Domain Topology of Micron-Scale, Ferromagnetic Pancakes

Transcription

1 UCRL-JC PREPRINT Domain Topology of Micron-Scale, Ferromagnetic Pancakes Peter J. Bedrossian Matthew R. Gibbons Charles J. Cerjan This paper was prepared for submittal to the Materials Research Society San Francisco, CA March 31- April 4,1997 February 1998 This is a preprint of a paper intended for publication in a journal or proceedings. Since changes may be made before publication, this preprint is made available with the understanding that it will not be cited or reproduced without the permission of the author.

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3 DOMAIN TOPOLOGY OF MICRON-SCALE, FERROMAGNETIC PANCAKES Peter J. Bedrossian *, Matthew R. Gibbons, and Charles J. Cerjan Lawrence Livermore National Laboratory, Livermore CA * bedrossian ABSTRACT Planar, micron-scale ellipses patterned from 7OOA-thick Co films exhibit nearly-complete suppression of hysteresis when magnetized in-plane along their short axes. Using a combination of Magnetic Force Microscopy and Vibrating Sample Magnetometry, we find that the suppression of hysteresis is associated with the continuous deformation of a dipole field configuration. The presence of hysteresis for in-plane, long-axis magnetization is associated with transitions between topologically inequivalent configurations. JNTRODUCTION The magnetic behavior of micron-scale, patterned, ferromagnetic films has recently attracted attention for possible application to both recording heads and novel media [12,,11,,* Discrete events such as domain wall nucleation and annihilation have previously been associated with jumps detected in hysteresis loops for Co particles with sensitive magnetometty. [lo] Ferromagnetic structures of such length scales generally contain few domains and therefore fall between the two limiting, classical regimes which have been described analytically, the single-domain structure on the small end [ 1 I] and the macroscopic neighboring domains, and magnetostatic into i contributions from magnetostriction, anisotropy, and domain-wall-edge interactions [ 121. i Despite the nonlinearity of the various energetic contributions and the overall complexity of such systems, we show that the behavior of patterned films magnetized in-plane is still : governed qualitatively by simple, topological considerations. The topological classification of defects has proven useful for the characterization of local,,i, energetic minima in a class of condensed matter systems in which an order parameter occupies $ a manifold of lower dimensionality than the system under consideration [ 131. For example, in r an ideal two-dimensional ferromagnet in which the magnetizations of all domains are in-plane CL and the magnitude of the magnetic moment per unit area is uniform, the local magnetization ii s vector lies on a circle. Under such conditions, field configurations which am topologically aequivalent cannot be deformed into one another continuously, and a transformation between Wo topologically inequivalent configurations must involve a bifurcation [ 141. In a micron-scale hm magnetized in-plane, the M-H hysteresis loop should be sensitive to nucleation of adividual domains, so the formation of individual, topologically-stable defects which change he topological class of a particular structure should leave a distinctive signature in the hysteresis MP. We shall show that the occurrence of bifurcations is associated with hysteresis, of hysteresis is associated with continuous deformation of a field configuration of a jven topological index. ia, WERIMENTAL pi.~ys of Co ellipses with principal axis dimensions of 2x4,4x8,2x8, and 4xl6pm were $rrcated from 7OOA-thick films deposited on Si wafers by magnetron sputtering in a chamber <I F Mat. Res. Sot. Symp. Proc. Vol. 475 o 1997 Materials Research Society 277

4 with base pressure below IO-7 tom The films were patterned optically, using a mask which.~ had been written with electron-beam lithography, and then were etched in an Ar plasma, leavin 7OOA-high, elliptical Co islands. The Co ellipses were arranged on square grids. To mini& inter-ellipse interaction, the grid spacing was adjusted so that the fraction of the total substrat& area of 36mm2 covered by Co was l/30. The smallest, out-of-plane demagnetization factor & the ellipses above is out of a maximum 41~ [15]. Hysteresis loops for each array were d measured with a Vibrating Sample Magnetometer (VSM), and domain patters within indivic ellipses were mapped with Magnetic Force Microscopy (MFM). RESULTS Figure 1 displays magnetization measurements with the field applied in-plane along botl long and short axes of each of ellipse array. Using a VSM, the sample magnetization was 4 measured parallel to the applied field. Similar measurement of a 7OO,&thick, 7x7mm Co she-. film yields a square loop with 20 Oe coercivity. The short-axts loops for each ellipse geomet$ show dramatic reduction in hysteresis compared with the long-axis loops. The long-axis 100~ for the 2x4 and 4xSpm ellipses in figures 2 (a) and (b) show hysteresis with negligible remanence, while the long-axis loops for the 2x8 and 4x 16pm ellipses in figures 2 (c) and (d do show a remanent moment at zero applied field. Magnetic Force Microscopy (MFM) was used to detect domain patterns within individual res and to verify the uniformity of the domain patterns across each array. Figure 2 presents &field MFM images of individual ellipses, acquired using phase detection with a Digital ments R5000 Force Microscope, after initial saturation along the directions indicated with &Oe field. The detailed interpretation of such phase images has been described previously *The images do not determine the local magnetization uniquely, because they are twonsional projections of three-dimensional magnetization patterns. Because of the high outane demagnetization factor, we may assume that the domains are magnetized Anantly in-plane, and we present in figure 2 the in-plane projection of the domain tations for each image. k. ation Field Direction 4 ation Field Direction t H (koer) H (koer) H $Oer) Figure 1. Plots of magnetization versus applied field from a Vibrating Sample 7 Magnetometer for four arrays of ellipses with different, with the external field applied along 1 each of the principle axes. (a) 2x4 pm, (b) 4x8 pm, (c) 2x8 pm, and (d) 4x16 pm. I Figure 2. Remanent-state MFM images and corresponding in-plane domain orientations dividual ellipses acquired after initial saturation in the directions indicated. (a) 2x4 pm, (b) b, (c) 2x8 urn, and (d) 4x16 pm ellipse. 2s When magnetized initially along its short axis, each ellipse exhibits a pattern of two &-rotating vortices. The associated field therefore has winding number +2, and is logically equivalent to a dipole field. If magnetized initially along the long axis, remanent 8 of the 2x4 and 4x8pm ellipses are also highly-symmetric but with a net circulation, or!&g number, of +l. The 2x8 and 4x16 pm ellipses exhibit chaotic behavior if magnetized gthe long axes initially. Therefore, the absence of a remanent moment is associated with ecurrence of a symmetric pattern of topological excrtations, while the suppression of sis is associated with the preservation of a dipole field configuration. Z he total energies of the two magnetization configurations in figure 2(a) were compared ~nuxnerical micromagnetic analysis, The exchange contribution to the total energy was d,to be comparable for the two orientations, 1.56~10~~ erg/cc for initial saturation along the taxis, and 1.57 x IO9 erg/cc for initial saturation along the long axis. However, the lostatic contribution for the remanent state following saturation magnetization along the :&is, 0.53 x 10e9 erg/cc, was found to be substantially lower than that for initial tization along the short axis, 0.91 x 10s9 erg/cc., Therefore, the state with the lower g number has the lower total energy. The two-vortex pattern, once formed, must be A from jumping to the lower-energy state during execution of a hysteresis loop. 270!79

