evaluated using STM, LEED and XPS.STM measurements were performed at LN 2 temperature (77 K) using mechanically cut PtIr tips.The obtained images were processed using Gwyddion computer software [39].XPS measurements were performed with a Mg Kα 1253.6 eV x-ray source and a channeltron-based hemispherical energy analyzer.The survey spectra were obtained at a pass energy of 50 eV and the regions at 20 eV.The data were calibrated with respect to the position and intensity of the Cu 2p 3/2 peak (932.7 eV) [40] originating from the copper substrate, and analyzed using CasaXPS (Casa Software Ltd) and OriginPro (OriginLab Corporation) computer software.For the fitting of the Fe 2p 3/2 peak of metallic iron, the LA(1.2,4.8,3)lineshape was used [41], while for the Fe 2p 3/2 peak of iron oxides and for the O 1 s region, a linear combination of Gauss and Lorentz functions (GL(50)) was applied.All the fittings were performed with a Shirley background substraction.
The magnetic properties of the experimentally-observed structures were determined theoretically by performing micromagnetic simulations.The base calculations were carried out for the sets of 1-3 nanowires with simplified rectangular shapes and gable-like tops using the MuMax3 package for magnetic finite difference simulations [42].Two scenarios were considered: in the first scenario, there was no gap between the wires, while in the second one, the gap between the neighboring species was set to 0.2 nm, which excluded exchange interaction between adjacent wires.The width of each nanowire was set to 7 nm and the length to 70, 75 and 80 nm in the case of three nanowires, 75 and 80 nm for a set of two wires and 80 nm for one.The calculations were carried out at zero Kelvin, neglecting the thermal fluctuations.The magnetic parameters for the micromagnetic simulations, i.e. saturation magnetization M s and exchange stiffness A ex , were adopted from [43,44] and equaled 0.3 × 10 6 A m −1 and 1.0 × 10 −13 J m −1 , respectively.For the sake of simplicity, it was assumed that the magnetocrystalline cubic anisotropy of the simulated structure is the same as for bulk γ-Fe 2 O 3 and equals K c = 4.7 × 10 6 J m −3 [43][44][45].The whole system was discretized into cubic unit cells (voxels) with a size of 0.2 × 0.2 × 0.2 nm 3 , which is smaller by over two orders of magnitude compared to the exchange length.The relaxation procedure was started from a high energy state, where the direction of all magnetic moments was randomly chosen.Then, using the Bogacki-Shampine solver, the energy and the torque were minimized according to Landau-Lifshitz-Gilbert equation: where m = M/M S is the normalized magnetization, M S is the saturation magnetization, H eff is the effective magnetic field acting on the magnetization, γ = 187 rad/ (s • T) is the gyromagnetic ratio and α is the damping constant.The damping parameter α has been set to 1 to ensure faster coverage to the relaxed state.The results of the calculations were found not to depend on the initial orientation of magnetization (in-plane or out-of-plane).Additional micromagnetic simulations were performed for a single nanowire with a complex shape reflecting that of experimentally-observed species using Boris Computational Spintronics [46].The software, similarly to MuMax3, solves the Landau-Lifshitz-Gilbert equation.The bottom plane of the simulated nanowire had a trapezoidal shape, with the trapezoid height (or nanowire width) of 10 nm, bottom base length (nanowire length) of either 50 or 100 nm (both cases were considered to compare the convergence of numerical results) and the bottom base angles equal to 30 and 45 • .The nanowire itself was 1 nm-thick (in the z direction) and had a gable-like top.In the simulations, the nanowires were discretized into approximately 0.15 nm cells along the z-axis (i.e. 1 nm, giving 7 cells in total), 0.25 nm cells along the y-axis (10 nm, 20 cells) and 0.5 nm cells along the x-axis (50/100 nm, 200/400 cells).The following components were considered in the effective field: magnetic demagnetizing field, exchange field and bulk magnetocrystalline anisotropy field.Thermal effects and damping were neglected.The magnetic parameters of maghemite, i.e. bulk anisotropy constant K 1 = 4.7 × 10 3 J m −3 , saturation magnetization M S = 0.3 × 10 6 A m −1 and exchange stiffness A ex = 1.3 × 10 −11 J m −1 , were taken from Solov'yov and Greinerr [43].

