Anomalous Codeposition of fcc NiFe Nanowires with 5–55% Fe and Their Morphology, Crystal Structure and Magnetic Properties

The anomalous codeposition phenomenon known as a "volcano" type curve-with a maximum in Fe-content in NiFe as a function of the applied potential or current density-was observed in the literature for the thin NiFe films^32–34 and NiFe nanowires.²⁰ The observed results were explained through the limited mass transport of Fe⁺² ions after the peak. This explantion is partially correct, but not complete. We propose in this work an alternative explanation of anomalous codeposition-through the surface concentration of H⁺ dependent adsorption/desorption of FeOH⁺ and NiOH⁺ electroactive species. We have used the same concept recently explaining the concentration gradient in thin CoNiFe³⁵ and NiFe³⁶ films, as a special case of anomalous codeposition. In the text below, we will outline two important features of the alternative view on anomalous codeposition, i.e. modified Bocris-Drazic-Despic (BDD) mechanism and the role of H⁺ in the anomalous codeposition of NiFe alloys.

We have modified the earlier BDD-mechanism and used it to explain some of the observed experimental results in the literature like: decrease of current efficiency in CoFe alloys with the increase of Fe-content in deposit,³⁰ and the increase of tensile stress of CoFe alloys with the increase of Fe-content in deposit.³⁷ The modified BDD-mechanism, which is relevant to all iron group metal electrodeposition in acidic media, is shown in reactions 1-4.

Our previous studies demonstrated that the higher concentration of M⁺² ions in solution bring about a higher concentration of H⁺ through the hydrolysis reaction 1.³⁰ The calculated concentrations³⁸ of FeOH⁺ and NiOH⁺ species in the plating solution at pH 3.0 are negligible, i.e. [FeOH⁺] ∼ 10⁻⁹ M and [NiOH⁺] ∼ 10⁻⁹ M. Therefore, both species must be formed at the electrode surface through the diffusion and hydrolysis of solvated ions present in relatively high – calculated-concentration, i.e. [Fe⁺²] = 0.01 M and [Ni⁺²] = 0.15 M, according to the reaction 1, which is the first step in the Bockris, Drazic, Despic (BDD) mechanism.³⁹

The formed MOH⁺_ads species is reduced in the rate determining step³⁹ in reaction 2 leading to the formation of neutral monovalent metal hydroxide. The key in modified BDD-mechanism is that the proton liberated through hydrolysis reaction1increases the concentration of protons at the electrode surface and can be reduced together with MOH⁺_ads ions in reaction 3at a more negative potential than the H⁺ from the plating solution. Thereby, the total concentration of protons at the electrode surface, [H⁺]_Total, is the sum of the concentrations of protons from the solution and protons liberated from the reaction 1, i.e. [H⁺]_Total = [H⁺]_Solution + [H⁺] _Reaction.

Another key for anomalous codeposition is that H⁺ may act as a catalyst in the dissociation reaction of MOH⁺_ads in reaction5, which is actually the backward reaction6in the first step of BDD-mechanism. The reaction5is an overall reaction which probably proceeds through two steps,i.e. protonation of MOH⁺_ads followed by dissociation of the formed dication.

There is a competition for the protonation reaction between two adsorbed species, i.e. NiOH⁺ and FeOH⁺. Due to ∼1000 times higher dissociation constant of NiOH⁺ (pKa = 4.3)⁴⁴ than FeOH⁺ (pKa = 7.2),⁴⁰ NiOH⁺ is thermodynamically more favored to dissociate into solution while FeOH⁺ accumulates adsorbed at the surface. The rates of discharge of monohydroxide ions, FeOH⁺_ads and NiOH⁺_ads, are proportional to their respective surface fractions.

The last step in modified BDD-mechanism is reaction 4, i.e. one electron reduction of MOH_ads to M and OH⁻ at the electrode surface. The liberated OH⁻ base is protonated in acid-base reaction 6

Figure 3-left shows a typical "volcano" type curve obtained at controlled potential electrodepositions of thin film NiFe alloys using a Pt-RDE (125 rpm) with the peak in Fe-content at the potential −1.05 V/SCE. The "selectivity ratio" (SR) increases with the increase of negative potential from −0.7 V/SCE to −1.05 V/SCE (Fig. 3-right) indicating more anomalous codeposition and decreases toward less anomalous codeposition in the range of potentials from −1.05 V to −1.3 V/SCE.

