Effect of shape and magnetocrystalline anisotropies in ordered Co nanorod arrays with smaller diameter

Author’s Accepted Manuscript Effect of shape and magnetocrystalline anisotropies in ordered Co nanorod arrays with smaller diameter B. Sellarajan, H.S. Nagaraja, Harish C. Barshilia, P. Chowdhury www.elsevier.com/locate/jmmm

PII: DOI: Reference:

S0304-8853(15)30876-3 http://dx.doi.org/10.1016/j.jmmm.2015.12.010 MAGMA60934

To appear in: Journal of Magnetism and Magnetic Materials Received date: 22 July 2015 Revised date: 9 November 2015 Accepted date: 2 December 2015 Cite this article as: B. Sellarajan, H.S. Nagaraja, Harish C. Barshilia and P. Chowdhury, Effect of shape and magnetocrystalline anisotropies in ordered Co nanorod arrays with smaller diameter, Journal of Magnetism and Magnetic Materials, http://dx.doi.org/10.1016/j.jmmm.2015.12.010 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Effect of shape and magnetocrystalline anisotropies in ordered Co nanorod arrays with smaller diameter B. Sellarajan1,2, H. S. Nagaraja2, Harish C. Barshilia1 and P. Chowdhury1,∗ Nanomaterials Research Laboratory,surface Engineering Division, Council of Scientific and Industrial Research-National Aerospace Laboratories, Bangalore-560 017, India. Department of Physics, National Institute of Technology Karnataka, Surathkal 575 025, India.

Abstract Template assisted growth of Co nanorod arrays through electrochemical route was investigated. During this investigation, the template with nano-pore diameter was kept at a fixed value of 45 nm, whereas, the length of the as grown nanorod array was varied from 25 to 400 nm keeping in mind that the aspect ratio (L/D) covers both below and above the unity. X-Ray diffraction patterns indicate that the nanorod arrays initiates its textured growth with fcc (111) phase, however, the change in growth texture to hcp (100) was observed as it grows above 200 nm in length. The anisotropy fields extracted from the measured magnetization data reveal that a cross-over from in-plane to out- of plane anisotropy takes place for L/D ∼ 2.0. Based on the analytical approach, it seems that the shape anisotropy originated from the demagnetization factor with the change in geometry and magnetostatic interaction among the nanorods cause this crossover. However the micromagnetic simulation yields that both magnetocrystalline anisotropy and the magnetostatic interaction along with shape anisotropy are very much important to explain the experimental observations.

1. Introduction Large aspect ratio of 1D magnetic nanowire arrays of Fe, Ni, Co and their alloys have been extensively investigated to understand fundamental physics behind the reversal processes. This helps to explore them for potential use in Preprint submitted to Elsevier

December 7, 2015

technological applications such as, hard disk storage media, magnetic random access memory, and other spintronic devices [1, 2]. So far, the interpretation of magnetization reversal process was limited by the shape anisotropy for the nanowire arrays of soft magnetic materials [3], whereas in the case of hard magnetic materials with uni-axial anisotropy such as Co nanowires, consideration of both shape and magnetocrystalline anisotropies [4, 5, 6, 7] was found to be very important to understand their unusual behavior of the reversal process. In fact, magnetocrystalline anisotropy, originated from the crystalline growth structures of the nanowire, provides an added advantage to tune the anisotropy of the system for spintronic applications. For the last couple of years, 1D growth of Co nanowire arrays through anodic alumina oxide (AAO) template became common interest due to several reasons. Among them, tunable nano-pore channels in AAO template assist to grow nanowire arrays in the wide range of diameters from 35 to 200 nm using electrochemical technique. Interestingly, under identical bath conditions, the growth initiation takes place with different crystal textures for different pore diameters. In our previous work, we reported that the nanowire growth initiates with hcp (002) structure and changes to other orientation with hcp (100) phase as it grows few hundred nm in length [8, 9]. However, with reducing the nanwoire diameter to less than 50 nm, fcc (111) was found to be stable phase at the beginning of the growth and transition to hcp (100) phase occurs while nanowire grows few hundred nm in length [10, 11, 12]. The reason behind this structural transition is still unclear. However, this may be due to a twisted wire with circumferential strain while growing nanowires in a constrained AAO pore wall structure as suggested by Hu et al. [13]. The presence of bi-layer with different phases within a single nanowire complicates the understanding of the magnetization reversal process in the system. This leads to an increase in interest to work in the intermediate length of the nanorod regime, where the length lies in between magnetic nanodots and nanowires. Recently, Vivas et al. have shown the effect of nanowire diameter on both crystalline structure and magnetic anisotropy for an array of Co nanorods with 2