Results and discussion
Firstly, Cu(410) was cleaned and faceted by annealing in O 2 (which leads to the formation of Cu(410)-O surface structure [30,31,33]).Figure 1(a) presents an STM image of the reconstructed surface together with its fast Fourier transform (FFT) (inset).The LEED pattern obtained for the as-prepared surface is shown in figure 1(b), while the one recorded prior to the faceting is presented in figure 1(c).The STM image reveals the characteristic surface structure with 4-atom-wide atomic terraces separated by monoatomic steps.In addition to these, every 50-100 nm a larger step was observed (not shown).The FFT fits well the diffraction pattern obtained following O 2 annealing.Importantly, both patterns-recorded before and after faceting-were found to be similar to that published in the literature [31,47,48].
Then, iron oxide islands were epitaxially grown on the Cu(410)-O substrate by Fe deposition at RT and postoxidation in 1 × 10 −6 mbar O 2 at 850 K. Three cumulative cycles of deposition and oxidation were performed, leading to the total amount of deposited Fe of ∼0.4,0.8 and 1.6 ML.The STM images obtained following each deposition/oxidation cycle are presented in figures 2(a)-(c).After the first cycle, the growing iron oxide species were starting to form nanowires with an average width of 4-7 nm and a length of 50-80 nm.By comparing the image with an STM image of a clean Cu(410)-O surface (figure 1(a)), it may be concluded that the long axes of the wires are oriented parallel to the substrate steps.Assuming a width of a single substrate terrace of 7.2 Å [31], each nanowire covers 7-11 monoatomic steps of Cu(410)-O.Following the growth, the substrate became restructured, with the step edges exhibiting less regular shapes and angles of 120 • .The wires were initially growing in pairs (figure 2(a)), however, with increasing coverage they were switching to triple (figure 2(b)) and, ultimately, multiple (or to large and uniform species) with the formation of a continuous film (figure 2(c)).Notably, the short edges of the islands were found to be oriented 30 or 60 • with respect to step edges of the substrate.
In the cross section, the wires had a height of ∼1 nm and non-symmetric triangular shapes (i.e.gable-like topssee figure 3(a) and the inset).An atomically-resolved STM image of an exemplary island is presented in figure 3(b).The atomic structure is visible only on one side of the wire and exhibits a close-packed arrangement with ∼3.5 Å periodicity.The atomic rows are oriented 60 • with respect to substrate step edges, which coincides with the orientation of one of the short island edges.Such an atomic arrangement suggests that the oxide grows in the [111] direction, which is the same as in the case of iron oxides on Cu(001) [49].Notably, the atomic periodicity roughly fits the Fe-Fe distance in magnetite and maghemite.
Interestingly, on top of some of the wires, especially the biggest ones formed at 2.8 MLs coverage, hexagonal atomically-flat islands were observed (figure 3(c), marked with an orange circle).These islands could be formed by copper atoms that migrate on top of iron oxide (as copper is known to migrate on top of metallic iron on Cu(001) [50]).On the other hand, the studies of Koveshinkov et al indicated that copper does not migrate onto iron oxide in a similar Fe 3 O 4 /Cu(001) system [38].Thus, unambiguous assignment of the nature of these islands would require additional studies.