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Figure 4 shows the change of the partial current densities of metals (Ni, Fe) and hydrogen (H) during the electrodeposition of NiFe films as a function of the potential of Pt-RDE with the rotation rate of 125 rpm. The total current density i_T, (i_T = i_Fe + i_Ni + i_H) shows the current plateau in the range of potentials from −0.7 to −0.95 V/SCE. The potential region of the plateau coincides with the reduction of all four electroactive species: FeOH⁺, NiOH⁺, H⁺_reaction and H⁺_solution, giving rise to the gradual increase of plateau. The total current density, i_T, at the plateau is higher than the limiting current density, i_L, calculated for H⁺_solution for the solution at pH 3.0 under the same hydrodynamic conditions of Pt-RDE (i_L = 0.63 mA/cm²).⁴⁰ The total current density takes off in the range of potentials from −0.95 V to −1.1 V/SCE, where codeposition of NiFe alloys becomes more anomalous. Notably, in the same region of potentials the hydrogen partial current density, i_H, is 2–3 times larger than the limiting current density measured for proton in solution at pH 3.0.⁴⁰ The electrodeposition of Ni and Fe starts at the potential −0.7 V/SCE but with low current efficiency.

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Figure 5 shows dependence of the current efficiency and the hydrogen partial current density, i_H, on the electrode potential of Pt-RDE. The current efficiency, η, was calculated from the partial current densities using formula: η = (i_Fe + i_Ni)/(i_Fe +i_Ni + i_H) × 100 (%). The current efficiency increases from 5 to 80% in the range of the potentials from −0.7 to −1.2 V/SCE and decreases at the more negative potentials due to the reduction of H₂O according to Eq. 7.

The produced OH⁻ base in reaction 12 is neutralized in acid-base reaction 11. The "parasitic" currents due to the reduction of H⁺ and H₂O generally decrease current efficiency and increase hydrogen partial current density, i_H. The rough potential distribution of the dominant hydrogen electroactive species- participating in the increase of hydrogen partial current density-are shown in Fig. 12. It is important to note that the reduction of the proton from solution on Pt electrode starts at potential ∼−0.5 V/SCE.³⁰ It continues to be dominant together with proton from the reaction in the range of potentials from −0.7 V to −0.95 V/SCE. The proton liberated in reaction 6, H⁺_react, is dominant hydrogen elctroactive species, together with FeOH⁺ and NiOH⁺, in the potential range of −1.0 V to −1.2 V/SCE.

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The areas of three different Au electrodes, i.e. Au-thin film, Au-AAO template, and Au-electrodeposited into nanowire template at different time/length(Au-ED), were evaluated using K₂Fe(CN)₆ as a reversible one electron transfer oxidation (Eq. 8).

Figure 6 shows a reversible one electron cyclic voltammogram obtained at Au-thin film electrode at a 10 mV/s sweep rate. The cyclic voltammogram shows the peak separation, ΔEp = Ep_a – Ep_c = 60 mV and the peak ratio ip_a/ip_c = 1.0, which is close to the "ideal" reversible voltammogram.⁴¹ It is important to note that the results of ΔEp measured at the same sweep rate for Au-ED and Au-AOO template (not shown here) are somewhat higher than that obtained for Au thin film electrode and follow the order: Au-thin film > Au-ED > Au-AAO template. This might indicate the relatively slower electron transfer on Au-ED and Au-AAO template electrodes, compared to the sputtered Au-thin film electrode, possibly due to different crystalline structures and morphology of the Au surfaces. The anodic peak current, i_p, is defined by the Randles-Sevcik equation⁴¹ (Eq. 9), which is proportional to the bulk concentration, C^b (mol/cm³), area, A (cm²), and square root of the sweep rate, ν^1/2 (V/cm).

