The angular dependence of Neel wall resistance by magnetotransport in the centipedelike Permalloy structures

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The angular dependence of Néel wall resistance by magnetotransport in the

centipedelike Permalloy structures

T. Y. Chung and S. Y. Hsu

Citation: Journal of Applied Physics 105, 07D123 (2009); doi: 10.1063/1.3068629

View online: http://dx.doi.org/10.1063/1.3068629

View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/105/7?ver=pdfcov Published by the AIP Publishing

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The angular dependence of Néel wall resistance by magnetotransport

in the centipedelike Permalloy structures

T. Y. Chunga兲and S. Y. Hsu

Institute of Electrophysics, National Chiao Tung University, Hsinchu 300, Taiwan

共Presented 11 November 2008; received 17 September 2008; accepted 8 November 2008; published online 27 February 2009兲

The angular dependence of Néel wall resistance has been studied by measuring the in-plane magnetoresistances共MRs兲 of the centipedelike Permalloy 共Py兲 structure, which consists of a central wire with numerous orthogonally bisecting finger wires. All Py wires were designed to have a single domain structure at remanence and high anisotropy by the geometric control. The remanent domain at the junction between the central and finger wires is determined by the anisotropy constants of both wires and hence, variable angles of Néel wall can be achieved. Using a simple resistance-in-series model in corporation with the anisotropic MR effect, the analyses of the longitudinal and transverse MRs of the centipedelike structure give the domain wall resistance. Our results show that the Néel wall resistance is about milliohm and decreases with decreasing the relative angle between two domains. © 2009 American Institute of Physics.

关DOI:10.1063/1.3068629兴

The dynamic behavior of domain wall 共DW兲 has been studied intensively in recent years. In addition to its funda-mental interest, it is a potential candidate for the next gen-eration of magnetic memory.1A detailed knowledge of the contribution to the resistivity when conduction electrons pass through DW has important consequences in the understand-ing of dynamic behavior.

In general cases, the contribution of DW scattering to the magnetoresistance 共MR兲 is concealed by conventional sources of low temperature MR such as anisotropic magne-toresistance共AMR兲 and Lorentz MR in a ferromagnetic sys-tem. In order to isolate the domain wall resistance共DWR兲, it is necessary to create artificial domain walls using a unique pattern such as adding a neck to the wires,2designing zigzag structures,3 forming a striped domain by thickness modulation4 or exchange biases,5 and implementing an elaborate magnetic field history process.6 Although the DWRs were observed in various systems, both positive2–8 and negative9 values were reported with their theoretical justifications.10–12Up to now, the sign and the magnitude of the DWR and the fundamental mechanism of DW scattering are still controversial.

Most investigations to this subject focus on either 90° or 180° DW structures, regardless of the Néel or Bloch wall. In this work, we have fabricated the centipedelike Permalloy 共Py兲 structures to obtain a series of Néel wall with various relative angles between two domains. The angular depen-dence of Néel wall resistance is explored by analyzing the longitudinal and transverse MRs based on a simple resistance-in-series model.

The centipedelike Py structures in submicron scale were made using standard e-beam lithography, thermal evapora-tion, and lift-off techniques. As shown in Fig.1, each struc-ture consists of a central wire and several finger wires that

bisect orthogonally the central wire. All wires have a thick-ness of 30 nm. The central wire is 60 ␮m long and 1 ␮m wide共W兲. All finger wires are 20 ␮m long but have various widths共w: 0.3, 0.4, 0.5, 0.8, 1, and 1.5 ␮m兲. For a constant finger width, we made several series of structures with either different pitch l between the neighboring fingers 共1wⱕl ⱕ10w兲 or number of fingers n systematically. Figure 1 is a scanning electron microscopy 共SEM兲 picture of one typical sample with w = l = 0.5 ␮m. Brighter stripes are the nonmag-netic Au contacts serving as the voltage leads for MR mea-surements.

Magnetic domain structure and magnetotransport mea-surements were performed. The former was obtained using a magnetic force microscope 共Digital Instruments Nanoscope IIIa兲 in tapping/lift mode. In this mode the topography and magnetic contrast can be well separated. The magnetic con-figuration was then imaged by monitoring the frequency or phase shift of the cantilever at a lift height of 100 nm. The latter was performed at the center of an in-plane electromag-net in a pumped 4He cryostat. To avoid thermal fluctuation,

a兲_{Electronic mail: [email protected].}

5µm

FIG. 1. A SEM image of one typical sample. The gray area is Py and the brighter wires are Au. The central wire of Py is 60 ␮m long and 1 ␮m wide. Two structures of three and seven finger wires are arranged with w = l = 0.5 ␮m. The other structure at the center is arranged for the PHE measurement.

