# The evolution of magnetic behavior in FeCoNi nanowires with different geometry

Anna Nykiel, Arkadiusz Zarzycki, Wojciech Maziarz, Jaafar Ghanbaja, Alain

Walcarius, Malgorzata Kac

► To cite this version:

Anna Nykiel, Arkadiusz Zarzycki, Wojciech Maziarz, Jaafar Ghanbaja, Alain Walcarius, et al. The evolution of magnetic behavior in FeCoNi nanowires with different geometry. Materials Science and Engineering: B, 2025, 322, pp.118645. 10.1016/j.mseb.2025.118645. hal-05210567

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Submitted on 14 Aug 2025

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# The evolution of magnetic behavior in FeCoNi nanowires with different geometry

Anna Nykiel<sup>a,b</sup>, Arkadiusz Zarzycki<sup>a</sup>, Wojciech Maziarz<sup>c</sup>, Jaafar Ghanbaja<sup>d</sup>, Alain Walcarius<sup>b</sup>,
Malgorzata Kac<sup>a,*</sup> ◆

## ARTICLE INFO

### Keywords:

Nanowire

FeCoNi alloys

Nanotwins

Electrodeposition

Magnetic properties

Lorentz microscopy

## ABSTRACT

FeCoNi nanowires (NWs) with different diameters (40–120 nm) and lengths (1.5–6 µm) were electrodeposited in the polycarbonate membranes. Magnetic measurements confirmed anisotropy along the NW axis. Changes in the nanowire geometry resulted in increased coercivity and squareness for smaller diameters. Studies of the magnetization reversal mechanism showed a non-monotonic coercivity variation as a function of angle, pointing out the initial vortex domain wall propagation that transformed into a transverse or coherent rotation at angles closer to the hard direction. FORC analysis confirmed that the nanowire diameter is the main factor determining magnetostatic interaction between nanowires and indicated a non-interacting system in the case of a small diameter NW matrix. Magnetic imaging of the sample using Lorentz microscopy did not reveal domain walls, which together with FORC results, implies a single-domain structure of nanowires. Therefore, the obtained nanowires meet the criteria required for 3D racetrack memory applications.

## 1. Introduction

In the field of nanoscience and nanotechnology, the manipulation of matter at the atomic and molecular scale has opened up unprecedented possibilities for revolutionizing various industries, from electronics and energy to medicine and materials science [1–11]. Materials in the nanoscale, such as nanoparticles, nanocomposites, nanotubes, and nanowire often exhibit properties distinct from their bulk counterparts, including altered electrical and magnetic properties as well as enhanced mechanical strength. Among these materials, nanowires, defined as one-dimensional objects with specific geometric features, are characterized by exceptional properties that deserve special attention due to their wide range of applications and sattractiveness in fundamental studies [1,12–14]. The nanostructures of interest may focus on metallic or oxide materials. Although oxide structures have undoubtedly advantages, related to their excellent stability under extreme conditions [15,16], in these studies, a ferromagnetic metallic compound will be analyzed.

Geometry-dependent mechanical, electrical, optical, and magnetic properties of nanowires can be easily modified using the template-

assisted electrodeposition technique, in which the utilization of various membranes and process parameters results in the formation of nanowires with different diameters (Φ), lengths (L), shapes, and distributions (d – inter-wire distance). Of particular interest, the magnetic properties of nanowires are strongly affected by the aspect ratio, which describes the length of an object to its diameter (L/Φ). This parameter, together with NW structure and their distribution, influences the magnetic behavior of nanowires determined by shape anisotropy, magnetocrystalline anisotropy, and dipolar interactions between nanowires. All these factors compete with each other and contribute to effective anisotropy, which is defined as the energy required to deflect the magnetic moment from the easy to the hard direction [17,18].

The high aspect ratio causes an increase in the shape anisotropy, favoring magnetization alignment along the NW axis. However, as shown in the theoretical studies [19,20] and experimental works [21,22], significant changes are observed only up to L/Φ = 10. Above this value, the contribution originating from the shape anisotropy remains constant. The next component of effective anisotropy – the magnetocrystalline anisotropy – depends on the crystallographic

<footnote><sup>a</sup> Institute of Nuclear Physics, Polish Academy of Sciences, Kraków PL-31-342, Poland</footnote>

<footnote><sup>b</sup> Universite de Lorraine, CNRS, LCPME, Nancy F-54000, France</footnote>

<footnote><sup>c</sup> Institute of Metallurgy and Materials Science, Polish Academy of Sciences, Kraków PL-30-059, Poland</footnote>

<footnote><sup>d</sup> Universite de Lorraine, CNRS, IJL, Nancy F-54000, France</footnote>

<footnote>* Corresponding author at: ul. Radzikowskiego 152, Kraków 31-342, Poland.</footnote>

<footnote>E-mail addresses: anna.nykiel@ifj.edu.pl (A. Nykiel), arkadiusz.zarzycki@ifj.edu.pl (A. Zarzycki), w.maziarz@imim.pl (W. Maziarz), jaafar.ghanbaja@univ-lorraine.fr (J. Ghanbaja), alain.walcarius@univ-lorraine.fr (A. Walcarius), malgorzata.kac@ifj.edu.pl (M. Kac).</footnote>
orientation of the material and is neglected in polycrystalline samples but can make a significant contribution when the sample shows a strong texture [23]. The third important component is dipolar interactions between nanowires. This factor (proportional to the saturation magnetization, nanowire length, and diameter) decreases with the cube of distance (−6.3 π M<sub>s</sub> (Φ/2)<sup>2</sup> L/d<sup>3</sup>) [24] and contributes to the alignment of the magnetization vector perpendicular to the NW axis [25].