Taking the concentration of K₄Fe(CN)_6, C^b = 2.08 × 10⁻⁶ (mol/cm³), the number of electrons (n = 1), nF/RT = 38.92 (1/V), the Faraday constant (96484 C) and diffusion coefficient, D = 0.63 × 10⁻⁵ cm²/s,⁴⁵ the area of Au-thin film electrode was calculated to be A = 0.754 cm². The diameter of the O-ring opening is 2r = 1.0 cm, therefore, the calculated geometrical area is A = 0.785 cm² and very close to the experimentally determined area of the Au-thin film electrode.

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In order to study surface area development during the nanowire electrodeposition and growth of Au we have used a cyanide-based gold solution. Figure 7 shows linear sweep voltammograms obtained at Au-thin film (1) and Au-AAO template electrodes (2) at the sweep rate of 20 mV/s. Two waves with the peaks observed around −0.8 V/SCE and −1.2 V/SCE were attributed to the reduction of adsorbed Au(CN)_ads electroactive species at the less negative potential (Eq. 4)-formed in the preceding chemical reaction (Eq. 10,11)-and direct reduction of Au(CN)₂⁻ at the more negative potential (Eq. 12).⁴²

The current ratio at the second peak potential obtained at both Au-AAO template electrode (curve 2) and Au-thin film electrode (curve 1), i.e 1.0/0.4 = 2.5, reflects the ratio of electrode area calculated from the Randles-Sevcik equation using K₄Fe(CN)₆ as a probe (see Fig. 9).

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The electrodeposition of gold nanowires into the AAO-template at the controlled potential of −1.0 V/SCE was carried out every 20 min through 4 hours. After each deposition the formed Au-ED electrode was washed with water and transferred into potassium hexacyanoferrate solution to evaluate surface area. The results of first 20 min deposition produced a uniform 500 nm thick Au nanowire shown in Fig. 8-left. It is clearly visible a rough surface of sputtered 300 nm of Au at the alumina surface.

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The shape of current-time transient recorded during 20 minutes of gold deposition, shown in Fig. 8-right, is very close to the calculated transient from the model for the growth of nanowires published recently.⁴² The advancing diffusive front is characterized in this model by four stages of mass transport control: linear flux within the pores, localized hemispherical flux at the mouth of the pore, semi-infinite linear diffusion, and the last stage where fluxes inside and outside pores are in balance by the continuity condition giving rise to the current minimum. Notably, the time spent in the first two stages of mass transport is less than 2 seconds.⁴²

The results of CV (Figure 9-left) obtained through one electron oxidation of Fe(CN)₆⁻⁴ showed a linear plot of i_p-ν^1/2 curve, which passes through the origin for all three kinds of Au electrodes. The current function, i_p/ν^1/2, is constant with the increase of the sweep rate. Therefore, both observations suggest that electrode reaction is controlled by diffusion. From the obtained slopes-proportional to the electrode area- all the areas were calculated using Randles-Sevcik equation. The results are summarized in Fig. 9-right. The area for Au-thin film is A = 0.785 cm², for Au-AAO template is A = 1.91 cm² or 2.43 times larger than area of Au-thin film electrode, for Au-ED the area is decreasing from A = 1.42 cm² (after 20 min of deposition) to A = 0.82 cm² (after 240 min of deposition). A similar increase of the electrode area for ∼2.3 times for Au-AAO template electrode compared to the geometrical area of the cross-section of the porous AAO template with d_w = 200 nm was found recently.⁴³ There are two main reasons for the increase of electrochemical area of Au-AAO template electrode. First, the sputtering of 300 nm of Au was found enough to completely close the pore with d_w = 200 nm, preventing the leaking of the solution to the Cu-stage. The deposition of Au along the sides of the pores brings about a hemispherical shape of the Au electrode.⁴³ Second, is the increase of the roughness factor by increase of Au thickness, which is defined here as a ratio of rms- roughness of sputtered 50 nm Au thin film to the rms-roughness of the 300 nm Au thin film. Figure 10 shows the images of thin film surfaces of Au sputtered on alumina. It is obvious that grain size on the surface of the 300 nm Au film is higher than on 50 nm Au film. The AFM rms-rougness (5 × 5 μm) measured on the 50 nm Au film is 1.5 nm and on 300 nm is 5.8 nm. Thus, the roughness factor is 3.8. The results obtained on measured electrochemical surface area-which changes with growth of nanowire inside the pores-suggest that the electrodeposition using constant current would produce the composition change along the NiFe nanowire length during the growth due to the changes in current density.