JOURNAL OF APPLIED PHYSICS 105, 07D123共2009兲

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the MR was carried out at 10 K using a lock-in method. In this study, the driving current of less than 0.1 mA always flows along the axis of the central wire. The magnetic field is applied either along the current for longitudinal magnetore-sistance共LMR兲 or normal to the current for transverse mag-netoresistance共TMR兲.

The magnetic configuration in the polycrystalline mag-netic wire is dominated by the aspect ratio as a result of shape anisotropy. The uniaxial anisotropy constant共Ku兲 can

be quantified by the fit of TMR to the Stoner–Wohlfarth model. Our previous studies show that the remanent mag-netic configuration is a single domain and Kudecreases from

10.5 to 1.3⫻105 ergs/cm3 for a 20 ␮m long Py wire with width from 0.1 to 2 ␮m.13 These values are much larger than the magnetocrystalline anisotropic energy density by two orders of magnitude due to shape anisotropy. In our centipedelike structures, the moment of the central wire pref-erably lies parallel with the axis of the central wire, while those of the finger wires preferably lie perpendicularly.

LMR and TMR of one structure with four fingers are plotted in Fig. 2共a兲. The LMR is saturated at 1 kOe and slightly decreases as the magnetic field approaches zero due to the coherent rotation of finger wires. When the field sweeps to the opposite direction and about 35 Oe, the rever-sal is completed via a single jump, which is the switching characteristics of the central wire. The TMR has the lowest resistance at saturated field of 1 kOe. When the field is re-duced to zero, the magnetization of the pitch coherently ro-tates to the axis of the central wire, while the magnetization of the fingers remains. When the field sweeps to the opposite direction in the range between 77 and 101 Oe, the MR curve exhibits clearly four successive plateaus, a staircase. Figure 2共b兲 is the magnification of TMR shown in Fig. 2共a兲. The

number of steps is the same as the number of fingers. This is confirmed by a systematic investigation in structures, which have the same geometries of both wires but different number of fingers 共3ⱕNⱕ40兲. The abrupt resistance drop is as-cribed to the switching of each finger wire. After the step sequence, all magnetizations almost lie along the field direc-tion and the resistance smoothly back to the saturadirec-tion value. It is important to note that the resistance at remanence is a constant despite of different field scanning processes. As shown in Fig.2共a兲, both LMR and TMR have the same value at H = 0. As described in the last paragraph, we believe that there is a very stable remanent magnetic configuration that the moment of the pitch is along the axis of the central wire and the moment of the finger is perpendicular to the axis of the central wire. As to the junction, there are orthogonal mo-ments at its four corners resulting in a tilted moment of the junction.

In order to obtain the tilted angle of the moments at the junction, the transverse voltage Vxy across the junction via

the orthogonal finger in the presence of the in-plane mag-netic field was measured. The measurement is the so-called planar Hall effect共PHE兲, which arises from the anisotropy of spin-orbital scattering in magnetic materials. Vxyis sensitive

to the angle␪ between the current density J and magnetiza-tion M.14Here, the magnetic field is along the axis of fingers 共the y-axis兲. As shown in the inset in Fig. 2共c兲, the abrupt drops in Vxy of fingers 1 and 2 correspond to the dramatic

rotations of moments at the junctions 1 and 2 in the coercive fields, 77 and 101 Oe, respectively. Both fields of the drops are the same as the first and last steps in the TMR of one centipedelike structure that consists of both fingers indicating the sequentially one-by-one moment switching of fingers. Furthermore, the sin 2␪dependence of Vxyallows us to

esti-mate the tiled angle of moment at the junction for a series of fingers with various widths. The values obtained from PHE are very close to tan−1_共K

u finger_/K

u

central_{兲 within an uncertainty}

of 3°. K_ufingerand K_ucentralare the anisotropy constants of the finger and central wires, respectively. Therefore, remanent moment direction at the junction is fairly determined by the shape anisotropies of the pair of orthogonal intersecting wires. Here, the tilted angles in this study range from 40° to 80° with decreasing the finger width. Figure2共d兲 is a rema-nent magnetic force microscopy共MFM兲 image for one seg-ment of a centipedelike structure. The deviation in contrast of magnetic moments at each junction shows a regular pat-tern as opposed to showing no contrast at other position in the wires. The image can be roughly confirmed by a micro-magnetic simulation using object oriented micromicro-magnetic framework15关also see Fig.2共d兲兴.

For our centipedelike structures, a central wire orthogo-nally bisects n of individual finger wires as shown in the inset in Fig. 3. The whole structure can be divided to n junctions and n + 1 central wire pitches. Each junction is con-nected to two central wire pitches. At remanence, the mo-ment of the central wire lies preferably along the wire axis but the moment at the junction tilts due to finger wire. Hence, a Néel domain wall is present between the junction 共 domain兲 and pitch 共→ domain兲.