The main magnetic parameters, such as coercivity ($H_c$) and squareness of hysteresis loop ($M_r/M_s$), which are a measure of material resistance to changes in magnetization and show the magnetization of the sample after removal of the saturating field, respectively, are strongly geometry-dependent. An increase in the nanowire length enhances the shape anisotropy (up to $L/Φ = 10$), causing a coercivity increase, but on the other hand, it increases the dipole interactions, which reduce coercivity [21,22,26]. Thus, the nanowire length acts in opposite directions depending on its range. However, a sufficiently high aspect ratio impacts the nanowire susceptibility to external magnetic fields, preventing undesired magnetization reversal that could result in the loss of magnetic information [27]. In the case of nanowire diameter, its increase causes a decrease in coercivity and squareness due to weakening the perpendicular anisotropy (easy axis along NWs) and increasing magnetostatic interactions between nanowires [28–33]. The changes in the diameter and the aspect ratio of nanowires also affect their magnetic structure, which transforms from single-domain with uniformly aligned magnetization vector to pseudo-single- or multi-domain forms [29–31]. Moreover, the nanowire geometry influences the reversal mechanism [31], which can occur via coherent rotation (C) with simultaneously rotating spins or by vortex (V) or transverse (T) domain wall propagation. To identify the magnetization reversal mechanism, it is necessary to analyze the coercivity dependence on the angle between the magnetic field and the nanowire axis.

An important aspect that should also be considered is the nanowire distribution, especially the distance between nanowires. In template-assisted electrodeposition, changes in the nanowire diameter occur through the selection of the appropriate template, in which the changes in the pore size induce the modification of the inter-pore distance. As mentioned above, this has a direct effect on the dipole interactions between nanowires, strongly affecting the magnetic parameters of the system.

A major advantage of controlling the geometry of nanowires is the ability to tune their properties appropriately to the chosen applications. In the era of artificial intelligence, computers with multitasking systems and swift and reliable data storage options are needed. A promising solution seems to be three-dimensional magnetic memory units using a racetrack system proposed by Parkin [34,35]. This system should contain domain walls that are anchored at desired positions and moved by polarized nanosecond current pulses. The use of 3D magnetic memory devices can increase the density of magnetic bits per unit area while simultaneously lowering energy consumption, increasing the reading speeds, and improving reliability by eliminating the mechanical motion that occurs when hard drives rotate [36–39]. Such memories can be produced based on segmented nanowires consisting of a sequence of magnetic domains with magnetic information encoded in domain walls in parallel arrays of nanowires [34]. In the first stage, a procedure for producing single segments with well-defined properties composed of semi-hard magnetic materials should be developed. It starts from the selection of suitable materials and the segment geometry, which will determine the chemical composition, morphology, and structure of nanowires and allow us to create segments with the desired magnetic properties.

Our previous studies on FeCo and FeNi nanowires revealed that these alloys were insensitive to cathodic potential (FeCo) or lost their magnetic anisotropy (FeNi), which eliminated them from the candidates meeting the criteria required for 3D racetrack memory [40]. In subsequent studies, the appropriately selected electrolyte composition enabled us to prepare ternary FeCoNi alloy nanowires with significantly

different chemical compositions, structures, and magnetic properties at varying cathodic potentials [25].

Therefore, in this study, the FeCoNi nanowires with different geometries will be tested as single-domain segments. As a template, we chose a polycarbonate membrane, which is characterized by a larger inter-pore distance compared to alumina membranes widely reported in the literature. For this reason, such objects, in addition to well-defined magnetic properties, should create a matrix of non-interacting single-domain structures. To analyze the magnetic behavior of nanowires and precisely characterize their magnetic structure, reversal mechanism, and dominant interactions in nanowires and between them, we performed angular coercivity dependence measurements, first-order reversal curve studies, and Lorentz microscopy observations. The required material, in the next stage of the project, will be produced in the form of multi-segmented nanowires, with each segment separated by a domain wall pinned in the desired position. To our knowledge, this will be the first attempt to produce such hybrid structures based on FeCoNi nanowire arrays, demonstrating potential application in 3D racetrack memory systems. First, however, it was necessary to fabricate single-domain non-interacting nanowires, which is the goal of this work.