length of about 120 nm [10]. They also showed that the decrease in diameter causes a structural transition from hcp (100) to fcc (111) phases. This leads to a change in the reversal mode with the increased diameter from vortex propagation to curling for the field applied along cylindrical axis and from coherent rotation to curling for the perpendicular one. To the best of our knowledge, there is no report on the reversible process so far on nanorods with length less than 120 nm. Therefore it will be interesting to work in this regime due to the following reasons: (i) decrease in aspect ratio leads to an enhancement of shape anisotropy due to geometry effect and (ii) growth of single crystalline structure in lower length regime enables us to see effect of magnetocrystalline anisotropy against the shape anisotropy. In this paper, we attempt to understand the effect of both magnetocrystalline and shape anisotropies on magnetization reversal process with varying the length of Co nanorod arrays while keeping the rod diameter constant. For this, Co nanorod array with individual wire diameter of 45 nm was fabricated by pulse dc electro-deposition process. A crossover from in-plane to out-of-plane anisotropy was observed unexpectedly for L/D ∼ 2.0. An approach was made to explain this experimental observation using both micromagnetic simulation and an analytical formula developed based on the shape anisotropy and the magnetostatic interaction among the rods. 2. Experimental details The AAO templates were prepared by a two-step dc anodization process as described previously [8, 9, 14, 15]. In the present work, a hexagonally close packed pore arrays of uniform pore diameter and periodicity were obtained under the appropriate conditions (i.e., 0.3 M H2 SO4 ; 25 V at 3 ◦ C). The typical pore parameters of AAO templates with highly ordered pore arrays are of 27±4 nm pore size and 66±3 nm of inter-pore distance. The final pore size of 45 ±4 nm was adjusted by the isotropic wet-chemical etching (i.e., 6 wt% of H3 PO4 for 29 min) process, without affecting the inter-pore distance. Hence, the template is prepared and then the top surface of the AAO membrane was sputter coated 3

with an Ag layer of 300 nm, which served as a working electrode in a three terminal electro-plating cell. To facilitate the penetration of Co2+ ions through the pores of the templates, the wetability of the pore channels was performed by immersing the working electrode into the de-ionized water. This enhances the adhesion of the Co2+ ions as a homogenous pore filling at the pore bottom during the deposition. The filling of pore channels was achieved by a dc pulse height of 2.0 V with Ton = Tof f = 20 ms, as described in our previous papers [8, 9]. The Co electrolyte is an aqueous solution consisting of 120 g/l CoSO4 and 30 g/l H3 BO3 at room temperature with pH ∼ 2.8. The rods grew in the usual bottom-up fashion starting from the Ag electrode at the pore bottoms and the average rod length was controlled by varying the deposition time (i.e., adjusting the number of cycles of a pulse width ∼ 4 nm / cycle). Several samples were prepared using templates having different nanorod lengths, where the pore diameter and the inter-pore distance were kept constant. Moreover, the structural analysis of Co nanorod arrays was performed by D8 Advanced Brucker X-ray diffractometer by using a source of Cu Kα = 1.5461 ˚ A. A high sensitivity vibrating sample magnetometer (VSM; LakeShore) was used to measure the coercivity and anisotropy of the Co nanorod arrays. 3. Array morphology and structural characterization Porous alumina membranes with hexagonally ordered nano-pore arrays were prepared using a two-step anodization of Al in an electrolyte using 0.3 M of H2 SO4 . Figures 1(a)-(c) show the surface morphology of the porous films with bottom, top and cross-sectional views, respectively. It is also expected that the diameter of the pore should be uniform throughout the channel length, and is shown in Fig. 1(c). Pores filled Co nanorod arrays were obtained by a dc pulse deposition technique, hence the growth was found to be uniform throughout the nano channels. Partially etched porous alumina membranes, which were embedded with Co nanorod arrays, are shown in Figs. 1(d)-(f) with different nanorod lengths of 100, 200 and 400 nm, respectively. The diameter of each Co