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Two cyclic voltammograms for NiFe solution obtained on Au-thin films and Au-AAO template electrodes, respectively-in the range of potentials from +0.4 V to −1.4 V/SCE at the sweep rate of 20 mV/s-are overlaid in Fig. 11-left. Both CV curves showed the same characteristic regions (a-c), which were already discussed for the case of Au-thin film electrode shown in Fig. 2. The major difference between two CV voltammograms is the appearance of a reduction new peak at −0.19 V/SCE, which is a product of the oxidation at the starting anodic potential of +0.4 V/SCE. In the double-sweep cyclic voltammogram (Fig. 11-right) run from +0.4 V/SCE to −0.45 V/SCE, the peak at −0.19 V appeared which on returned sweep produce chemically reversible peak at +0.08 V/SCE. The chemical nature of this redox couple on Au-AAO template electrode is not known at the present time. In region (a) the reduction of H⁺ diffusing from the solution starts at the less negative potential in the case of Au-AAO template electrode. In the region (b)-i.e. reduction and deposition of Ni⁺² and Fe⁺² electroactive species-the cathodic current in the case of Au-AAO template electrode is higher than the current obtained for Au-thin film electrode, due to the larger surface area at Au-AAO template.

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Figure 12 shows the chronoamperometry curves for electrodeposition of NiFe on Au-thin film and Au-AAO template electrodes at two controlled potentials during 60 s, i.e. at −1.1 and −1.4 V/SCE, respectively. It is shown that the cathodic steady-state current obtained at the potential of −1.1 V/SCE is 2.4–3.0 times higher for Au-AAO template electrode due to the larger surface area. The electrodeposition of NiFe at −1.4 V/SCE into the AAO template gave higher current which decreased after 10–20 s by ∼30%. Importantly, the potential region between −1.2 V and −1.4 V/SCE is a region where H₂O is reduced producing H₂ bubbles which block the surface area of the growing nanowires, giving rise to the lower current and generally nonuniformity in the nanowire length.

Figure 13 shows a typical potential-dependent "volcano" curve with a peak in Fe-content at −1.1 V/SCE for NiFe nanowires deposited in quiescent solution on Au-thin film electrode (Fig. 13-left) and Au-AAO template electrode (Fig. 3-right) using a three electrode cell described in Fig. 1. The "selectivity ratio" increases to the maximum value of ∼13-with increase of negative potential from −0.9 V/SCE to −1.1 V/SCE- indicating more anomalous codeposition in this potential range. Note that the potential at which a maximum in Fe-content in NiFe is obtained is less negative in quiescent solution (Fig. 13) compared to that obtained in agitated solution (Fig. 3), which is in agreement with the previous studies³² on the effect of agitation in anomalous codeposition. The selectivity ratio in NiFe nanowires (Fig. 13-right) decreases to the value ∼1.0 in the range of more negative potentials where codeposition of NiFe alloys becomes non-anomalous.

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The stable composition of Ni₅₆Fe₄₄ nanowire arrays with lengths of 3.0, 5.0 and 9.0 μm, respectively was obtained (Fig. 14-left, open circles). The composition along the length of 9.0 μm nanowire (Fig. 14-left, filled circles) was in the range of ±1% of the mean composition of Ni₅₆Fe₄₄. The Ni₅₆Fe₄₄ nanowires with a length of 9.0 μm shown in Fig. 14-right were uniformly deposited into Au-AAO template. For magnetic studies we used NiFe nanowires with the same length (L ∼ 3 μm) and the nanowire diameter (d_w = 200 nm). An example of uniformly deposited Ni₇₉Fe₂₁ nanowire with L ∼ 3.0 μm is shown in Fig. 15-right with a focus on a single nanowire with d_w ∼ 200 nm shown in Fig. 15-left, which had grown with a convex shape.