## 2. Experimental

FeCoNi nanowires were electrodeposited into the nanochannels of commercial polycarbonate membranes (purchased from the Sterlitech Corporation) with a nominal thickness of 6 µm and a pore diameter ranging from 40 to 120 nm. The templates used showed inhomogeneous pore distribution with different porosities presented in Table 1. Before the process, each membrane was covered with a gold layer sputtered on one side to ensure electric contact and close pores. The electrodeposition processes performed in a three-electrode system were controlled by the AUTOLAB PGSTAT302N potentiostat (Metrohm Autolab B.V., Utrecht, The Netherlands) operating in the potentiostatic mode (−1.2 V vs. Ag/AgCl). The gold-covered membrane served as a working electrode with a platinum sheet counter electrode and Ag/AgCl junction reference electrodes. The electrolyte bath, maintained at 25 °C contained 0.01 M FeSO<sub>4</sub>, 0.02 M CoSO<sub>4</sub>, 0.17 M NiSO<sub>4</sub>, with the addition of 0.65 M boric acid (to stabilize pH = 3.0) and 6 mM ascorbic acid (to prevent Fe(II) oxidation).

The morphology of nanowires was observed after membrane dissolution using a Tescan Vega 3 scanning electron microscope (SEM) while the chemical analysis was performed by energy dispersive spectroscopy (EDS). The structure of nanowires was studied by X-ray diffraction (XRD) using a Philips X'Pert MRD Pro diffractometer with Cu K<sub>α</sub> radiation. The magnetic properties of nanowires were measured at room temperature in two directions with an external field of up to 40 kOe applied in the plane and out of the plane of the membrane, using a Quantum Design MPMS superconducting quantum interference device magnetometer (SQUID). Additionally, the angular coercivity dependences were measured at the magnetic field applied from the direction along the NW axis (0 deg.) to the direction in the membrane plane (90 deg.) to indicate the magnetization reversal mechanism. First-order reversal curves (FORC) analysis was also performed using SQUID measurements to study the magnetic behavior of nanowires. The measurements were performed at 300 K in out-of-plane geometry. The samples were initially subjected to a maximum magnetic field of 40,000 Oe. Before each FORC measurement, the sample was saturated at 10,000 Oe.

<table><caption>**Table 1**

Parameters of the polycarbonate membranes used.</caption><thead><tr><th>Pore diameter φ [nm]</th><th>Pore density [pores/cm²]</th><th>Open area [%]</th></tr></thead><tbody><tr><td>40</td><td>6 × 10<sup>8</sup></td><td>0.7</td></tr><tr><td>100</td><td>4 × 10<sup>8</sup></td><td>3.1</td></tr><tr><td>120</td><td>4 × 10<sup>8</sup></td><td>4.5</td></tr></tbody></table>
Oe, and FORC was measured with the reversal field range from –5000 to 5000 Oe with a step of 100 Oe. Moreover, the magnetic structure of nanowires was depicted by a Lorentz microscope using a Thermo Fisher Scientific Titan Themis Cs corrected 200 kV scanning /transmission electron microscope (S/TEM) equipped with a SuperX EDX detector system. Fresnel images were taken under-focus in low magnification mode, using an objective mini-lens as the imaging lens, with the objective lens removed. Transmission electron microscopy (TEM) investigations were carried out using a JEM-ARM 200F Cold FEG TEM/ STEM operating at 200 kV and equipped with a spherical aberration (Cs) probe and image correctors (point resolution 0.12 nm in TEM mode and 0.078 nm in STEM mode). The chemical composition was also analyzed using high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM).

## 3. Results and discussion

FeCoNi nanowires with the chemical composition defined by the appropriately selected cathodic potential (–1.2 V) [20] were studied as a function of their geometry. In particular, we investigated the morphology, structure, and magnetic behavior of nanowires.

### 3.1. Electrodeposition process

During the electrodeposition processes, in which the pore filling occurred, the current and the charge values vs. time were measured for different nanowire lengths and diameters (Fig. 1). Four different zones can be distinguished in the current transient plot. In addition to the capacitive contribution occurring directly after applying the cathodic potential, the first electrodeposition step, indicated by a rapid current increase, informs about crystal nucleation and growth. The next step, visible as a current decrease, is connected with the mass transport limitations and ends when the steady mass transport rate is reached. Starting from this stage, the current values increase slightly as the wires approach the membrane surface. The initial current decrease observed for large nanowire diameter ($\phi$ = 120 nm) may result from a small voltage drop along the pores [41]. When the nanowires completely fill the pores, there is a sudden increase in the current value due to the evolution of the active surface when the deposit spreads over the membrane surface. At this point, all processes were stopped to avoid the growth of the overdeposition caps on the membrane surface. To obtain shorter nanowires, the charge value was adjusted accordingly, based on the charge generated when the pores were completely filled. As can be seen in Fig. 1a and b, not only does the charge value change proportionally to the nanowire length, but a similar relationship can be observed over time. The current curves measured for the same nanowire diameters have the same shape, which proves the repeatability of the process.

Considering the nanowires with different diameters (Fig. 1c), it can be seen that with decreasing diameter, the time needed to fill the pores was shorter due to the lower membrane porosity. Additionally, larger pore diameters offer larger electroactive surface areas for electrodeposition, which is reflected in the higher current and charge measured during the process. The current density estimated from the sample porosity was 315, 120, and 95 mA/cm² (for diameters of 40, 100, and 120 nm, respectively) and decreased with increasing pore diameters (due to increasing porosity), which is consistent with previous studies performed as a function of cathodic potential [25].