4

nanorod was found to be same as the diameter of the nano-pore (i.e., Dp = 45 ± 5 nm) in the alumina membrane. The recorded X-ray diffraction patterns for Co nanorod arrays with varying lengths are shown in Fig. 2(a). The 2θ scan provides the information of Co nanorods with a preferential growth of fcc (111) for length up to 200 nm and further growth indicates the change of the crystalline structure into hcp poly-crystalline phases with presence of peaks from (100) at 41.6◦ and (110) at 75.9◦ respectively. Some of the additional peaks at 38.2◦ , 64.6◦ , and 77.5◦ are obtained from the Ag (filled square) coated thick film, which served as an electrical contact in one of the faces of the porous membrane. The peak corresponding to Co fcc (111) at 2θ ∼ 44.4o is shown in Fig. 2(b) in the expanded form, which indicates that the decrease in FWHM while growing the length of Co nanorod arrays from 40 to 400 nm, as expected in a nano-scale regime. Moreover, it is well known that to distinguish between the peaks arising from hcp (002) and fcc (111) Co phases is very difficult, as the 2θ lies very close to each other i.e, at 44.2◦ and 44.4◦, respectively. In particular, we know that for bulk Co, the hcp structure is more stable than the fcc structure at room temperature [16], whereas, the plausible growth of hcp (002) phase for larger diameter (∼ 70 nm) was reported in our previous work [8, 9]. However, it is still unclear why the amount of fcc phase increases in small diameter [2, 11, 17]. In particular, this agrees with very recent studies of diameter influenced crystalline phase diagram, which reported that fcc Co phase formation is favorable for 35 nm pore size while growing them through electro-chemical route [10, 11, 12, 17]. 4. Magnetic properties 4.1. Experimental results We have also performed magnetic characterization with applied field both parallel ()and perpendicular (⊥) to the nanorod axis at room temperature. Figures 3(a)-(e) show the complete data set of the hysteresis loop for different lengths of the nanorod arrays. Table 1 presents the extracted physical pa

rameters from the measured M(H) curves. In this table, Mr /Ms and M⊥ r /Ms 5

represent the remanence ratio for parallel and perpendicular directions, respec

tively. Hence, the ratio, Mr /M⊥ r , greater or less than unity determines the easy axis parallel or perpendicular to the nanorod axis, respectively. The magnetization easy axis may also be defined by the sign of the effective 

anisotropy field, Hs [18]. Here the estimated values of Hs (= H⊥ s - Hs ) 

for our samples are given in table 1, where Hs is the saturation field when the magnetic field is applied parallel to the nanorod axis and H⊥ s is the saturation field when the magnetic field is applied perpendicular to the nanorod axis. The dependence of Hs on L and hence the changeover in easy axis direction from perpendicular to parallel direction supports the observation made on remanence ratio data, as mentioned above. From table 1, it is confirmed that the easy axis lies along the longitudinal direction for L≥100 nm as expected from the shape anisotropy. However, a 



reduction in both Hc and Mr was observed for L = 200 nm. The origin of such discrepancy might be due to the change of the crystalline structure from fcc (111) phase to hcp (100) phase while nanorod growing in length beyond 200 nm. This is further confirmed from the X-ray diffraction data where the appearance of hcp (100) phase was observed for a nanorod of length 400 nm (see Fig 2 (a)). The fcc (111) phases orient one of their easy magnetization direction along the nanorod axis, which reinforces the shape anisotropy. Whereas, the small contribution from the hcp (100) phase, in which the c axis is aligned normal to the rod axis, 



may result in the decrease of Mr and Hc [8, 10, 11, 12]. As the presence of hcp (100) phase within a nanorod complicates the magnetization reversal process [8], our theoretical explanation on observed behavior of anisotropy field, Hs as a function of L was restricted to the nanorod length, L ≤ 200 nm. To explain Hs (L), the following two approaches are made which are provided below.

4.2. Analytical calculations An analytical approach has been made to estimate the effective magnetic anisotropy field on array of nano-cylinders based on the following assumptions: 6

Table 1: Extracted magnetic parameters of Co nanorods.

