2854
IEEE TRANSACTIONS ON MAGNETICS, VOL. 43, NO. 6, JUNE 2007
Magnetization Reversal of Micron-Scale Cobalt Structures With a Nanoconstriction G. Sarau1 , S. Gliga1 , R. Hertel1 , and C. M. Schneider1
Institut für Festkörperforschung, Forschungzentrum Jülich, 52425 Jülich, Germany The magnetization reversal behavior of 20 nm thick cobalt microstructures with a nanoconstriction of variable size has been studied using magnetoresistance measurements and micromagnetic simulations. Depending on the direction of the applied field relative to the current, reversible and irreversible switching events are observed, which can be explained using micromagnetic simulations. Anisotropic magnetoresistance (AMR) is the dominant resistance contribution in the systems measured. The simulations show that instead of one sharp domain wall, which may lead to ballistic magnetoresistance (BMR), two domain walls on each side of the nanocontact precede the complete reversal. Index Terms—Cobalt, magnetic domain walls, magnetoresistance, micromagnetic simulations, nancontacts.
I. INTRODUCTION S THE tendency towards miniaturization increases, it is necessary to understand how magnetoresistive effects are influenced by size reduction. Reports of ballistic magnetoresistance in ferromagnetic nanocontacts [1], [2] have triggered considerable interest and controversy. The BMR effect is usually attributed to a non-adiabatical accommodation of the electron spin, when passing through a sharp domain wall pinned at the nanocontact [3]. It has also been shown that large magnetoresistance can be caused by artifacts involving magnetostrictive or magnetostatic forces establishing and breaking the contact [4], [5] and the movement of magnetic nanoparticles placed in the contact region during the fabrication using a plating process [6]. In this work we study the interrelation between magnetotransport in rigid, lithographically prepared nanocontacts free of magnetostriction contributions [7] and the magnetic microstructure described by micromagnetic simulations.
A
II. EXPERIMENTAL DETAILS The cobalt nanocontacts have been defined in a planar geometry between two wider electrodes by electron beam lithography (EBL) on a Si/SiO substrate spin-coated with a two-layer polymethylmethacrylate (PMMA) resist system and a standard lift-off process. Nanocontacts with different widths were realized in the same batch and on the same sample by varying the e-beam dose and designing the electrodes with a gap of 5 to 15 nm in between, using the proximity effect of EBL to expose the gap. The 20 nm thick cobalt structures were connected to the bonding pads, previously defined by optical lithography, in a second EBL step by 100 nm thick Au electrodes, which connect to the structures as indicated by the dashed lines in Fig. 1(a). We have used magnetoresistance (MR) measurements as an indirect sensing tool based on the AMR effect. MR measurements were performed at room temperature in a four-point probe geometry with a bias current of 0.1 mA. The resistance of the samples at
Digital Object Identifier 10.1109/TMAG.2007.892180 Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.
Fig. 1. (a) MFM image taken at remanence after saturating the magnetization along the x direction. From the magnetic contrast one can infer a dominant monodomain-like remanence state due to the shape anisotropy. (b) SEM image of the 36 nm wide nanocontact.
+
zero magnetic field was ranging between 150 to 190 . The magnetic field was applied in the sample’s plane, parallel (longitudinal configuration) and perpendicular (transversal configuration) to the current direction. Fig. 1(a) shows a representative Magnetic Force Microscopy (MFM) image taken at remanence following positive saturation in a magnetic field of 200 mT applied along the long axis of the electrodes. III. EXPERIMENTAL RESULTS Representative longitudinal magnetoresistance curves for nanocontacts with three different widths (18, 36 and 77 nm) are shown in Fig. 2(a). The MR curves suggest that the underlying magnetization reversal processes should be similar. The small differences are due to the asymmetry of the nanocontacts, which results from the EBL writing. Starting from positive saturation mT , the resistance remains almost constant mT indicating that the magnetization in the up to nanocontact region remains unchanged: the MFM image taken at remanence (Fig. 1(a)) reveals a dominant monodomain-like state and domain flux closure patterns mostly visible at the ends of the electrodes. After applying the magnetic field in the opposite direction, transversal magnetization components develop in the electrodes as the magnetization reverses leading to a continuous resistance decrease with increasing magnetic in Fig. 2(a)), the field. Upon reaching the coercive field ( resistance sharply jumps to its saturation value. The behavior is similar for the opposite sweep direction. Additional insight into the low resistance state can be gained by measuring minor
0018-9464/$25.00 © 2007 IEEE
SARAU et al.: MAGNETIZATION REVERSAL OF MICRON-SCALE COBALT STRUCTURES WITH A NANOCONSTRICTION
2855
Fig. 3. Transversal MR measurements performed on three nanocontacts of different widths: 18 nm (squares), 36 nm (triangles), 77 nm (stars). The arrows represent the measurement sequence. The curves are offset for clarity. Fig. 2. (a) Longitudinal MR measurements performed on three nanocontacts of different widths: 18 nm (squares), 36 nm (triangles), 77 nm (stars). The arrows represent the measurement sequence. (b) Two minor loops showing a reversible (circles) and an irreversible (squares) change in MR for the 18 nm wide nanocontact.