### 3.2. Chemical composition

In the previous publication, we observed a strong dependence of the chemical composition of FeCoNi nanowires on the applied voltage during electrodeposition [25]. It was interesting to see whether the nanowire composition changes with their geometry, and in particular with their length. The chemical composition and elemental distribution were analyzed using energy-dispersive spectroscopy measurements on the nanowires released from the membranes. The atomic concentrations of Fe, Co, and Ni in the FeCoNi nanowires of different lengths and diameters are plotted in Fig. 2. All samples show similar concentrations, regardless of nanowire geometry. The same results with the composition of 13 % Fe, 24 % Co, and 63 % Ni were obtained by high-angle annular dark-field scanning transmission electron microscopy micrographs (HHDF-STEM) analysis performed at different nanowire areas (Fig. 2 c). The lack of observed changes in the chemical composition of nanowires for the lengths of 1.5 µm, 3 µm, and 6 µm suggests uniform element distribution along nanowires, confirmed by EDS maps. The literature shows that with pore filling, the composition of nanowires changes along the length, which is caused by a shorter diffusion length [42,43]. However, such behavior is observed for long nanowires above 40 µm (usually in anodic aluminum oxide membranes). In our case, the maximum NW length, resulting from the membrane thickness, is 6 µm, which is most likely not long enough to change the kinetics of element deposition.

Another important aspect concerns the type of co-deposition, which depends on the applied voltage and can be determined based on the selectivity ratio parameter (SR). The SR parameter calculated for nanowires deposited at –1.2 V is slightly larger than 1, suggesting that strongly anomalous co-deposition occurs below this potential (going to more anodic values) and was identified for the samples deposited at –1.0 V [25]. The normal character of co-deposition should be manifested by the similarity of the elemental contents in the deposit and electrolyte. The observed deviation indicates a hindered reduction of nickel ions in favor of less noble metals such as iron and cobalt. The mechanism of this behavior, although not fully understood, is explained assuming the competition of metal ions with hydroxide ions in the

<figure><img src="image_2.png" /><figcaption>**Fig. 1.** Variation of cathodic currents recorded as a function of time during the electrodeposition of FeCoNi nanowires with different lengths – L (a, b) and diameters – $\phi$ (c). The insets show the corresponding change of electrical charge over time.</figcaption></figure>
<figure><img src="image_3.png" /><figcaption>**Fig. 2.** Atomic composition of Fe, Co, Ni in FeCoNi nanowires with different lengths (a) and diameters (b) deposited at –1.2 V. The example STEM-EDS maps for nanowires with a length of 6 µm and a diameter of 40 nm (c).</figcaption></figure>

reduction process and has been described in detail in the literature [25,44–46].

### 3.3. Morphology and structure

To observe the morphology of nanowires, polycarbonate membranes were dissolved. Fig. 3 shows that regardless of the length (a-c) and diameter (d-f), the nanowires are continuous, without any noticeable porosity. Additionally, SEM measurements confirmed the desired nanowire lengths (1.5 µm, 3 µm, 6 µm) obtained by appropriate selection of the charge value during electrodeposition.

The microstructure of the alloyed FeCoNi nanowires was investigated by TEM measurements. Fig. 4 presents the bright field TEM images (BF-TEM), high-resolution TEM micrographs (HRTEM), fast Fourier transform (FFT), high-angle annular dark-field scanning transmission electron microscopy micrographs (HAADF-STEM), and selected area electron diffraction patterns (SAED) of the nanowires with a diameter of 40 nm. The overview images indicate long nanowires with uniform diameters and smooth lateral surfaces (Fig. 4a, b). The thin coating covering nanowires visible in Fig. 4c is a polycarbonate layer remaining after the dissolution of the membrane [47]. This layer protects

nanowires from oxidation. The pattern shown in Fig. 4c also revealed a fine crystalline structure with a crystal size below 10 nm. The images of nanowires demonstrate long straight lines along the nanowire growth direction (Fig. 4d). The electron diffraction pattern taken in this area indicates the doubled spots, suggesting that the straight lines are twinning defects with a (111) twinning plane. When the size of the twin domains becomes very small, the discrete diffraction spots change into diffuse lines (also observed in the case of a sequence of stacking faults), shown in the FFT pattern (Fig. 4e). Fig. 4f shows a high-resolution TEM micrograph with mirror-like boundaries between planes on the left and right sides, confirming the nanotwin formation. Such twins oriented along the nanowire axis or slightly tilted vertically are common structural defects in our nanowires. These defects are primary twins that appear during the nanowire growth due to the deposition of atoms at incorrect lattice positions, causing a fault in the stacking sequence. The stacking layer creates two single crystals separated by a twin plane, which is a symmetry plane for them. The mechanism of nanotwin formation can be explained based on the strains associated with differences in the crystal structure of alloying metals (fcc, bcc, and hcp), which generate defects such as dislocations and faults in the stacking sequence directly responsible for the twin formation [48].