Length (nm) 25 40 60 100 200



Hc (Oe) 710 563 1781 2151 1730

H⊥ c (Oe) 530 588 474 626 472



Mr /Ms

M⊥ r /Ms

0.16 0.15 0.43 0.74 0.64

0.64 0.56 0.43 0.33 0.22



Hs = H⊥ s -Hs Expt. Analytical Simulated Hs (Oe) (Hk )(Oe) Hs (Oe) -5676±275 -3355 -2394 -3854±265 -604 -2380 -1344±224 1408 -1195 1016±230 3188 1492 1595±350 4002 3276

1) the shape anisotropy related with demagnetization factor of the geometry, 2) the magneto-crystalline anisotropy, depending on the crystal symmetry of the material used and 3) the magneto-static coupling among the nano-cylinder arrays, and can be written as [18, 19, 20] Hk = 4πN(L)Ms − 6.3πMs r2 L/S 3 ± Hma ,

(1)

where Hma is the magnetocrystalline anisotropy field (material property), r (D /2), L and S are the nanorod parameters such as radius of the nanorod, length of the rod and the separation between the rods (in nm), respectively, and N (L)=Nx (L)-Nz (L); with Nx and Nz are the demagnetization factor along the x and z axis respectively, and can be determined using the relations [21], Nz (L) = 1 − F21 (D2 /L2 ) +

4D . 3πL

(2)

and Nx = (1 − Nz )/2

(3)

Here, F21 (y)= F21 [-1/2,1/2,2,-y] is a hypergeometric function. Figure 4(a) presents the variations of Nx , and Nz as a function of L. It is interesting to see that for the ratio of L/D = 0.9065, the values of Nx and Nz become 1/3, where the effect of shape anisotropy gets nullified due to the spherical symmetry of the nanorods. Hence, equation (1) predicts the crossover of HK from negative to positive value at a critical length, Lc (= 4N S3 /6.3r2 ∼ 45.9 nm) with a rod diameter of 45 nm. In other words, for L>Lc the easy axis lies along the 7

rod axis, whereas for L
8

4.3.1. For field applied perpendicular to nano-rod axis For L = 25 nm with L/D  1, the simulated M(H) loop shows a sharp transition at a nucleation field, Hn = -1200 Oe due to the coherent transition of magnetic spin vectors (Fig 5 (a)). However, with increasing the nanorod length to L = 40 nm, Hn was shifted at -900 Oe (Fig. 5 (b)) due to the formation of a vortex state within a nanorod in the xy-plane. A process of vortex annihilation was depicted by a long tail as observed in M(H) loop near the negative stauartion field. Figure 6 (a) shows 3D view of z-component magnetic distributions (outer shell) within a nanorod at a field of -900 Oe, presenting the vortex configuration in the xy-plane. For further clarity, a 2D view of spin distribution on the xz-plane with y = 0 is shown in the inset (i) of this figure. The angular distribution, χz (r), of M vector (see fig 6 (b)) predicts that the vortex intensity is uniform irrespective of the z values and the switching of vortex core in negative z direction, i.e., χz (r) = 180o at r = 0, occurs at the nucleation field itself. The origin of such vortex formation for L = 40 nm is due to both the shape and magnetocrystalline anisotropies in the system. For L = 60 nm, the vortex nucleation within nanorod array initiates at 700 Oe and results in sharp fall in magnetization value by 80%. Then, M follows a reversible behavior and maintains a linear relationship with the decreasing field till H = -700 Oe. With further decreasing the field, the deviation from the linearity indicates the beginning of vortex annihilation process. In the reversible region, it was observed that the hexagonal symmetry of the nanorod array and the magneto-static interaction among them initiate the vortex chiralities within a nanorod either in xy, yz or xz planes, keeping equal percentage of contribution in mx as a function of field H (not shown here). Figure 6(c) shows 3D view of z -component magnetic distributions (outer shell) within a nanorod at a field of 700 Oe, presenting the vortex configuration in the xz-plane. Two dimensional representation of the M vector in xz-plane at y= 0, shown in inset (i) of Fig. 6(c) further confirms the presence of vortex structure with the core along the y direction. The values of χy and χz extracted from this plane from different