5 The reason that the lower-energy state is accessible only for the case of initial saturation along the long axis is revealed in MFM measurements in the presence of an external field. Figure 3 displays a sequence of MFM images of a 2x4 pm ellipse, acquired while reducing field from initial saturation along the long axis. Domain formation occurs by buckling of th magnetizations at the ends, followed by the formation of a vortex in the lower portion of the ellipse, with sense opposite to that of the rest of the ellipse. The expulsion of that vortex is associated is with a reduction of total vorticity, or a change in the winding number of the : associated field, which in turn underlies the presence of hysteresis. The reason is that upon reversal of the external field, the ellipse need not snap back to a configuration of higher voi.ti it can respond to the external field simply by displacement of the 180 domain wall. k. l be situation IS quite different for the case of initial saturation along the short axis. Figure )lavs a seauence of edge-enhanced MFM images acquired during - application of a field saturation fieid. In?his case, the ellipse responds through ter-rotating vortices. Increasing the field drives the two As external field is reduced from saturation, the two. At each stage, the associated field retains its dipole &and there is no change in vorticity. Unlyke the case of iniual saturation along a long :re is no continuous pathway to switch from the topologically-stable state with two, rotating vortices to the lower-energy state with the lower winding number. Figure 3: MFM imaaes of a 2x4 urn elliose acauired in the nresence of an external i rich variety of magnetizanon behaviors is observed for 700A high, Co ellipses with four ent sizes (2x4,4x8,2x8, and 4x16 urn) magnetrzed along one of their prmciple axes. Use omain microstructure durmg the execution of a on of hysteresis is associated wrth the occurrence of ns. The occurrence of such configurations is in turn that is specific to the particular size and shape of the iand the orientation of the applied field relative to the ellipse. p e authors thank B. Law and F. Grabner for fabricatron, S. Vernon for discussions, and &ken for use of equipment. Work was performed at Lawrence Liver-more National $ory under the auspices of the US DOE under Contract W-7405Eng Oer 100 Oer 200 Oer :w, R. Pease, and R. White, J. Magnetism and Magnetic Materials 155, 140 (1996); J. i. Technol. B 13, 1089 (1995). u1 den Berg, J. Appl Phys. 57,2168 (1985). ehn et al., Science 272, 1782 (1996); J. Appl. Phys. 79,5068 and S. Schultz, J. Appl. Phys 73,4516 (1993). myth et az., J. Appl. Phys. 69,5262 (1991); J. Appl. Phys. 63,4237 (1988). LOU, M. Wei, P. Krauss, and P. Fischer, J. Appl. Phys. 76,6673 (1994). bmez et al., J. Appl. Phys. 80,342 (1996). &kin and T. Koehler, J. Appl. Phys. 67,5544 (1990). 300 Oer 400 Oer 200 Oer Q analis, K. Babcock, J. Massie, V. Elings, and M. Dugas, Appl. Phys. Lett. 66,2585.I Figure 4: MFM images of the same ellipse as in fig. 3, in the presence of an external fif applied along the short axis, as indicated, pamile to the initial saturation field. Edges have d; Wemsdorfer, et al., Phys. Rev. B 53,334l (1996). --L ^_^_ 2 L_ L:-Lll-L.rL- a uranceu LO mgruignr ffle uornam wans

6 11. L. Landau, E. Lifshitz, and L. Pitaevskii, Electrodynamics of Continuous Media (Pergamon, Elmsford NY, 1984), pp C. Kittel and J. Galt, in Solid Stare Physics 3, edited by F. Seitz and D. Tumbull (Academi NY, 1956), p N. D. Mermin, Rev. Mod. Phys. 51,591 (1979). 14. M. Kleman, in Formation and Interaction of Topological Defects, edited by A. Davis and R. Brandenberger (Plenum, NY, 1995), p J. Osbom, Phys. Rev. 67,351 (1945). 16. K. Babcock, M. Dugas, S. Manalis, and V. Elings, m Evolutron of Thin-Film and S&ace Structure and Morphology, edited by B. Demczyk et al., MRS Symposium Proceedings Vol. 355 (MRS, Pittsburgh, 1995). 282

7 Technical Information Department Lawrence Livermore National Laboratory University of California Livermore, California 94551