<figure><img src="image_4.png" /><figcaption>**Fig. 3.** SEM images of the FeCoNi nanowires with a diameter of 100 nm and different lengths: 6 µm (a), 3 µm (b), 1.5 µm (c) and length of 6 µm and different diameters: 40 nm (d), 100 nm (e), 120 nm (f).</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Fig. 4. BF-TEM images (a, b, c), BF-TEM micrograph and corresponding SAED pattern (d), HRTEM micrograph and corresponding FFT pattern (inset) (e), HAADF-STEM micrograph (f) of FeCoNi nanowires with a diameter of 40 nm deposited at –1.2 V.</figcaption></figure>

The structure of the nanowires was also analyzed by X-ray diffrac-
tion. Fig. 5 shows measurements of nanowires with a length of 6 µm and
different diameters. The most intense peaks, marked with an asterisk,
come from the gold contact layer. The indexed peaks correspond to the
two crystal FeCoNi phases in the fcc (marked in blue) and hcp (marked in
red) structure [25,49–51]. Detailed studies of the crystal structure are
difficult because of the superposition of peaks coming from FeCoNi and
Au. The (200) Au peak has the same position (2θ = 44.2 deg.) as the most
intense (111) peak originating from the fcc phase of FeCoNi. Never-
theless, the studies show the presence of a mixture of fcc and hcp
structures. Such coexistence of two phases with a small fraction of hcp
structure was observed only at this cathodic voltage (–1.2 V) and was
previously reported for nanowires with diameters of 40 nm and 100 nm
[25]. These studies confirm that the mixture of fcc and hcp phases also
occurs in 120 nm diameter nanowires.

Diffractograms measured for nanowires deposited at different
membrane diameters did not show changes in the peak positions (the
lattice parameters are kept constant), but a significant increase in peak
intensity can be observed as the diameter of the nanowires increases,
which is related to the larger amount of material. Interestingly, with
increasing diameter, the hcp phase fraction increases clearly, reaching
very high peak intensity values for a diameter of 120 nm.

The analysis of the peak broadening using the Scherrer equation
allows for the calculation of the crystal size. The low peak intensities
only enable a rough estimation of the crystal size in the range from 15
nm to 20 nm, with the smallest values calculated for nanowires with the
largest diameter.

Thus, the changes in the nanowire geometry caused an increase in
the fraction of crystals in the hcp structure in the nanowires with the
largest diameter (the largest (100) hcp peak intensity as compared to
(220) and (200) peaks of fcc structure) without significant structural
changes in the 40 nm and 100 nm diameter nanowires.

3.4. Magnetic measurements

Magnetic studies of FeCoNi nanowires, including hysteresis loops

with their angular measurements and FORC diagrams, were performed
at room temperature. Hysteresis loops with a magnetic field applied
along the nanowire axis and perpendicular to it, measured as a function
of NW length (Φ = 100 nm) and diameter (L = 6 µm), are shown in
Fig. 6. A pronounced magnetic anisotropy with an easy axis along the
nanowires was observed for all nanowires, regardless of length and
diameter.

Increasing the nanowire length (from 1.5 µm to 6 µm) causes a
decrease in the coercivity and squareness from 450 Oe to 410 Oe and
from 80 % to 65 %, respectively (Fig. 7a). In the considered range of the
aspect ratio (15–60), the shape anisotropy contribution should remain
constant, but increasing the NW lengths can significantly strengthen the
dipole interactions between nanowires, which may be responsible for
the observed decrease in the values of magnetic parameters [19,21,52].

An unexpected change is observed in the shape of the hysteresis loop
measured in the membrane plane (H ⊥ NW axis) (Fig. 6a). There are two
interesting aspects: a broadening of the loops with increasing nanowire
length and a small contribution from the rectangular loop. The shortest
nanowires show a narrow, almost closed loop typical of measurements
in hard directions. As nanowire length increases, the loops become more
open, with a visible jump associated with the appearance of an addi-
tional loop. This two-step magnetic switching, especially pronounced in
the case of the longest nanowires, suggesting the appearance of a soft
magnetic material with an easy magnetic axis perpendicular to the NW
axis, may originate from overdeposited caps.

The clear changes are observed in the hysteresis loops measured for
nanowires with different diameters (Fig. 6b). First of all, as the diameter
decreases, the out-of-plane loops become wider with a significant in-
crease in the coercivity and squareness (Fig. 7b). This behavior can be
attributed to strongly reduced dipolar interactions in smaller-diameter
nanowires due to lower saturation magnetization and larger inter-wire
distance connected with lower porosities [21,53–55]. The in-plane
hysteresis loops (H ⊥ NW axis) are open and show a clear super-
position of magnetic curves typical for materials magnetized along hard
and easy directions, explained above.

Therefore, the nanowires with a diameter of 100 nm (or less) and a
<figure><img src="image_6.png" /><figcaption>Fig. 5. X-ray diffraction patterns measured for the FeCoNi nanowires with different diameters (40, 100, and 120 nm) embedded in the polycarbonate membranes. The indexed peaks correspond to the fcc FeCoNi (blue description; JCPDS:04-003-2245) and hcp FeCoNi (red description; AtomWork calculator). The peaks marked with an asterisk come from the gold layer.</figcaption></figure>

length corresponding to the length of the segment (1.5 µm–2 µm) in multi-segmented nanowires can be considered as magnetically non-interacting objects and can meet the requirements for 3D magnetic memory media. Such materials should show high magnetic anisotropy energy, which can be described by a parameter $S_{qout}/S_{qin}$, defined as the ratio of squarenesses measured out-of-plane and in-plane of the membrane ($M_r/M_s$)$_{out}$/$M_r/M_s$)$_{in}$ [24]. The larger this parameter, the greater the magnetic anisotropy.