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The crystalline structure of electrodeposited NiFe nanowire arrays into AAO template was determined by XRD measurements. As expected, the NiFe nanowires have fcc structure shown in Fig. 16. The NiFe (111) and (200) diffraction peaks were present in all electrodeposited NiFe nanowires with 5–55%Fe. The average grain size was determined to be 9–11 nm based on (111) diffraction peak using the Scherer's equation, which is close to the value found in Ni-rich NiFe nanowires.¹⁶ The Au (111) diffraction peak shown in Fig. 16 is from the Au-seed layer deposited at the bottom of AAO template.

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Figure 17 shows the normalized hysteresis loop for the NiFe nanowire arrays with the same length (L∼3 μm), diameter (d_w = 200 nm), interwire distance (D = 250 nm) and diameter/interwire distance ratio of 0.8 as a function of their composition. All of the hysteresis curves are tilted with a low sureness (M_r/M_s). When the value of magnetic field is high enough to overcome the effective magnetic anisotropy the magnetization of nanowire arrays switches to its saturation value. A similar behavior was observed for Ni₇₉Fe₂₁ nanowire arrays with d_w = 70 nm and ratio of diameter/interwire distance of 0.7.¹⁸

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The values of coercivities (H_c), and squareness (M_r/M_s), when field is applied parallel and perpendicular to the nanowire axes are given in Table I. The parallel coercivity, H_c||, is higher than perpendicular, H_c⊥, for Ni₉₂Fe₈ and Ni₇₉Fe₂₁ alloys, but it is smaller for Ni₆₀Fe₄₀, Ni₄₄Fe₅₆ and Ni₄₅Fe₅₅ alloys. The observed sureness (M_r/M_s < 0.1) is close to zero revealing better orientation along the wire axis. We will discuss the two sets of magnetic behavior of NiFe nanowires depending on composition (Ni₉₂Fe₈ and Ni₇₉Fe₂₁ vs. Ni₆₀Fe₄₀, Ni₅₆Fe₄₄, and Ni₄₅Fe₅₅) including the difference of coercivities, ΔH_c = H_c, parallel – H_c, perpendicular, and the process of magnetization reversal.

The effective anisotropy energy, K_eff, (Eq. 13) is determined by shape anisotropy (K_sh = 6 × 10⁶ erg/cm³)⁴⁵ and magnetostatic anisotropy (K_ms) that overcome magnetocrystalline (K_mc = −7 to 5 × 10³ erg/cm³)^1,46 and magnetoelastic anisotropy (K_me = 4.3 to 75 × 10³ erg/cm³) (see Table II)

The coercivity is a quantitative measure of magnetic field required to reverse the magnetization direction in the thin film or nanowire arrays. The impact of two dominant anisotropy energies (K_sh and K_ms) in nanowire arrays is the best illustrated if one compare the coercivities obtained in thin films in which the shape anisotropy is zero.⁴⁸ Notably, the thin films of 500 nm NiFe with the same composition as two samples of electrodeposited nanowire arrays, i.e., Ni₇₉Fe₂₁ and Ni₄₅Fe₅₅ showed easy axis coercivities as 0.8 and 2.1 Oe, respectively. The easy axis coercivity, H_ce,, obtained with the thin films is about 25–120 times lower than the easy axis coercivity, H_c, parallel, in nanowire arrays. It is important to note, that in the studies of magnetic properties of NiFe nanowires^13–20 a magnetocrystalline anisotropy was taken into consideration as very small or "negligible"-which is true if one compares with the values of K_sh and K_mc. However, although the K_me is larger than K_mc, the magnetoelastic, K_me, anisotropy of NiFe nanowires-obtained and measured at the room temperature-was completely ignored.

In Figure 18 are presented results of stress and magnetostriction measurements obtained for 500 nm thin films of NiFe alloys with 5–95%Fe prepared by galvanostatic electrodeposition (5 mA/cm²) under the applied magnetic field in order to induce in-plane anisotropy, using acidic solution (pH 2.8).²⁵ Notably, saccharin was added into the plating solution as a stress reliever.

