Magnetization reversal in single domain Permalloy

Magnetization reversal in single domain Permalloy wires probed by magnetotransport T. Y. Chung and S. Y. Hsu Citation: Journal of Applied Physics 103, 07C506 (2008); doi: 10.1063/1.2834709 View online: http://dx.doi.org/10.1063/1.2834709 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/103/7?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Reversible and irreversible magnetoresistance of quasisingle domain permalloy microstructures J. Appl. Phys. 95, 6759 (2004); 10.1063/1.1688216 Construction of hysteresis loops of single domain elements and coupled permalloy ring arrays by magnetic force microscopy J. Appl. Phys. 93, 8540 (2003); 10.1063/1.1540129 Magnetic switching of single vortex permalloy elements Appl. Phys. Lett. 79, 3113 (2001); 10.1063/1.1410873 Magnetic domain formation in perforated permalloy films Appl. Phys. Lett. 79, 1315 (2001); 10.1063/1.1396623 Observation of magnetization reversal of thin-film permalloy nanostructures using ballistic electron magnetic microscopy Appl. Phys. Lett. 77, 1357 (2000); 10.1063/1.1290150

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JOURNAL OF APPLIED PHYSICS 103, 07C506 共2008兲

Magnetization reversal in single domain Permalloy wires probed by magnetotransport T. Y. Chung and S. Y. Hsua兲 Institute of Electrophysics, National Chiao Tung University, Hsinchu 300, Taiwan

共Presented on 6 November 2007; received 11 September 2007; accepted 31 October 2007; published online 7 February 2008兲 We have measured the in-plane magnetoresistance 共MR兲 of a series of submicron single domain Permalloy wires to study two important magnetization reversal modes, coherent rotation and curling. With the consideration of both micromagnetic configurations, the MR curve can be decomposed in a reversibly bell-shaped curve and an irreversibly V-shaped discontinuity in low field, respectively. The discontinuity jump occurs at a switching field characterizing the curling mode. The angular dependence of the switching field is well described by the theoretical prediction of Aharoni model under the consideration of the whole volume curling. Moreover, we found that the low angle switching field decreases with increasing wire width 共decreasing the aspect ratio兲 as 1/width, consistent with the curling model for a long slender ellipsoid. © 2008 American Institute of Physics. 关DOI: 10.1063/1.2834709兴 I. INTRODUCTION

Recent advances in the nanofabrication methods have made the possibility of studying the magnetism at small length scale, in which can be potential applications in high density recording and modern magnetoelectronic devices.1–4 The investigation of the magnetic reversal processes in micro- and nanostructured ferromagnetic systems is currently stimulating intense practical and theoretical attention.4–10 The mechanisms of magnetization reversal process have been much discussed and promoted intensively research activities in recent years. The direct observation of magnetization reversal processes in micro- and nanostructured ferromagnetic systems is difficult to achieve since the magnetic moment is so small. Although new methods such as photoemission electron microscopy11,12 and spin-polarized scanning electron microscopy13,14 have been developed to investigate these systems, there are few data and the resolution is somehow limited. Magnetoresistance measurements have been found to be a well qualified tool for studying the magnetization reversal processes instead because the anisotropic magnetoresistance 共AMR兲 effect is sensitive to the magnetization distribution during the reversal process.15,16 For nanowires both mechanisms of coherent rotation and magnetization curling are believed to be responsible for magnetization reversal.4,5 In this work, we have performed magnetic structure and magnetotransport measurements in a series of submicron single domain Permalloy wires to study these two important magnetization reversal modes. II. EXPERIMENTAL DETAILS

Our Permalloy 共Ni80Fe20兲 wires are prepared by standard e-beam lithography, thermal evaporation, and lift-off techniques on naturally oxidized 共100兲 Si substrates. The length a兲

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0021-8979/2008/103共7兲/07C506/3/$23.00

and thickness of all samples are kept constant, ᐉ = 20 ␮m and t = 30 nm. Several widths w are chosen ranging from 0.1 to 2 ␮m, respectively. Nonmagnetic Au contact configuration is arranged for four-terminal electrical transport measurement. Magnetic structure and magnetotransport measurements are performed. The former is obtained using magnetic force microscope 共Nanoscope Dimension 3100兲 in the tapping/lift mode. The magnetic configurations are imaged at a lift height of 100 nm by commercial CoCr coated Si cantilever tips. The latter is performed in a pumped 4He cryostat and at the center of an electromagnet. Sample resistance is obtained using a low frequency resistance bridge with a low excitation current 共⬍0.1 mA兲 at T = 10 K. Current is applied along the long axis of the sample corresponding to its easy axis. Here, the magnetic field always lies in the sample plane. In the longitudinal geometry 共␪ = 0兲, the magnetic field points along the easy axis and hence is parallel to the current through the sample. In the transverse geometry 共␪ = 90° 兲, the magnetic field points along the width axis and hence is perpendicular to the current through the sample. The complete hysteresis loop of in-plane magnetoresistance is measured for different relative angles 共␪兲 between the long axis 共current direction兲 and applied magnetic field. III. RESULTS AND DISCUSSION