9

z-values are shown in Fig. 6(d). At z = 30 nm, i.e., at the middle of the nanorod, χy (r) represents the vortex structure with angular variation from 0 to 90 o , whereas the change of χz (r) from 0 to 180 o confirms the vortex chiralities around y axis. For L = 100 nm, with L D, the shape anisotropy dominates and causes to align the magnetic spins along the z axis. This results in shift of Hn towards higher +ve value to 2510 Oe. At this field, the nucleation initiates with two different spin configurations among the nano-rods: (i) inhomogeneous twisting of magnetic spin distributions (M) around the rod axis, as shown in Fig. 6(e) for H = 0, and (ii) initiation of spin flipping along the z-axis in the xy-plane located at the center of the nanorod (not shown here). In case of former one, the spin distribution are in ”C” state within the xy plane for z = 48 nm(see inset (ii) in Fig. 6(e)), whereas along the rod axis, they are confined in ”S” state (i.e., in the xz-plane, see inset (i) of Fig. 6(e)) as reported previously [24]. Figure 6(f) presents the variation of χy (r) extracted from the inset (ii) of Fig. 6(e) for two different x values to further quantify the ”C” state. For x = -9 nm , χy (r) shows a variation in angle from 75 to 15o along the radial direction confirming the rotation of M vector within the xy-plane. Whereas, for x = 9 nm, a constant χy (r) = 900 indicates M vector along z-axis, which moves towards the edge during the annihilation processes. In case of later one, with decreasing field, the progress of spin flipping moves towards both top and bottom ends in antiparallel configuration with its nearest neighbor and form a flux closure pattern at the end. Further increase in L to 200 nm, the formation of vortex structure is fully disappeared. Rather, the reversal process initiates with spin flipping along the z-axis in the xy-plane located at the center of the nanorod as observed in some of the nanorods with 100 nm in length. It is to be mentioned that the spin flipping always occurs simultaneously with its neighboring rod in the antiparallel configuration. In the reversible region, the linearity of M(H) loop was nothing but due to the rate of change of spin flipping towards z-axis with decreasing the field value. 10

4.3.2. For field applied parallel to nano-rod axis For field parallel to the rod axis, the simulated M(H) loops for nanorod length varying from 25 to 200 nm are shown in Fig. 5 (blue square). With L < D, i.e., for the nanorods with lengths of 25 and 40 nm, initiation of vortex formation with respect to the z-axis occurs at nucleation fields, Hn , of 2250 and 1990 Oe, respectively, followed by a sharp drop in magnetization values by 70%. At this nucleation field, the remaining 30% of net mz contribution comes from the angular distribution of M vector along the radial direction, i.e., for constant z-value. The spin distribution along the outer shell of a nanorod at H = 2000 Oe is shown in Fig. 7(a). As shown in inset of Fig. 7(b), for z = 12, 21 and 30 nm, χz (r) changes from 90o to 0o along the radial direction as one approaches towards center. This implies that along the z direction for a constant (x,y) co-ordinate, χz remains unchanged. Therefore, a solid nanorod with fcc (111) structure can be defined as parallel cylindrical shells with constant M as reported for a case of hcp (100) [8, 9]. With further decreasing in field, M vs H shows a linear relationship. This can be correlated with the change in the rate of change of angular distribution of M vector, i.e., ∂χz /∂(r) along the radial direction. When the field increases in reverse direction, the M vector initiates it’s rotation towards negative z-direction from the edges (see Fig. 7(b)), whereas the core size reduces in diameter (shadow region) with reduction in +ve mz contribution. At H = Hc , the coercive field, with equal contribution of negative mz from larger outer shell and +ve mz from the shrinkage core makes the net mz to zero value. When the external field becomes strong enough, the vortex annihilation starts and the reversal process completes with annihilation of vortex from all nanorods giving M = -Ms . For L D the simulated M(H) shows several Barkhausen jumps in the M(H) loops, as shown in Fig. 5(c)-(e). For L = 60 nm, the reversal process occurs with two different spin configurations: (i) formation of single vortex within a nanorod as mentioned above for L = 40 nm, and (ii) two vortices with opposite chiralities (clockwise and anti-clockwise) separated by a domain at the center