MR loops shown in Fig. 2(b) for an 18 nm wide nanocontact. In the curve represented by circles the magnetic field is swept from positive saturation and stopped just before the sharp jump in resistance (full arrow). Then, the field is swept back, the MR curve indicating a reversible transition (dashed arrow). When the sweep is stopped just after the jump, the high resistance mT, and a positive transition is state persisted up to on the curve represented observed at the coercive field ( by squares in Fig. 2(b)). The resistance jumps correspond to irreversible switching events at the nanocontact. In the transversal configuration, Fig. 3, the magnetic field is applied perpendicular to the current and the easy axis defined by the shape anisotropy ( direction in Fig. 1(a)). Decreasing the magnetic field from positive saturation ( mT, ), longitudinal magnetization components develop in the electrodes. The resistance increases and reaches the same remanent resistance value as in the longitudinal configuration. Passing mT towards negative saturation ( mT), transversal magnetization components develop in the electrodes leading to a decrease in resistance back to its saturation value. The magnetization switching is reversible and is mostly attributed to coherent rotation of the magnetization between the magnetic easy axis and hard axis. The shape of the MR and the relative resistance changes of up to 1% indicate that AMR is the dominant resistance contribution in the measured systems. IV. SIMULATION RESULTS The magnetization reversal in the nanocontacts has been simulated using a finite-element micromagnetic code [8]. The
Fig. 4. Simulated normalized current density profile. Peak values are observed in the constriction.
sample shape has been modelled according to the experiment. We present the results on the 36 nm wide nanocontact (similar results were obtained on nanocontacts with 18 and 77 nm widths). The parameters used to model polycrystalline A/m (saturation magnetization), cobalt are: J/m (exchange constant), J/m (magnetocrystalline anisotropy). The size of the tetrahedral elements corresponds to a cell size of 5 nm. In addition to the micromagnetic simulations, the current density distribution in the elements has been simulated. It has been calculated considering the sample geometry and the position of the contact leads. A homogeneous conductivity was assumed. Fig. 4 shows that the current density is drastically increased in the region of the constriction as compared to the value in the leads. Therefore, in contrast to the magnetization structure in the leads, the magnetic structure in the vicinity of the constriction is expected to have a particularly strong influence on the magnetoresistance. The magnetization reversal has been simulated by linearly decreasing the external field in time, starting from 200 mT and
2856
IEEE TRANSACTIONS ON MAGNETICS, VOL. 43, NO. 6, JUNE 2007
in-plane shape anisotropy. The details of the magnetization reversal in the area close to the constriction are displayed in Fig. 5. It can be seen that the magnetization reversal is accomplished by dissolving the two domain walls by means of vortex nucleation and propagation. We have also simulated the magnetization reversal process in the case of transversally applied magnetic fields. This reversal is qualitatively different from the longitudinal one where the nanocontact no longer plays a critical role. In this case, the simulations (not shown) indicate that the magnetization in the nanoconstriction rotates coherently, while the reversal in the leads occurs by means of the formation and expulsion of vortices. V. CONCLUSION
Fig. 5. Top: Simulated magnetization dynamics for the complete structure under the influence of an instantaneously applied field in the x direction. The grey scale represents the x component of the magnetization (m ). The formation of a domain wall on each side of the nanoconstriction is visible in the last configuration. Bottom: The magnetization dynamics are shown in the nanocontact region, right after the domain walls have formed around it. In this simulation, the externally applied field was linearly ramped from 200 mT to 200 mT in one ns. Due to these parameters used for the applied field in the simulations, the indicated times do not represent the experimental situation, where the field is changed quasistatically.