This parameter, calculated for nanowires of various lengths, shown in the inset of Fig. 7a, confirms that magnetic anisotropy energy decreases with increasing nanowire length. Similarly, an increase in the nanowire diameter results in a decrease in the magnetic anisotropy energy (inset of Fig. 7b).

The largest magnetic anisotropy is therefore achieved in nanowires with the smallest diameter and the shortest length [30,31,56]. However, nanowires that are too small may undergo uncontrolled changes in the magnetic state due to thermal fluctuation, stray currents, or magnetic fields. Thus, the nanowire geometry should be optimized to ensure their magnetic stability, but at the same time keep their size small enough to prevent the increase in the magnetostatic interaction, which causes a

decrease in magnetic anisotropy energy.

The magnetic behavior of nanowires is also connected with their magnetic structure, which depending on nanowire geometry, can change from a single-domain (SD) structure to a pseudo-single-domain (PSD) or multi-domain (MD) structure above a critical diameter [30,57] and critical length [22]. The magnetic structure of nanowires as well as their geometry affect the reversal mechanism, which will be analyzed based on the angular dependence of coercivity.

As mentioned earlier, there are three types of magnetization reversal, which are illustrated in Fig. 8. In a coherent rotation (C), all the spins rotate simultaneously (Fig. 8a); in the other two cases, the spins reverse gradually, propagating the vortex (V) (Fig. 8b) or transverse (T) domain wall (Fig. 8c).

To investigate the magnetization reversal mechanism in FeCoNi nanowires and the influence of nanowire length and diameter on this mechanism, the angular dependence of the hysteresis loops was studied. The angle (θ) changed from 0 deg. to 90 deg., where 0 deg. and 90 deg. correspond to the magnetic field applied along the nanowire axis and perpendicular to it. The results obtained for nanowires of different lengths and diameters are presented in Fig. 11. The increase in the angle caused a gradual tilting of the magnetic curves, which changed from a shape close to rectangular, typical for the easy axis measurements, to almost closed loops observed for measurements along the hard direction (Fig. 9a, b). The coercivity values taken from these measurements were plotted as a function of angle for different lengths (Fig. 9d) and diameters (Fig. 9e) of nanowires. The experimental results were compared with theoretically predicted angular coercivity dependence calculated for FeCoNi NWs (Fig. 9c) according to the equations describing the magnetization reversal mechanism using the coherent (1), transverse (2), and vortex domain wall (3) models [22,58–60]:

$$ \frac{H_n^C(\theta)}{M_S} = - \frac{1 - 3N_c \sqrt{1 - t^2 + t^4}}{2 (1 + t^2)} \quad (1) $$

$$ \frac{H_n^T(\theta)}{M_S} = - \frac{1 - 3N_a \sqrt{1 - t^2 + t^4}}{2 (1 + t^2)} \quad (2) $$

$$ \frac{H_n^V(\theta)}{M_S} = \frac{\left( N_c - \frac{q^2 l_{ex}^2}{R^2} \right) \left( N_a - \frac{q^2 l_{ex}^2}{R^2} \right)}{\sqrt{\left( N_c - \frac{q^2 l_{ex}^2}{R^2} \right) \sin^2 \theta_0 + \left( N_a - \frac{q^2 l_{ex}^2}{R^2} \right)^2 \cos^2 \theta_0}} \quad (3) $$

where $H_n^C(\theta)$, $H_n^T(\theta)$, $H_n^V(\theta)$ – nucleation field for coherent, transverse, and vortex models, $N_c = 0$, $N_a = 1/2$ – demagnetization factor along the major and minor axis respectively, $t = \tan^{1/3}(\theta)$, $M_S$ – saturation magnetization, $q^2 = 1.08\pi$, $L_{ex}$ – exchange length ($L_{ex} = 2.5$ µm [17]) and R – nanowire radius.

In the description of the magnetization reversal mechanism, three parameters can be involved: the appearing in the above equations – nucleation field ($H_n$), i.e., the magnetic field at which the magnetization reversal starts (theoretical concept, difficult to determine experimentally); the switching field ($H_{sw}$), at which magnetization rotates abruptly; and the field at which the magnetization sing changes – the coercivity ($H_c$) [61]. In the case of an ideally rectangular hysteresis loop, the magnetic moments suddenly reverse, and these values are equal ($H_n = H_{sw} = H_c$). We will assume this relationship to simplify our analysis.