11

of the nanorod, as shown in Fig. 7(c). The reversal process for the former case is discussed above and the contribution in net mz follows the similar procedure. In later case, for a set field, the intensity of vortices (i.e. angular distribution of M vector) decreases as it moves from top or bottom ends towards center (∼ 30 nm) and it diminishes at both sides of the domain wall having +ve mz components as shown by variation of χz along the radial direction for different z values. However, with decreasing field till H = Hc (see Fig. 7(d), left), the propagation of the vortex towards the center from both ends leads to reduce the width of the domain to minimum value along the z-direction. For H > Hc , the core spin flips to negative z-direction and the annihilation process starts in the whole nanorod through single vortex transition (Fig .7(d), (right)). For L > 100 nm, the reversal process begins at Hn = 700 Oe for L of 100 nm and -500 Oe for 200 nm, respectively. It forms two vortices at both the ends of the nanorod with a single domain state at the middle, as described above. It is to be noted that the size of this single domain state was increased to ∼ 50 nm of the nanorod length, at H = 0, as depicted in Fig. 7(e) for L = 100 nm. This indicates the rod length determines the size of the domain, which arises from the increase in magneto-static interaction with respect to L, as described in our 

previous report [8]. Therefore, increase in net Mr was observed as a function of L when the field is applied parallel to the nanorod axis, as shown in Fig. 5(d) and (e). However, for L = 100 nm, the spins of a nanorod in a hexagon seven nanorod array was flipped towards negative z axis near H = Hc . With consideration of shape of a nanorod, magnetostatic interaction among nanorods and magnetocrystalline anisotropies, the magnetization reversal process in Co nanorod arrays with fcc(111) structure was found to dominate by vortex structure and results in a crossover of easy axis from in-plane to out-ofplane direction in this system with critical length of 77 nm as observed in our experimental data. To reduce the discrepancy in the observed behavior of the M(H) loops, one needs to consider the following factors: (i) increase in number of nanorods (i.e., 108 for an area of 5×5 mm2 as in real case) in an array while carrying the simulation, (ii) presence of imperfection within nanorods, es12

pecially for the shorter nanorods, and (iii) physical shape variations among the nanorords. 5. Conclusion In summary, we have investigated the magnetic properties of Co nanorod arrays keeping the aspect ratio just below and above the unity. A crossover in their easy axis of magnetization was observed for nanorod arrays at a critical length, Lc , which is almost two times higher than its diameter. This is unexpected as the analytical formula derived based on the shape anisotropy and the magneto-static interaction among the nanorods yields Lc value of the order of its diameter. With consideration of shape, magnetocrystalline anisotropies and magnetostatic interaction among nanorods, micro-magnetic simulation explained well this crossover. The origin of this large Lc was found to be due to the complicated nature of reversal magnetization processes as the rod length grows. Acknowledgments Authors would like to thank the Director, NAL for supporting this activity. Mr. P. D. Kulkarni is thanked for Micro-magnetic simulations. B. Sellarajan thanks CSIR for providing SRF fellowship.

[1] Y. Henry, K. Ounadjela, L. Piraux, S. Dubois, J.-M. George, and J. L. Duvail, Magnetic anisotropy and domain patterns in electrodeposited cobalt nanowires, Eur. Phys. J. B 20 (2001) 35-54. [2] M. Darques, A. Encinas, L. Vila, and L. Piraux, Tailoring of the c-axis orientation and magnetic anisotropy in electrodeposited Co nanowires, J. Phys.: Condens. Matter 16 (2004) S2279-S2286. [3] C. L. Xu, H. Li, G. Y. Zhao, H. L. Li, Electrodeposition of ferromagnetic nanowire arrays on AAO/Ti/Si substrate for ultrahigh-density magnetic storage devices, Materials Letters 60 (2006) 2335-2338.