The LEED pattern recorded for the iron oxide film representing the highest studied coverage (2.8 MLs) is shown in figure 4(a).The pattern was acquired at a beam energy of 200 eV, as at lower energies the position and mutual arrangement of spots were not evident.A pattern taken at the same energy for Cu(410)-O is shown in figure 4(b) for comparison.While the diffraction pattern of an oxygen-faceted Cu(410) substrate is quite well understood [31], the one obtained for the iron oxide film on Cu(410)-O is not trivial to interpret.For the analysis, we have overlayed an uphill symmetry line on the pattern, as well as downhill lines that correspond to the rows of diffraction spots observed on the pattern of Cu(410)-O (dashed grey lines).By comparing the orientation of atomic steps visible on the STM image presented in figure 1(a) with the FFT pattern shown in the inset to the figure, it may be assumed that the lines of diffraction spots in the LEED pattern run along the [010] direction of Cu(410) terraces (or the [1 40] direction of the Cu(410) crystal [31]), while the direction perpendicular to the rows is the [001].As can be seen, following the growth of iron oxide the diffraction spots coming from the substrate almost completely extinguished, while several new diffuse spots appeared.Looking in the [001] direction, spots oriented ±30 • with respect to the vertical symmetry line (marked with yellow arrows) may be observed.As the angle between the spots is 60 • , it may be assumed that they originate from a hexagonal structure-most probably iron oxide growing in the [111] direction.This growth orientation agrees well with the one determined based on the atomicallyresolved STM image (figure 3(b)), as well as the one reported for iron oxides on Cu(001) [34][35][36][37][38] (the 4-atom-wide terraces of Cu(410)-O have a Cu(001) structure [29]).At the vicinity of the central line running in the [010] direction, spots positioned ±15 • with respect to the centre of symmetry can be seen (marked with red arrows).This kind of arrangement also complies with the reported growth of iron oxide islands on Cu(001), in the case of which a rotation by ±15 • with respect to the [010] direction of the substrate was observed [36][37][38].Even though the recorded LEED pattern does not allow to precisely determinate the iron oxide unit cell, it provides hints based on which it may be concluded that the growth is similar to that on Cu(001).Notably, on the latter substrate the oxide forms two rotational domains oriented 90 • with respect to each     other [34,[36][37][38]   spectrum could be fitted with two components: one located at the binding energy of 530.1 eV, related to oxygen-copper and oxygen-iron bonds [41], and one at 531.2 eV, which could be assigned to chemisorbed molecular oxygen or undercoordinated oxygen atoms located at the defect sites (such atoms are characterized by a lower electron density than the O 2− ions adsorbed at the regular sites) [51].After oxidation, the maximum of the Fe 2p 3/2 signal shifted from 707.0 to 711.2 eV (figure 5(d)).The spectrum exhibits broadening due to multiplet splitting effects [41], however, the peak position is in agreement with the literature data reported for bulk Fe 2 O 3 [52][53][54].The recorded line could be fitted with five components centered at around 709.8, 710.8, 711.8, 713.0 and 714.1 eV, which−based on the literature−can be ascribed to γ-Fe 2 O 3 (maghemite) (the Fe 2p 3/2 spectra of α-and γ-Fe 2 O 3 have a slightly different shape, as the two iron oxides differ with respect to the symmetry of the crystal field, which affects the observed change in the multiplet splitting of the Fe 2p levels [41]).Following the high-temperature oxidation, the signal at 707.0 eV disappeared and the above-mentioned iron oxide components increased in intensity.Figure 6(a) shows the Fe 3p spectrum recorded for the oxidized sample.The region could be fitted with one symmetric line centered at 56.1 eV, which is characteristic of Fe 2 O 3 [54].Figure 6(b), on the other hand, presents a wider Fe 2p region covering the Fe 2p 3/2,1/2 spin-orbital doublet.The satellite bands (marked with arrows), positioned approx.8 eV above the Fe 2p 3/2 and Fe 2p 1/2 lines, further confirm the Fe 2 O 3 assignment of the iron oxide phase [52][53][54].