Thus, the angular coercivity dependence will be discussed below. Regardless of nanowire geometry, the changes of coercivity versus θ showed similar transients (Fig. 9d, e). Initially, with increasing angle, the $H_c$ increased slightly, then reached a maximum at 70 degrees and decreased at θ = 90 deg. The most pronounced maxima were observed in the nanowires with the smallest length and diameter, while for longer nanowires with larger diameters, the changes of coercivity were much smaller. Similar $H_c(\theta)$ dependences with maxima close to 70 degrees observed by other groups [22,58,59,62,63] were interpreted as a
<figure><img src="image_7.png" /><figcaption>**Fig. 6.** Hysteresis loops measured at room temperature with a magnetic field applied in the membrane plane and out of the membrane plane for nanowires with a diameter of 100 nm and different lengths (a) and nanowires with 6 µm length and different diameters (b). The magnetization (M) value was normalized to the saturation magnetization (M<sub>s</sub>).</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 7.** Out-of-plane coercivity and squareness with the insets of Sq<sub>out</sub>/Sq<sub>in</sub> parameter shown as a function of nanowire length (a) and diameter (b). The error bars are contained in the symbol size.</figcaption></figure>

transition between different reversal modes. This non-monotonic coercivity variation can be explained by a combination of vortex domain wall propagation, dominating before the maximum is reached, and transverse or coherent rotation, which switches magnetic moments when the angles are close to the hard magnetic axis, as shown in the calculated reversal model (Fig. 9c). At low angles, the most energetically favorable mode is the vortex model. However, at higher angles, the energy required for propagation of the vortex domain wall increases significantly, and therefore, the magnetization reversal mode switches to coherent or transverse.

According to the literature, the switching mode is affected by the competition between the exchange energy and the demagnetization energy [22,61,62]. Coherent rotation is favored by the exchange energy,

which dominates in small objects. In larger, high aspect ratio objects, where the demagnetization energy plays a major role, vortex domain wall propagation is promoted. The critical radius, at which switching between reversal modes occurs, is smaller than the size of the considered nanowires, which further explains the initial vortex propagation [61,64].

The magnetic structure of FeCoNi nanowires and the interactions between nanowires were analyzed using the first-order reversal curves (FORC) method. This technique is mainly a qualitative tool for identifying the magnetic state in single-domain, pseudo-single-domain, and multi-domain nanostructures that interact or do not interact with each other. FORC measurements allow determining the coercive field distribution (ΔH<sub>c</sub> – arising from non-uniform length distribution in an array
<figure><img src="image_9.png" /><figcaption>**Fig. 8.** The reversal magnetization mechanism observed in nanowires: coherent rotation C (a), vortex mode V (b), and transverse mode T (c).</figcaption></figure>

of nanowires), the interaction field distribution (ΔH_u – describes magnetostatic interaction between nanowires), magnetic phases (soft/hard), magnetization reversal mode (coherent, transverse or vortex domain wall propagation).

Fig. 10 illustrates the out-of-plane FORC diagrams measured for nanowires with a length of 6 µm and diameters of 40 and 100 nm. In the FORC measurement, the sample was initially saturated (H_s = 10 kOe), then the field was reduced to the reversal field (H_r), and M(H) was acquired when sweeping the field from H_r back to H_s, for each H_r to obtain M(H_r, H). The second-mixed partial derivative of M(H_r, H) with respect

to H_r and H created the FORC diagram with a color scale from blue (minimum) to red (maximum). The coordinates (H_r, H) were replaced by H_c = (H-H_r)/2 and H_u = (H + H_r)/2 axes, which present the coercivity and interaction field distribution, respectively.

The shape of a FORC diagram along the H_c axis informs about magnetization reversal. The increase in the distribution along the H_c axis can be attributed to a magnetization reversal by the propagation of TDW, while in the case of VDW, the coercivity distribution is not affected [22]. The elongated FORC distribution with closed contours extending along H_c indicates a single-domain structure. Interacting SD systems have contours close to the central peak with a pattern extended along the H_u axis. The transition to PSD structure causes oval-like contours with the peak moving along H_u, while the MD structure shows broad and open contours with a less steep slope extending along the Hu, which diverges from the H_u = 0 axis and intersects the H_c axis [65,66].

Therefore, in the case of small-diameter nanowires, a single elongated region can be observed along the H_c axis at H_u = 0 with a slight extension in the perpendicular direction. This indicates a small coercivity distribution (920–1420 Oe), probably related to the small difference in the nanowire length. The coercivity value determined from the hysteresis loop (1110 Oe) corresponds to the maximum of the FORC diagram. This compatibility of the coercivities determined from the hysteresis loop and those obtained for individual NWs from the FORC diagram, and above all, the relatively narrow distribution along the H_u axis, suggests negligibly small inter-wire interactions. The distribution along the H_c axis points out the magnetization reversal by the propagation of the transverse domain wall [22]. Such a contour closed around the central peak indicates a single-domain structure of nanowires. The slight positive slope in this distribution can be interpreted as the appearance of another interaction field in addition to the almost

<figure><img src="image_10.png" /><figcaption>**Fig. 9.** Angular dependence of hysteresis loops for FeCoNi nanowires of different diameters (a, b), analytical calculations, and experimental results of H_c (0) for FeCoNi nanowires with L = 6 µm and Φ = 100 nm (c) and experimental results of coercivity for different lengths and diameters (d, e).</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Fig. 10. Out-of-plane FORC diagrams of FeCoNi nanowires with a length of 6 µm and different diameters: (a) 40 nm and (b) 100 nm.</figcaption></figure>

constant interactions, giving a small symmetrical broadening [65].