13

[4] G. Kartopu, O. Yal¸cin, M. Es-Souni, and A. C. Ba¸saran, Magnetization behavior of ordered and high density Co nanowire arrays with varying aspect ratio, J. Appl. Phys. 103 (2008) 093915. [5] J. Zhang, Grenville A. Jones, Tiehan H. Shen, and Steve E. Donnelly, and G. Li, Monocrystalline hexagonal-close-packed and polycrystalline facecentered-cubic Co nanowire arrays fabricated by pulse dc electrodeposition, J. Appl. Phys. 101 (2007) 054310. [6] L. G. Vivas, J. Escrig, D. G. Trabada, G. A. Badini-Confalonieri, and M. V´ azquez, Magnetic anisotropy in ordered textured Co nanowires, Appl. Phys. Lett. 100 (2012) 252405. [7] X. Han, Q. Liu, J. Wang, S. Li, Y. Ren, R. Liu, and F. Li, Influence of crystal orientation on magnetic properties of hcp Co nanowire arrays, J. Phys. D: Appl. Phys. 42 (2009) 095005. [8] B. Sellarajan, P. D. Kulkarni, M. Krishnan, Harish C. Barshilia, and P. Chowdhury, Magnetic properties of ordered bi-layer nanowire arrays with different Co crystallographic structures, Appl. Phys. Lett. 102 (2013) 122401. [9] P. D. Kulkarni, B. Sellarajan, M. Krishnan, Harish C. Barshilia, and P. Chowdhury, Anisotropic magnetic properties of bi-layered structure of ordered Co nanowire array: Micromagnetic simulations and experiments, J. Appl. Phys. 114 (2013) 173905. [10] L. G. Vivas, Y. P. Ivanov, D. G. Trabada, M. P. Proenca, O. ChubykaloFesenko and M. V´ azquez, Magnetic properties of Co nanopillar arrays prepared from alumina templates, Nanotechnology 24 (2013) 105703. [11] K. R. Pirota, F. B`eron, D. Zanchet, T. C. R. Rocha, D. Navas, J. Torrej´ on, M. V´ azquez, and M. Knobel, Magnetic and structural properties of fcc/hcp bi-crystalline multilayer Co nanowire arrays prepared by controlled electroplating, J. Appl. Phys. 109 (2011) 083919. 14

[12] L. G. Vivas, R. Yanes, O. Chubykalo-Fesenko, and M. V´ azquez, Coercivity of ordered arrays of magnetic Co nanowires with controlled variable lengths, Appl. Phys. Lett. 98 (2011) 232507. [13] H. N. Hu, H. Y. Chen, S. Y. Yu, J. L. Chen, G. H. Wu, F. B. Meng, J. P. Qu, Y. X. Li, H. Zhu, and J. Q. Xiao, Textured Co nanowire arrays withcontrolled magnetization direction, J. Magn. Magn. Mater. 295 (2005) 257. [14] P. Chowdhury, K. Raghuvaran, M. Krishnan, Harish C. Barshilia and K. S. Rajam, Effect of process parameters on growth rate and diameter of nano-porous alumina templates, Bull. Mater. Sci. 34 (3) (2011) 423. [15] P. Chowdhury, B. Sellarajan, M. Krishnan, K. Raghuvaran, Harish C. Barshilia, and K. S. Rajam, In Situ Electrochemical Thinning of Barrier Oxide Layer of Porous Anodic Alumina Template, Adv. Sci. Lett. 5 (2012) 253. [16] Z. Ye, H. Liu, Z. Luo, Han-Gil Lee, W. Wu, Changes in the crystalline structure of electroplated Co nanowires induced by small template pore size, J. Appl. Phys. 105 (2009) 07E126. [17] J. S´ anchez-Barriga, M. Lucas, F. Radu, E. Martin, M. Multigner, P. Marin, A. Hernando, and G. Rivero, Interplay between the magnetic anisotropy contributions of cobalt nanowires, Phys. Rev. B 80 (2009) 184424. [18] N. Ahmad, J. Y. Chen, J. Iqbal, W. X. Wang, W. P. Zhou, and X. F. Han, Temperature dependent magnetic properties of Co nanowires and nanotubes prepared by electrodeposition method, J. Appl. Phys. 109 (2011) 07A331. [19] G. J. Strijkers, J. H. J. Dalderop, M. A. A. Broeksteeg, H. J. M. Swagten, and W. J. M. de Jonge, Structure and magnetization of arrays of electrodeposited Co wires in anodic alumina, J. Appl. Phys. 86 (9) (1999) 5141.