0
0
The magnetization reversal process in cobalt microstructures with a nanoconstriction was studied for two orientations of an applied magnetic field using magnetoresistance measurements and micromagnetic simulations. For a longitudinally applied field, a domain wall on each side of the nanoconstriction precedes the reversal, which takes place by merging and dissolving of the two domain walls. This corresponds to the experimentally observed irreversible jumps. For a transversally applied field, reversal occurs by coherent rotation of the magnetization in the nanocontact as confirmed by the experiment. In both cases no sharp domain wall, which may lead to ballistic magnetoresistance, develops at the nanocontact. ACKNOWLEDGMENT The authors would like to thank A. van der Hart for EBL writing of the nanocontacts, and D. Bürgler, M. Buchmeier and C. Meyer for fruitful discussions. REFERENCES
ending at mT, within about 1 ns and by instantaneously mT. A large value of the damping conapplying a field of has been used to suppress spin waves. The restant sults show that the main features of the magnetization process are the same whether the external field is ramped or instantaneously applied. Some snapshots of the reversal process for a longitudinally applied field are shown in Fig. 5. It is observed that the constriction plays a distinct role during the reversal, being the last part of the sample in which the magnetization switches. The switching begins in the leads, where domains with reversed magnetization are nucleated. These domains expand until a domain wall is formed on each side of the constriction. Apparently, the nanocontact repels these domain walls. These are between 20 nm and 25 nm wide, which is larger than the spin flip scattering length (few ) and results in a MR effect embedded in AMR. Compared with the field required for the nucleation, a much larger field is required to dissolve these domain walls, thereby reversing the magnetization in the whole sample. We attribute this particular behavior of the magnetization in the nanocontact to an increased stability of the magnetization in the constriction, resulting from the locally increased
[1] N. Garcia, M. Muñoz, and Y.-W. Zhao, “Magnetoresistance in excess of 200% in ballistic Ni nanocontacts at room temperature and 100 Oe,” Phys. Rev. Lett., vol. 82, p. 2923, 1999. [2] H. D. Chopra and S. Z. Hua, “Ballistic magnetoresistance over 3000% in Ni nanocontacts at room temperature,” Phys. Rev. B, vol. 66, p. 020403, 2002. [3] P. Bruno, “Geometrically constrained magnetic wall,” Phys. Rev. Lett., vol. 83, pp. 2425–0, 1999. [4] W. F. Egelhoff, L. Gan, H. Ettedgui, Y. Kadmon, C. J. Powell, P. J. Chen, A. J. Shapiro, R. D. McMichael, J. J. Mallett, T. P. Moffat, M. D. Stiles, and E. B. Svedberg, “Artifacts in ballistic magnetoresistance measurements,” J. Appl. Phys., vol. 95, p. 7554, 2004. [5] K. Sekiguchi, M. Shimizu, and H. Miyajima, “Quantized e =h step and nonquantized step in nanocontact magnetoresistance,” IEEE Trans. Magn., vol. 42, p. 2618, 2006. [6] E. B. Svedberg, J. J. Mallett, H. Ettedgui, L. Gan, P. J. Chen, A. J. Shapiro, T. P. Moffat, and W. F. Egelhoff Jr, “Resistance changes similar to ballistic magnetoresistance in electrodeposited nanocontacts,” Appl. Phys. Lett., vol. 84, p. 236, 2004. [7] M. I. Montero, R. K. Dumas, G. Liu, M. Viret, O. M. Stoll, W. A. A. Macedo, and I. K. Schuller, “Magnetoresistance of mechanically stable Co nanoconstrictions,” Phys. Rev. B., vol. 70, p. 184418, 2004. [8] R. Hertel, O. Fruchart, S. Cherifi, P. O. Jubert, S. Heun, A. Locatelli, and J. Kirschner, “Three-dimensional magnetic-flux-closure patterns in mesoscopic Fe islands,” Phys. Rev. B., vol. 72, p. 214409, 2005.
Manuscript received October 31, 2006 (e-mail:
[email protected])
