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APPLIED PHYSICS LETTERS VOLUME 85, NUMBER 20 15 NOVEMBER 2004 Applied field Mössbauer study of shape anisotropy in Fe nanowire arrays Qing-feng Zhan, Wei He, Xiao Ma, Ya-qiong Liang, Zhi-qi Kou, Nai-li Di, and Zhao-hua Chenga) State Key Laboratory of Magnetism and International Center for Quantum Structures, Institute of Physics, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China (Received 14 June 2004; accepted 27 September 2004) In order to investigate the magnetic anisotropy of Fe nanowire arrays from microscopic point of view, 57Fe Mössbauer spectra were measured at various magnetic fields along and perpendicular to the nanowire axis, respectively. On the basis of the absorption intensities of the second and the fifth lines of sextet, the orientation of Fe magnetic moments can be detected. It was found that the shape anisotropy dominates the overall magnetic anisotropy in the Fe nanowires. Furthermore, the longitudinal and transverse demagnetizing fields of Fe nanowire, respectively, were deduced from the effective hyperfine field at 57Fe nuclei as a function of applied field. The chain-of-spheres model in conjunction with symmetric fanning mechanism was adopted to interpret the domain structure and the parallel coercivity of magnetic nanowire arrays. © 2004 American Institute of Physics. [DOI: 10.1063/1.1827330] Recently, the fabrication and magnetic properties of highly ordered magnetic nanowire arrays have been extensively investigated owing to their potential application in ultrahigh density magnetic recording media.1–4 The unique and tunable magnetic properties of nanowire arrays arise from the inherent shape anisotropy and the low dimension. In order to improve the density of magnetic recording approaching the super-paramagnetism limit, it is required that the magnetic nanowires possess large uniaxial magnetic anisotropy to overcome the thermal fluctuation. It was proved that Mössbauer spectroscopy is a powerful technique to investigate the magnetic anisotropy.5–7 Previous zero-field Mössbauer spectra of both Fe and FeCo nanowire arrays have the characteristics of disappearance of the second and fifth absorption peaks in the sextet, implying that the easy magnetization direction lies in the axes of nanowires.8,9 However, the dependence of hyperfine fields and the intensities of the second and fifth lines on the applied field is not well known. In this letter, the magnetization process, i.e., the magnitude and direction of Fe magnetic moments were investigated by applied Mössbauer spectroscopy on a local scale via the values of hyperfine fields and the ratios of the intensities of the second line to the third line or the fifth line to the fourth line of magnetically split spectra. (Hereafter, we define them as relative intensities of the second line and the fifth line, I2,5.) The demagnetizing field and the shape anisotropy constant of Fe nanowires were also derived from the hyperfine field as a function of applied field. The arrays of Fe nanowires were prepared by electrodepositing Fe into anodic aluminum oxide (AAO) templates. The detailed procedures for preparing AAO templates and electrodepositing Fe nanowires were described elsewhere.8–10 Figure 1(a) shows the x-ray diffraction pattern of the Fe nanowire arrays after completely dissolving the aluminum substrate in an HgCl2 saturated solution. Only the (110) diffraction peak is evident and the d value of average interplanar spacing matches perfectly with the value of bulk bcc Fe, which indicates the Fe nanowire arrays are bcc struca) Electronic mail: [email protected] ture with a [110]-preferred orientation along the nanowire axis. The inset of Fig. 1(a) shows a transmission electron microscopy image of a 20-nm-diam Fe nanowire after removal from the template, illustrating the nanowires were uniform with very large length-to-diameter ratio 共⬃375兲. Magnetization measurements of the Fe nanowire arrays were performed at 10 K using a superconducting quantum interference device magnetometer. Figure 1(b) shows the hysteresis loops of Fe nanowire arrays in AAO films with the applied field parallel and perpendicular to the wire axis at 10 K. The hysteresis loop measured along the wire axis indicates a relative square with M r / M s ratio of 0.98 and a coercivity of 2842 Oe, while the hysteresis loop measured perpendicular to the wire axis is sheared with a squareness of 0.07 and a coercivity of 444 Oe. It is clearly seen from those features that the easy magnetization direction of Fe nanowire is along the long axis of nanowire, i.e., the [110] direction, rather than the [100] in bulk bcc Fe. Magnetization measurement results suggest that the overall magnetic anisotropy is dominated by the shape anisotropy in Fe nanowires owing to the very large aspect ratio. In order to investigate the shape anisotropy of Fe nanowire arrays from a microscopic point of view, 57Fe Mössbauer spectra at various magnetic fields were measured by a constant-acceleration Mössbauer spectrometer with a 57 Co共Pd兲 source at 10 K, with the ␥ beam parallel to the FIG. 1. (a) X-ray diffraction patterns of Fe nanowire arrays. The inset shows a transmission electron microscopy image of 20-nm-diam Fe nanowire after removing from the template. (b) Hysteresis loops of Fe nanowire arrays at 10 K. H共//兲 indicates the magnetic field applied parallel to the nanowire axis. H共⬜兲 denotes perpendicular to the wire axis. 0003-6951/2004/85(20)/4690/3/$22.00 4690 © 2004 American Institute of Physics Downloaded 16 Nov 2004 to 159.226.36.37. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp Zhan et al. Appl. Phys. Lett., Vol. 85, No. 20, 15 November 2004 4691 FIG. 2. Mössbauer spectra of Fe nanowire arrays in AAO films at 10 K with various magnetic fields applied perpendicular to the nanowire axis. nanowire axis. The magnetic fields up to 50 kOe both parallel and perpendicular to the nanowire axis are provided by an Oxford Spectromag SM4000-9 superconducting split pair, horizontal field magnet system. The values of velocities were calibrated using a ␣-Fe foil at room temperature. Figure 2 shows the Mössbauer spectra of Fe nanowire arrays with the applied field perpendicular to the nanowire axis. For the zero-field Mössbauer spectrum, the second and fifth absorption peaks in the sextet almost disappear. As the magnetic field increases, the relative intensities of the 2–5 lines also increase. In magnetically split spectra, the relative intensities of the 2–5 lines (corresponding to the ⌬m = 0 nuclear transitions) are given by I2,5 = 4 sin2 / 共1 + cos2 兲, where is the angle between the magnetic moment and the ␥ beam direction.11 In the case of all Fe spins are collinear to the ␥ beam direction I2,5 = 0, while all magnetic moments are perpendicular to ␥ beam I2,5 = 4. Therefore, the disappearance of the 2–5 lines for Fe nanowire arrays at zero field indicates all Fe spins orient parallel to the nanowire axis. The increase of I2,5 denotes all magnetic moments rotate continuously approaching the direction of applied field with increasing applied field. Figure 3(a) illustrates the average 具sin 典 as a function of applied field. It can be noticed that all magnetic moments align completely to the direction of applied field, that is to say the Fe nanowires reach saturation completely at the applied fields above 10 kOe. Furthermore, it can be seen in Fig. 3(a) that the values of 具sin 典 obtained from Mössbauer results are in good agreement with the values of normal magnetization M / M s, where M / M S = 具cos共 / 2 − 兲典 = 具sin 典. The effective hyperfine field Heff at 57Fe nuclei can be expressed as Heff = Hhf + Happ + Hdm , 共1兲 where Hhf , Happ, and Hdm are the hyperfine field, the applied field, and the demagnetizing field, respectively. It should be noted that the hyperfine field at 57Fe nuclei is antiparallel to the magnetic moment. The demagnetizing field is given by Hdm = −NM, where N is the demagnetization factor which depends on the direction of magnetization, and M is the magnetization vector. Once the magnetization reaches the saturation value, the demagnetizing field is constant. In the case of applied field parallel to the nanowire, magnetic fields at iron sites are collinear to the axis of nanowire. Therefore, all Mössbauer spectra of Fe nanowire arrays with the applied FIG. 3. (a) A graph of average 具sin 典 vs applied field Happ, comparing with the magnetization curve of Fe nanowire arrays. (b) The effective field Heff for Fe nanowire arrays as a function of the applied field Happ. The dots and dashed lines are experimental and fitting results, respectively. The magnetic field is parallel and perpendicular to the nanowire axis, respectively. field parallel to the nanowire axis have the characteristics of the disappearance of the 2–5 lines, and the magnitude of Heff can be expressed as Heff = Hhf − Happ + Hdm . 共2兲 The effective hyperfine field with applied field parallel to the nanowire axis can be fitted in the formula of Heff = Hhf共Happ = 0兲 − Happ within the range of error. The fitting curve and the experimental dots are plotted in Fig. 3(b). Therefore, Hdm// = 0 can be deduced. This result is consistent with the theoretical value of an infinitely long cylinder. In the case of applied field perpendicular to the nanowire axis, the effective field is not antiparallel to the applied field until all Fe spins are collinear to applied field. Therefore, only after the magnetization reaches saturation, the magnitude of Heff can be expressed by formula (2). The effective field after the nanowires completely saturated can be fitted as Heff = Hhf共Happ = 0兲 − Happ + 7.21 kOe, where the 7.21 kOe is the saturation demagnetizing field. According to the demagnetizing field, the magnetization M and the angle between the magnetic moment and the ␥ beam [Fig. 3(a)], Eq. (1) can be used to calculate the magnitude of Heff in whole range of external field. The calculated curve matches the experimental data very well [Fig. 3(b)]. Herein, the chain-of-spheres model12 is quoted to interpret the domain structure and the magnetization process. Figure 4 is the sketches of the domain structure of a single nanowire in external field. Each nanowire can be considered as a chain of single-domain spheres. Since both the diameter of Fe nanowire and the critical diameter of single-domain sphere are about 20 nm, the chain-of-spheres structure is easy to be formed, and the multidomain is likely to appear in the transverse section of a thicker magnetic nanowire, which results in the reduction of parallel coercivity and squareness. Similar magnetic domain structure has been directly observed in Fe nanowire grown on the W(110) by scanning tunneling microscopy.13 It is well known that the coercivity and shape of the hysteresis loop depend on the magnetization reversal process. We adopt the chain-of-spheres model in Downloaded 16 Nov 2004 to 159.226.36.37. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp 4692 Zhan et al. Appl. Phys. Lett., Vol. 85, No. 20, 15 November 2004 between nanowires in AAO films is about 40 nm, which is far larger than the exchange length, the exchange coupling interaction between nanowires is not taken into account. Therefore, the magnetic energy W of the nanowire system in an applied field Happ on the angle can be written as p W = K sin − 2 FIG. 4. Schematic diagram of the chain-of-spheres domain structure of a single magnetic nanowire, and the spin-flip in external field. conjunction with symmetric fanning mechanism to interpret the longitudinal coercivity of magnetic nanowire. In this model, the magnetic nanowire is assumed to be an ideal chain of single-domain spheres with uniaxial magnetic anisotropy. Only the magnetostatic energy and the dipole interaction are taken into account, and the domain energy is neglected. Using the chain-of-spheres model with symmetric fanning mechanism, the longitudinal coercivity of the magnetic nanowires is deduced12 as HC// = M S 共6Kn − 4Ln兲, 6 共3兲 where n Kn = 兺 i=1 n−i , ni3 共n−1兲/2⬍i艋共n+1兲/2 Ln = 兺 i=1 n − 共2i − 1兲 . n共2i − 1兲3 Here M S is the saturation magnetization of the magnetic nanowires, and n is the number of the spheres in a single nanowire, which is equal to the aspect ratio 共n ⬇ 375兲. Due to the difficulty in measuring the weight of nanowires in AAO films, the saturation magnetization of Fe nanowires cannot be directly obtained from the magnetization measurement. Considering the hyperfine field of Fe nanowire arrays matches perfectly with that of bulk Fe at 10 K, it is reasonable to assume that the saturation magnetization of Fe nanowires is the same as that of bulk bcc Fe. According to the above-mentioned parameters, the longitudinal coercivity of the Fe nanowires at 10 K is calculated to be 2726 Oe, which agrees well with the experimental result 2842 Oe. For the nanowire is composed of single-domain spheres in our model, the transverse coercivity arises mainly from the magnetocrystalline anisotropy. However, the magnetocrystalline anisotropy field 共HK = 2K1 / M S = 598 Oe兲 of Fe at 10 K is fairly larger than the experimental coercivity 444 Oe.14 The large deviation likely results from the exchange coupling between the magnetic spheres, which reduces the coercivity. By means of applied field Mössbauer spectra, the shape anisotropy can be evaluated quantitatively. Since the distance 冉 冊 兺 FeHapp cos − , 2 共4兲 where the first term represents the overall magnetic anisotropy energy, the second term is the magnetostatic energy, the K is defined as the overall magnetic anisotropy constant, the Fe is the magnetic moment of Fe, and the p is the Fe atomic number per unit volume. This dependence gives rise to the expression K = M SHapp / 2具sin 典, where 0 ⬍ ⬍ / 2. Using M S of bulk Fe and the average 具sin 典 at different applied fields [Fig. 3(a)], one can estimate the average magnetic anisotropy constant K ⬇ 7.3⫻ 106 ergs/ cm3. The shape anisotropy constant is one order of magnitude larger than that of the magnetocrystalline anisotropy constant K1 of bulk Fe at 10 K,14 so the magnetocrystalline anisotropy can be neglected reasonably in Fe nanowires. In summary, Mössbauer spectra clearly show the process of Fe spins rotated from parallel to perpendicular to the wire axis with increasing the magnetic field perpendicular to the axis of nanowire. The longitudinal and transverse demagnetizing fields of Fe nanowire are deduced from the effective field of Fe nanowire arrays as a function of applied field. The chain-of-spheres model with symmetric fanning mechanism is adopted to interpret the domain structure and the high coercivity along the axis of magnetic nanowires. Compared with the shape anisotropy obtained from Mössbauer spectra, the magnetocrystalline anisotropy is too small to be taken into account in Fe nanowires. This work was supported by the State Key Project of Fundamental Research, and the National Natural Sciences Foundation of China. Z.H.C thanks the Alexander von Humboldt Foundation for financial support and generous donation of some of the Mössbauer equipment used. 1 A. Fert and L. Piraux, J. Magn. Magn. Mater. 200, 338 (1999). D. J. Sellmyer, M. Zheng, and R. Skomski, J. Phys.: Condens. Matter 13, R433 (2001). 3 K. Nielsch, R. B. Wehrspohn, J. Barthel, J. Kirschner, U. Gösele, S. F. Fischer, and H. 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