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The measured stress of fcc NiFe films with 5–55 At. % Fe increases with the increase of Fe-content in deposit, but is relatively low in the range from compressive −50 MPa to +200 MPa tensile stresses, which is typical for NiFe films deposited in the presence of saccharin as a stress relieving agent. The electrodeposition of the same films without the presence of saccharin could result in 2–3 times higher stresses.⁴⁹ The linear increase of tensile stress in fcc NiFe electrodeposited films was observed earlier.^23,50 Our results (Fig. 18) show the linear increase of tensile stress in both fcc and bcc NiFe alloys. We believe that the stress mechanism in these NiFe films could be due to adsorption/desorption of hydrogen similar to the described earlier in the case of CoFe,³⁷ i.e. through incorporation of hydrogen as a metal hydride at the grain boundaries, and subsequent recombination and diffusion out of hydrogen molecule leaving a grain vacancies at the boundaries. In the range of fcc/bcc and metastable (MS) NiFe alloys-in the so called Invar region²⁵ - other stress mechanisms possibly operate.

The measured values for magnetostriction, λ_s, agree, within error with the literature values.^1,47 The accepted value for λ_s = 0 is around Ni₈₀Fe₂₀ elemental composition. Our results show that the zero magnetostriction is obtained with the Ni₈₁Fe₁₉ elemental composition._. At the composition of NiFe film with Fe < 19%, magnetostriction is negative, above 19% of Fe in NiFe magnetostriction increases monotonously to the positive direction. Therefore, the calculated magnetoelastic anisotropy energy shown in Table II might be expected to exceed even more magnetocrystalline anisotropy of NiFe alloys with higher Fe-content and/or without the presence of saccharin in plating solution as a stress relieving agent.

Figure 19-left shows the decrease of the parallel coercivity, H_c||, with the increase of Fe-content in NiFe nanowires. The decrease of H_c|| correlates with the increase of the magnetic saturation, B_s, which follows the Slater-Pauling curve.²⁵ This can be attributed to the combined effect of shape anisotropy and magnetostatic anisotropy between the nanowires.⁴⁵ For the arrays of nanowirws the effective anisotropy containing only the magnetostatic contribution is given by Equation 14.⁴⁵

where M_s is the magnetic saturation and P is the packing factor or porosity given by r²/3.5D², which depends on diameter of nanowire, d_w = 2r, and the interwire distance, D. Thus, the increase in H_ms is due to the increase of saturation magnetization or due to the increase of Fe-content in NiFe alloys. The increase of H_ms enhances the stray field in nanowire arrays-resulting in lower H_c||. This can be also achieved by increasing the length of NiFe nanowire alloy, L, with the same composition or the same magnetic saturation value according to the Equation 15,⁵¹ due to the net contribution from the perpendicularly aligned dipole field, H_d, which reduces the effective anisotropy. The results in Fig. 19-right illustrate the effect of length (3 vs. 9 μm) of Ni₄₀Fe₆₀ nanowire arrays on coercivity measured at different angles.

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Our results clearly show the decrease of coercivity, H_c||, as a function of Fe-content (5–55%) in NiFe nanowire arrays electrodeposited in AAO templates with large diameter (d_w = 200 nm) and d_w/D ratio is 0.8. This is somewhat different from the results in the literature, obtained with NiFe nanowire arrays containing 15–35%Fe deposited in AAO templates with smaller diameters (d = 35–41 nm) and d_w/D ratio ∼0.4, which showed small increase of coercivity, H_c||,⁵¹ or no significant dependence of coercivity¹⁵ as a function of alloy composition. The values of H_c||, obtained with NiFe nanowires deposited in AAO templates with small diameters (d_w = 35–41 nm) are much higher^15,51 than that obtained in this work (d_w = 200 nm). The decrease of coercivity with increase of nanowire diameter is a general trend for the various ferromagnetic materials⁵² indicating that the shape anisotropy is dominant.