It has been known that magnetic structure of a ferromagnetic microelement depends on its geometrical factors such as the critical length and the aspect ratio, m = ᐉ / w. To check the magnetization state of our 30 nm thick and 20 ␮m long permalloy wires we investigate the remanent domain structure using magnetic force microscopy 共MFM兲 at room temperature. MFM images taken after easy-axis saturation show that the remanent domain state is the closure domain for m ⬍ 5 and is the single domain for m 艌 20 in agreement with the theoretical model by Aharoni.17 Such a domain structure transition tuned by the aspect ratio 共shape anisotropy兲 has

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FIG. 1. 共Color online兲共a兲 Magnetoresistance of a 0.43 ␮m wide Permalloy wire for different magnetic field directions at T = 10 K. The angles ␪ of the in-plane magnetic field relative to the long axis of the wire are 10, 20, 30, 40, 50, 60, and 70 in degrees 共from top to bottom兲, respectively. 共b兲 Zoom of 共a兲 to show the irreversible loops for all angles in low magnetic field.

also been found in Co wires.18 Most samples that we discuss later have a single domain structure at remanence with an easy axis along its long axis. Sample with 1.9 ␮m in width has vortex structures in the ends of the wire in addition. The AMR is sensitive to the variation of micromagnetic configuration since the AMR effect results from the anisotropically spin-orbit scattering. Therefore, different magnetic reversal processes can be distinguished by measuring the magnetoresistance in different field directions. For a long single domain wire, the corresponding magnetoresistance based on the Stoner-Wohlfarth model19 with coherent rotation of magnetic reversal process is given by R共H, ␪兲 = R⬜

冉冉冊冉冊冊 ⌬Rmax 1+ R⬜

M共H兲 Ms

2

.

共1兲

⌬Rmax is defined as R储 − R⬜, where R⬜ and R储 are the resistances when the magnetization is completely perpendicular and parallel to the current at saturation, respectively. M s is the saturation magnetization. We also define the MR ratio as ⌬R / R⬜ = 共R − R⬜兲 / R⬜ at saturation. The MR ratio is proportional to cos2 ␪, where ␪ is the angle between the current 共which is parallel to the wire axis兲 and the magnetization. The angular dependence of magnetoresistance for a sample of w = 0.4 ␮m is shown in Fig. 1共a兲. Overall, large reversibly bell-shaped negative MR curves are present. For TMR 共transverse MR兲共␪ = 90° 兲, the MR decreases with magnetic field in a parabolic behavior.20 Moreover, the saturated MR ratio increases with increasing the angle ␪ following the relation of cos2 ␪ as expected in Eq. 共1兲. The scenario confirms that the reversible MR is caused by the AMR effect incorporation with the coherent rotation of the magnetic moment

with magnetic field. The full magnetoresistance curves can be well described by the AMR effect and the StonerWohlfarth model. Meanwhile in addition to the reversible MR, there is an irreversible jump in low magnetic field. When the field is decreased from saturation the resistance increases smoothly. Further increase of the field toward saturation in the opposite direction leads to the hysteresis in the curve. As shown in Fig. 1共b兲, zoom of the low field MR, an irreversibly V-shaped discontinuity in low field, can be clearly found for all angles ␪ ⬍ 90°. The magnetization of ferromagnetic submicron wires is certainly like that of magnetic ellipsoids and has the curling mode in low fields in addition to the coherent rotation mode in high fields. While the bell-shaped reversible curve is attributed to the latter mode, the irreversible discontinuity characterizes the former mode. The jump of MR corresponding to the transition from curling to coherent rotation occurs at the switch field Hsw, as indicated in Fig. 1共b兲. We compare the obtained Hsw with the Aharoni model for a slender ellipsoid.21 For the single domain nanowires, two modes are considered as being important; coherent rotation and curling magnetization. The threshold diameter between coherent rotation and curling is the critical radius rc which is about the same as the exchange length ᐉex, 2冑A / M s, where A is the exchange constant and M s is the saturation magnetization. Permalloy is a soft magnetic material with low intrinsic magnetic anisotropy and has the exchange length of about 5.7 nm. Taken the effective radius r = 冑wt / 2 into account, r is always bigger than rc and the curling mode is present in our samples. In the curling mode, magnetization switching is an abrupt process. For a prolate spheroid, the switching field is given by4,21