With the diameter increase, the shape of the FORC diagram undergoes a large change. In contrast to the previous case, the diagram is elongated in the direction parallel to the $H_u$ axis. Such a distribution indicates the presence of magnetostatic interactions between nanowires [67,68]. The shift of the pattern towards a lower $H_c$ value (compared to Fig. 10a) confirms a lower individual coercivity of nanowires with larger diameters. The contours are symmetrically arranged with respect to $H_u = 0$ (–400 Oe–400 Oe) and slightly spread along $H_c$ with a distribution between 280 and 570 (Δ = 290 Oe). The closed contours with a steep

slope suggest a single-domain structure of the nanowires [68–70]. The tail extending along the $H_c$ axis may originate from a non-uniform NW length distribution [71]. Moreover, one can distinguish another small separated region with low coercivity, which can be assigned to the soft magnetic phase originating from overdeposited caps.

In summary, the analyzed patterns revealed that the larger diameter nanowires exhibited lower coercivity of individual nanowires compared to 40 nm diameter nanowires and higher inter-wire interactions while maintaining a single-domain structure for both considered diameters. Thus, the nanowires with a diameter of 40 nm are non-interacting,

<figure><img src="image_12.png" /><figcaption>Fig. 11. Lorentz-TEM in-focus (left) and under-focus (right) images of FeCoNi NWs for (a) 40 nm and (b) 100 nm diameter.</figcaption></figure>
single-domain structures, which seems to better meet the criteria required for the desired application.

Further investigations of the magnetic properties of the FeCoNi nanowires were carried out using Lorentz-TEM. Fig. 11 shows the images obtained for nanowires with a length of 6 µm and a diameter of 40 nm and 100 nm (as in FORC). Under-focus and in-focus Lorentz-TEM images show bright and dark fringes along both sides of the nanowires and inside them, respectively. For smaller diameter nanowires, uniform Fresnel fringes along the whole nanowires indicate the single-domain structure without a domain wall in the analyzed area of nanowires [72]. Small perturbations along the nanowires reflect the sample morphology shown in the in-focus image. On this basis, it can be concluded that the presented nanowires behave like a material with a single-domain structure. The same observations were made for nanowires of a larger diameter. Analysis performed at different locations did not reveal the features expected in a multi-domain structure. Thus, studies carried out using a Lorentz microscope suggest a single-domain structure in nanowires of both diameters.

Among the studied nanowire geometries, nanowires with a diameter of 40 nm seem to be the most promising candidate for racetrack memory application. However, considering the magnetic stability of the designed magnetic memories and their reliability, as well as the much greater ease of sample fabrication and measurement, we chose 100 nm diameter nanowires as the first candidate for the preparation of segmented nanowires. On the other hand, high thermal stability of FeCoNi-based alloys, along with maintained magnetic properties even after annealing at 500 °C [73] and relatively high Curie temperature (600 K for Ni NWs with similar size [74–76]) allows us to expect that 40 nm diameter nanowires would also be attractive for race track memory application, which will be tested next.

## 4. Conclusions

FeCoNi nanowires, due to the possibility of tuning their chemical composition by varying applied cathodic potential (as observed in our previous studies [25]), could be basically produced in the form of segmented nanowires in a single bath electrolyte. However, before preparing such a segmented structure, it is necessary to determine the geometrical parameters, which was the aim of this research.

The obtained nanowires are semi-hard magnetic materials that, at selected potential, exhibit a stable chemical composition and structure unaffected by their geometry in the range interesting from the application point of view ($\phi \le 100$ nm). Moreover, such nanowires show a single-domain structure, in which the magnetic moment rotation occurs via the propagation of the vortex domain wall (at angles close to the easy axis). The required non-interacting nanowire matrix was achieved for nanowires with a diameter of 40 nm.

Thus, the nanowires with diameters of 40 nm and 100 nm (short length), showing single domain structure and reversal mechanism based on vortex domain wall propagation, meet the criteria required for 3D magnetic memory racetrack systems, and can be produced in the form of segmented nanowires.

## CRediT authorship contribution statement

**Anna Nykiel:** Writing – original draft, Visualization, Validation, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Arkadiusz Zarzycki:** Visualization, Validation, Methodology, Formal analysis, Data curation. **Wojciech Maziarz:** Visualization, Validation, Methodology, Formal analysis, Data curation. **Jaafar Ghanbaja:** Visualization, Validation, Methodology, Formal analysis, Data curation. **Alain Walcarius:** Writing – review & editing, Validation, Supervision, Project administration, Conceptualization. **Magorzata Kac:** Writing – review & editing, Validation, Supervision, Project administration, Methodology, Investigation, Formal analysis, Data curation, Conceptualization.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

This research was supported by a French Government Scholarship.

## Data availability

The Repository of the Institute of Nuclear Physics, Polish Academy of Sciences (https://rif.jif.edu.pl/handle/item/473) contains the raw data [DOI: https://doi.org/10.48733/no3.25.019].

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