15

[20] G. C. Han, B. Y. Zong, P. Luo, and Y. H. Wu, Angular dependence of the coercivity and remanence of ferromagnetic nanowire arrays, J. Appl. Phy. 93 (2003) 9202. [21] R. Lavin, J. C. Denardin, J. Escrig, D. Altbir, A. Cort´ es, and H. G´ omez, Angular dependence of magnetic properties in Ni nanowire arrays, J. Appl. Phys. 106 (2009) 103903. [22] M. J. Donahue, and D. G. Porter, OOMMF User’s Guide, Version 1.0, Interagency report NISTIR 6376, National Institute of Standards and Technology, Gaithersburg, MD. [23] M. Jamet, V. Dupuis, P. M´ elinon, G. Guiraud, and A. P´ erez, Structure and magnetism of well defined cobalt nanoparticles embedded in a niobium matrix, Phys. Rev. B 62, (2000) 493. [24] W. Scholz, K. Yu Guslienko, V. Novosad, D. Suess, T. Schrefl, R. W. Chantrell, J Fidler, Transition from single-domain to vortex state in soft magnetic cylindrical nanodots, J. Magn. Magn. Mater. 266, (2003) 155.

16

Figure Captions:

Figure 1. The surface morphology of porous anodic alumina membrane (a) bottom, b) top, c) cross-section view. The partially embedded Co nanorod arrays with variable length (d) L=100 nm, e) L=200 nm and f) L=400 nm, respectively.

Figure 2. The structural characterization of Co embedded porous anodic alumina by X-ray diffractometer, b) Expanded view of XRD plots as a function of length of the nanorod arrys (symbols: square and the triangle represents the Ag substrate and the deposited Co, respectively).

Figure 3. Magnetic behavior of Co nanorod arrays with variable length a) L=25 nm, b) L=40 nm, c) L=60 nm, d) L=100 nm, e) L=200 nm. Figure 4. a) The behavior of the demagnetization factors (Nx and Nz ) as a function of L for circular cylinders, calculated using on Eqns. 2 and 3, and b) the effective anisotropy field (Hk ): experimental, micromagnetic simulated, and analytical expression (Eqn. 1) as a function of length (L).

Figure 5. M(H) loops obtained from the micro-magnetic simulation with field applied parallel and perpendicular to the rod axis for variable nanorod lengths (L); a) L=25 nm, b) L=40 nm, c) L=60 nm, d) L=100 nm, e) L=200 nm.

Figure 6. shows 3D view of z-component magnetic distribution a for nanorods with L; a) 40 nm at H = Hn , c) 60 nm at H = Hn , and e) 100 nm at H = 0 Oe, respectively. The outer shell of the cylindrical rod is shown here for better clarity. The arrows schematically indicate the magnetization direction and the colors indicate the longitudinal magnetization, Mz . The external field applied here was perpendicular to the rod axis. Inset (i) shows the 2D xz-plane at y=0, for solid cylinder of the same rod. Inset of Fig. 6(e)(ii) presents 2D view in 17

xy plane at z=48 nm to represent the C-state. The variation of χi vs r along the length of the rod in the xz plane at y = 0 was shown in (b) and (d) for corresponding Figs (a) and (c), respectively (Here i represents y and z). Fig. 6(f) shows the angular variation of M vector at x= -9 and 9 nm, which is shown by the dotted line in inset (ii).

Figure 7. shows 3D view of z-component magnetic distribution as a function of nanorod length, a) for L = 40 nm at H = Hn , c) 60 nm at H = 0 Oe, and e) 100 nm at H = 0 Oe, respectively. The outer shell is only shown for better clarity of the image. The arrows schematically indicate the magnetization direction and the colors indicate the longitudinal magnetization, Mz . Inset (i) shows the 2D xz-plane at y=0, for solid cylinder of the same rod. Dotted marked lines guided to eye for identifying the vortex core or the domain in the xz-plane. The external field applied here was parallel to the rod axis. The variation of χi vs r along the length of the rod in the xz plane with y = 0 (Here i represents y and z). (b) shows the values of χi , which were extracted for L = 40 nm at different field values and the inset shows the same for different z values at H = H n . (d) shows the value of χi for different z values at fields of H < Hc = 0 Oe (left), and H > Hc = -1200 Oe,(right).

18

Figure 1:

Figure 2:

19

Figure 3:

Figure 4:

20

Figure 5:

21

Figure 6:

22

Figure 7:

23