Hsw = 2␲ M s

冑冉

冉

2DL −

k 2DL − 2 S

冊

2

k S2

冊冉

2Dr −

冉

k S2

冊

k sin ␪ + 2Dr − 2 S 2

冊

2

, cos ␪ 2

共2兲 where DL and Dr are the demagnetizing factors of the spheroid along the major and minor axes, respectively. The parameters DL, Dr, and k are determined by the sample’s dimensions.4,21 The parameter S is the reduced radius, r / ᐉex. The angular dependence of the switching field for four samples and their numerical fits based on Eq. 共2兲 are plotted in Fig. 2. ␪ is referred as the angle between the in-plane magnetic field and the easy axis 共the long axis兲 of the wire. As seen, Hsw changes barely at low angle and increases at large angle as expected by Eq. 共2兲. With decreasing width of the wire 共the effective radius兲 Hsw increases. Theoretical line describes very well for sample of width w = 0.4 ␮m while there are some deviations at large angle for two narrower samples. The deviations arise at large angle when r is close to rc and may be attributed to the pinning of magnetization by surface defects.7 The irreversible part of the 1.9 ␮m wide wires shows the complex behaviors of two jumps implying the extra micromagnetic domain beside the single domain. In fact, its MFM image displays two vortexlike structures in both ends of the wire at remanence.


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The scenario confirms that the irreversible MR is caused by the AMR effect incorporation with the curling of the magnetic moment. IV. CONCLUSIONS

FIG. 2. Angular dependence of the switching field for four permalloy wires with different widths. The widths of the wires are 共䊏兲 0.14 ␮m, 共쎲兲 0.22 ␮m, 共䉱兲 0.43 ␮m, and 共⽧兲 1.90 ␮m, respectively. Solid lines are fits using Eq. 共2兲 with only one adjustable parameter S. ᐉex = 5.7 nm and M s = 830 emu/ cm3.

Wernsdorfer measured the switching time of Ni cylinders using micro-SQUID 共SQUID denotes superconducting quantum interference device兲 and concluded that the “activation volume” of their wire is two orders of magnitude smaller than the whole wire volume.5 However, measurements of this are difficult and rare. On the other hand, the theoretical prediction based on the curling in a prolate spheroid gives a good description to our data. The parameter S was obtained from the fit implying the curling over 30% of the whole wire volume. To unambiguously show that the reversal occurs by curling, measurements of activation volume are necessary.5 For an applied magnetic field oriented along the long ␪=0 = 2␲ M s共k / S2兲 and axis 共␪ = 0兲, Eq. 共2兲 is reduced to Hsw ␪=0 2 Hsw is expected to increase with 1 / r for a prolate spheroid. ␪=0 The log-log plot of Hsw obtained from the LMR 共longitudinal MR兲共␪ = 0兲 versus the sample’s width is shown in Fig. 3. The linear fit to all data points gives a slope of −0.97⫾ 0.07 ␪=0 is proportional to 1 / w.22 Since our indicating that Hsw samples are orthorhombic with a constant thickness, the effective radius r is 冑wt / 2 and hence our experimental result ␪=0 ⬀ w−1 is consistent with the theoretical prediction. that Hsw

FIG. 3. 共Color online兲 The log-log plot of the switching field obtained from the longitudinal MR 共␪ = 0兲 vs the Permalloy wire’s width. The solid line is the linear fit to the data.

In summary, for our single domain Permalloy wires, two micromagnetic configurations are clearly distinguished by magnetoresistance measurements. The TMR and LMR show the coherent rotation and irreversible curling of the magnetic moments during the reversible process, respectively. When the applied current is neither perpendicular nor parallel to the in-plane magnetic field, both mechanisms contribute to MR.23 Moreover, the angular dependence of the switching field can be described by the theoretical prediction of Aharoni model. The result that the low angle switching field decreases with increasing wire width 共decreasing the aspect ratio兲 as 1 / w is indeed consistent with the curling model for a long slender ellipsoid. ACKNOWLEDGMENTS

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