Figure 20-left shows dependence of coercivity, H_c, measured parallel and perpendicular to the nanowire axis as a function of Fe-content in NiFe. The difference ΔH_c = H_c||, -H_c⊥ is positive for Ni₉₂Fe₈ and Ni₇₉Fe₂₁ alloys and negative for other three NiFe alloys with Fe > 30%. At the Fe-content in NiFe around the composition of 30 At. % Fe there is a crossing of parallel and perpendicular curves where ΔH_c = 0. Since the magnetocrystalline, H_mc, and magnetoelastic, M_me, anisotropies are acting in-plane direction, or perpendicular to the nanowire axis, the effective anisotropy can be expressed as:

The positive ΔH_c difference is observed with NiFe nanowires having a "negligible" both H_mc and H_me anisotropies. The negative ΔH_c was observed with the NiFe nanowires, having a higher M_s-values and increasing H_mc and H_me anisotropy fields, which are acting simultaneously on both shape, H_sh, and magnetostatic, H_ms, anisotropy fields giving rise to the decrease of easy axis coercivity, H_c||, in nanowire arrays. Figure 20-right shows decrease of ΔH_c, as a function of Fe-content in NiFe nanowire arrays reaching the minimum at 40% Fe and increase followed by increase of Fe content in NiFe alloys.

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The comparison of some properties of thin films and nanowires of NiFe alloys with 8–55 At. % Fe are given in Table II. The results demonstrate that the magnetism of nanowires is dominated by shape and magnetostatic anisotropy. The shape anisotropy for an infinite cylinder is 2π Ms,¹² where Ms is the saturation magnetization determined by measurements on NiFe thin films.²⁵ The corresponding values for H_ms and H_eff were calculated using the Equations 14 and 16, respectively. The values for H_mc (not shown) were calculated using literature data for K_mc, while H_me values (not shown) were calculated from K_me based on experimental data presented in Fig. 18 and Table II. The parallel coercivity, H_c||, is only the small fraction fraction of H_ms. The ratio H_c||,/H_ms decreases with increase of Ms value or Fe-content in NiFe alloys. The ratio ΔH_c/H_eff vs. Fe-content in NiFe exhibit the same shape as the ΔH_c vs. Fe-content in NiFe curve shown in Fig. 20-right.

The process of magnetization reversal in NiFe nanowire arrays was investigated. We have obtained two sets of behavior depending on the composition of NiFe nanowires. In the case of Ni₉₂Fe₈ and Ni₇₉Fe₂₁ nanowire coercivities decrease in the 0–90° and increase in 90–180° angular range (Fig. 21). In the case of Ni₄₀Fe₆₀, Ni₅₆Fe₄₄, and Ni₄₅Fe_55, the coercivities increase in the 0–90° and decrease in 90–180° angular range.

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Two of the most common magnetization reversal mechanisms are coherent rotation (CR) and curling mode (C).⁵³ For a specific magnetic material, the critical diameter, d_cr,-given by Equation 17 where A is the exchange stiffness and M_s is magnetic saturation⁵⁴ - has been considered as a criteria for transition between CR and C mode.

For the small nanowire diameters (d_w < d_cr) the preferred mode is coherent rotation (CR), while for d_w > d_cr the curling mode (C) is expected.⁵⁴ By assuming A = 10⁻⁶ erg/cm and taking Ms-values in emu/cm³ from Table II-the critical diameters for Ni₉₂Fe₈, Ni₇₉Fe₂₁ Ni₄₀Fe₆₀, Ni₅₆Fe₄₄, and Ni₄₅Fe₅₅ nanowires were calculated as: 37.2, 25.6, 18.0, 17.4 and 16.3 nm, respectively. Since d_w > d_cr is characteristic for all of NiFe nanowires studied one could expect that C-mode would be a dominant reversal mechanism. We have observed experimentally an angular dependence of Ni₉₂Fe₈ and Ni₇₉Fe₂₁ nanowire coercivity, with the lowest value at the 90° angle, which theoretically corresponds to the curling reversal mechanism (C-mode).⁵⁴ For Ni₄₀Fe₆₀, Ni₅₆Fe₄₄, and Ni₄₅Fe₅₅ nanowire coercivity, we have observed the highest value at the 90° angle, which theoretically corresponds to the coherent rotation (CR).⁵⁵