Although the response of moment distribution during the 32.0 32.2 32.4 32.6 0 50 100 0.05 0.10 0.15 0.20 0.25 -1.0 -0.5 0.0 0.5 1.0 32.0 32.2 32.4 32.6 32.8 (b) R (Ω ) H 2 1 I -I+ V -V+ Vxy /Ix (Ω ) H( Oe ) (c) finger2 finger1 (d) (a) TMR R (Ω ) H( kOe ) LMR

FIG. 2. 共Color online兲共a兲 LMR and TMR of one sample with w=l = 0.8 ␮m and n = 4.共b兲 An enlargement of the TMR at low field. Magnetic field is applied from 0 to 170 Oe.共c兲 Field dependence of transverse volt-ages Vxydivided by the current Ixfor two fingers labeled as 1 and 2 in the scheme.共d兲共Top兲 Remanent MFM image of one sample with w=0.5 ␮m and l = 1.5 ␮m.共Bottom兲 Micromagnetic simulation of the magnetization configuration of the similar sample with the reduced dimensions by a factor of 0.1.

07D123-2 T. Y. Chung and S. Y. Hsu J. Appl. Phys. 105, 07D123共2009兲

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field reversal process is quite complicated, the moment dis-tributions at remanence and saturation field can easily be figured out. Upon these situations, we develop a resistance-in-series model to analyze the DWR. In this model, the MR is composed of the resistances contributed from these three regions and is written as

R共Hជ兲 =共n + 1兲l W Rpitch共Hជ兲 + nw ␣WRjunction共Hជ兲 + 2n

冋

RDW− lDW W Rpitch共Hជ兲 + RDW AMR

册

. 共1兲

Here␣ is the current distribution factor, which involves the influence of the nonuniform current density at the junction due to both open ends of a finger wire. R_pitchand R_junctionare the sheet resistances of the pitch and junction, respectively. At the saturation field共⬎1 kOe兲, all moments lie along the magnetic field and the domain wall is absent. Only the first two terms contribute the whole resistance with that R_pitch = R_junction. The last term is a correction under the consider-ation of DWs 共H⬍H_sat兲. Linear dependences of saturated LMR and TMR on both l and n give Rpitch共Hជ兲, Rjunction共Hជ兲,

and␣.

At remanence共H=0兲, the moments at the junction tile at an angle␪DWwhile those at most area of pitch lie along the

axis of the central wire. The domain wall of length lDW is

created at both ends of each pitch. For the structure, there are 2n of domain wall and correspondingly, extra contribution of domain wall resistance, 2nRDW, is expected. Since moments

of each domain wall rotate smoothly from angle␪DWto zero

relative to the axis of the central wire as shown in the inset in Fig.3, original resistance of the region included in the first term of Eq.共1兲should be deleted and additional AMR resis-tance should be taken into account. The domain wall width study in T-shaped Py structures by Haug et al.16 gives the rough estimate of l_DW. The domain wall profile is assumed as a hyperbolic tangent function based on spin-polarized SEM studies in H shaped Py structures by Jubert et al.17 and hence, R_DWAMRcan be estimated for a given␪DW. A systematic

fit of remanent resistance to Eq.共1兲 give the self-consistent

quantities of RDW. Figure3 demonstrates the angular

depen-dence of RDW. DWRs are positive and increase with

increas-ing␪DW from 42° to 76°.

One explanation for the positive DWRs is the mistrack-ing effect10,11that DWR results from the scattering between the polarized conduction electrons with the localized mag-netic moments and will be enhanced by the large spatial variation in magnetic moments in a DW.11 Here, lDW

in-creases monotonically from 120 to 220 nm when ␪DW is

changed from 76° to 42° implying a monotonic change in spatial variation in magnetic moments in a DW. Therefore, the result that DWR increases with increasing ␪DW can be

attributed to the mistracking effect. For large ␪DW, the

DWMR is about 0.75% close to the theoretical expectation by Levy and Zhang.9

The artificial Néel walls were created in the centipede-like Py structures. Measurements of LMR and TMR reveal information of their magnetic reversals. Due to the shape anisotropy, there is a stable periodic domain configuration of alternating pitch and junction. The tilted angle of moment at the junction is determined by anisotropy constants of both wires and is verified by the PHE measurement. A model of resistance-in-series is developed to analyze both MRs and the intrinsic DWR can be obtained. We find that DWR is positive and decreases with decreasing the angle. The result is indeed consistent with the prediction by consideration of the spin-mistracking effect.

MFM images were taken in the nanostructure laboratory of Dr. J. C. Wu. This work was supported by the NSC of Taiwan grant under Project No. NSC96-2112-M-009-030-MY3 and MOE ATU program.

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θ

DW((((o)))) θDW _n lDW

FIG. 3. 共Color online兲 The angular dependence of the intrinsic DWR. The dashed line is a guide to the eye. The moment configuration of one segment of one typical sample is sketched in the inset.

07D123-3 T. Y. Chung and S. Y. Hsu J. Appl. Phys. 105, 07D123共2009兲