Based on the analysis of STM, LEED and XPS results, a structural model of an iron oxide nanowire representing Finally, to gain insight into the magnetic properties of fabricated structures, micromagnetic simulations were performed.The magnetic states of sets of 1-3 γ-Fe 2 O 3 nanowires lying next and parallel to each, simulated using MuMax3 [42], are presented in figure 8.In the case of an isolated nanowire (figure 8(a)), a single-domain state is preferred, with the magnetization vector being oriented in-plane and along the long axis of the wire (due to shape anisotropy).For the sets of two and three nanowires (figures 8(b)-(d)), each nanowire is relaxed in a monodomain state, however, the nanowires exhibit a uniformly ferromagnetic state when there are no gaps between them (figures 8(b) and (c)) and an antiferromagnetic arrangement when they are separated by small (0.2 nm) gaps (figures 8(d) and (e)) (from the experimental data, it is not trivial to determine if the wires are interconnected or separated by atomic-size gaps; thus, both cases were considered).The ferromagnetic state originates from the nearest-neighbor exchange interaction between the wires and the minimization of the exchange energy.The antiferromagnetic state, on the  other hand, is related to the minimization of the magnetostatic energy when there is no exchange interaction between the wires.
We have also determined the influence of fine geometric details of the nanowires on their magnetic properties by simulating a single nanowire with a shape reflecting that of experimentally-observed species.These calculations were performed using the Boris Simulation Package [46].The simulated nanowire, similarly to the one constructed based on the simplified model, had a homogenous magnetic texture (monodomain state), which did not depend on the selected discretization or the length of the structure.The magnetization was found to exhibit a slight deviation in the diagonal direction due to the asymmetric geometry (2% in m x and m y directions, as shown on the example of the 50 nm-long nanowire in figure 9).However, no significant impact of the edges and curvatures was observed.

Conclusions
Iron oxide islands and films were grown on a vicinal Cu(410)-O surface by room-temperature Fe deposition under ultrahigh vacuum and post-oxidation in 1 × 10 −6 mbar O 2 at 850 K.The islands were found to grow along the step edges of the substrate, forming nanowires with gable-like tops.The growth direction was determined to be [111], with each of the islands being rotated by ±15 • with respect to the underlying copper terrace.Detailed structural analysis revealed that the wires represent the ferrimagnetic γ-Fe 2 O 3 iron oxide phase.Based on these findings, a structural model of the observed nanowires was proposed.The performed micromagnetic simulations indicated that a single nanowire prefers a monodomain state, with an in-plane orientation of magnetization and the easy axis oriented along the long axis of the wire.When it comes to double-and triple-wires, that were also observed in experiments, they were found to either couple ferromagnetically-when there is no gap between the wires and the nearest-neighbor exchange interactions define the magnetic ordering-or arrange antiferromagnetically, when there is a small gap between the wires and the magnetostatic energy defines the ordering.

Figure 4 .
Figure 4. LEED patterns of iron oxide on Cu(410)-O (2.8 MLs coverage) (a) and Cu(410)-O (b), recorded using the beam energy of 200 eV.The uphill dashed line in (a) indicates the symmetry, while the downhill ones correspond to the lines of diffraction spots visible in (b).
, while on Cu(410)-O the step edge texture forces the oxide to grow in one direction only.The chemical structure of the wires was assessed with XPS.The survey spectra (not shown) revealed the exclusive presence of Cu, Fe and O in the studies samples (with oxygen being detected only for the Cu(410)-O and the iron oxide/Cu(410)-O), with no traces of contaminating elements.

Figure 5
presents the Fe 2p 3/2 spectrum obtained for Fe deposited onto a clean Cu(410) at RT (a), the O 1 s region recorded for this sample (b), as well as Fe 2p 3/2 (c), (e) and O

Figure 8 .
Figure 8.The relaxed magnetic state of sets of 1-3 γ-Fe 2 O 3 nanowires.(a) shows a single nanowire, while (b), (d) and (c), (e) present sets of two and three nanowires, respectively, lying next and parallel to each other, with no gaps between the wires (d), (c) or with 0.2 nm gaps (d), (e).The colors and directions of the arrows indicate the directions of magnetic moments.

Figure 9 .
Figure 9. Simulated static magnetization distribution in a 50 nm-long γ-Fe 2 O 3 nanowire with an experimentally-derived geometry.The three panels show the individual magnetization components mx, my and mz.