JOURNAL OF APPLIED PHYSICS VOLUME 88, NUMBER 5 1 SEPTEMBER 2000 Quantitative analysis on correlation between local coercivity and reversal time in ferromagnetic thin films Sug-Bong Choea) and Sung-Chul Shin Department of Physics and Center for Nanospinics of Spintronic Materials, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea Received 28 January 2000; accepted for publication 15 June 2000 We report a method to quantitatively analyze the correlation between the local coercivity variation and the local reversal-time distribution in ferromagnetic thin films. The spatial distribution of the local coercivity on a film plane was directly measured from the hysteresis loops of each local area of 320 320 nm2 and then, the local coercivity distribution was quantitatively correlated with the local reversal-time distribution obtained from time-resolved domain evolution patterns grabbed at precisely the same position of the film. We demonstrate a clear experimental evidence of the direct correlation between the real coercivity distribution and the magnetization reversal dynamics, which could be explained within a context of a thermally activated relaxation process. © 2000 American Institute of Physics. S0021-8979 00 07718-5 Magnetization reversal dynamics in ferromagnetic thin real time by a magneto-optical microscope magnetometer films is of current fundamental interest in achieving high MOMM system.3 performance of technological applications as well as in ex- A number of Co/Pd multilayers were prepared on glass ploring fundamental curiosity in magnetism.1­4 Recently, ad- substrates by alternatively exposing two e-beam sources of vanced magnetic imaging techniques provide direct observa- Co and Pd under a base pressure of 2.0 10 7 Torr at the tion of domain evolution patterns and promptly, the ambient temperature. The layer thickness was carefully con- experimental observations of the ragged domain boundaries trolled within a 4% accuracy. Low-angle x-ray diffraction evidence the existence of the local magnetic irregularities studies using Cu K radiation revealed that all samples had and their influence on the domain reversal dynamics.5­7 distinct peaks indicating an existence of the multilayer struc- Much effort has been devoted to clarify the influence of ture. High-angle x-ray diffraction studies showed that the the local magnetic irregularities on the domain reversal samples grew along the 111 cubic orientation. All the dynamics.7­14 For instance, Bruno et al.9 took into account samples have perpendicular magnetic anisotropy and show the distribution of activation energies to explain the hyster- hysteresis loops of unit squareness. We will designate the esis loop and the distortion in wall displacement of ferro- samples as (tCo-Å Co/tPd-Å Pd)n , where tCo is the Co- magnetic Au/Co/Au film. Ferre´ et al.7,8 introduced the local sublayer thickness, tPd is the Pd-sublayer thickness, and n is coercivity field distribution into a micromagnetic consider- the number of repeats. ation to analyze the direct/indirect magnetization processes The hysteresis loops of every local area from two- and the ``Swiss cheese''-shaped domain patterns. However, dimensional array of 8000 spots on the Co/Pd multilayers to the best of our knowledge, all the previous investigations were simultaneously measured utilizing the MOMM have been done based on the models of the coercivity distri- system.15 The system, mainly composed of an optical polar- bution and thus, actual correlation still remains open. The izing microscope equipped with a charge-coupled device present work was motivated to directly measure the distribu- CCD camera, could grab domain images with 300 nm spa- tion of the local coercivity to quantitatively analyze the in- tial resolution with sweeping the external magnetic field by fluence of the local coercivity variation on the domain rever- an electromagnet.3 The local Kerr hysteresis loops were mea- sal dynamics. This letter first demonstrates the experimental sured by simultaneously tracing the Kerr intensity variation evidence that the reversal time of each local area in ferro- at every corresponding CCD pixel for every 10 Oe interval magnetic thin films is directly determined by its local coer- per 0.4 s and then, converting the Kerr intensity to the Kerr civity. rotational angle.8,15,16 The Kerr intensity was averaged by In this work, the spatial distribution of the local coerciv- 16-times measurements of the major loops for a given ity has been measured from each local hysteresis loop of sample to reduce the error from the statistical reversal prob- local area on two-dimensional array of 320 320 nm2 spots ability. Care was taken to maintain the observation sight of on a ferromagnetic film.8,15,16 The local coercivity distribu- the MOMM measurement preventing the thermal and/or tion was directly analyzed with the local reversal-time distri- gravitational drift and the mechanical vibration of the sample bution at precisely the same position of the film obtained stage during the measurement. The coercivity H from time-resolved domain evolution patterns grabbed in C was deter- mined by interpolating an applied field for the condition of zero Kerr rotational angle. The experimental error in the co- a Electronic mail: sugbong@kaist.ac.kr ercivity determination was confirmed to be smaller than 2 Oe 0021-8979/2000/88(5)/3096/3/$17.00 3096 © 2000 American Institute of Physics Downloaded 20 Mar 2001 to 148.6.169.65. Redistribution subject to AIP copyright, see http://ojps.aip.org/japo/japcpyrts.html J. Appl. Phys., Vol. 88, No. 5, 1 September 2000 S.-B. Choe and S.-C. Shin 3097 FIG. 1. The local coercivity distributions HC(x,y) of the 2.5 Å Co/ FIG. 3. a The time-resolved domain reversal pattern of the 2.5 Å Co/ 11 Å Pd)10 sample. The plots show the hysteresis loops measured at the unit 11 Å Pd)10 sample at exactly the same position shown in Fig. 1. The gray pixels corresponding to two local areas designated by each arrow. Here, x level corresponds to the time (x,y) in a logarithmic scale for reversal of axis is an applied field ranging from 2 to 2 kOe and y axis is the normal- the corresponding region (x,y). b The correlated distribution of the num- ized Kerr rotational angle. ber of pixels N(HC , ) with logarithmic gray level in HC coordinate for the 2.5 Å Co/11 Å Pd)10 sample. The solid line represents the best fit using Eq. 1 . for these particular Co/Pd multilayers having the maximum Kerr rotational angle of about 0.15°. The most striking feature of the MOMM system is the fact that we can generate the two-dimensional spatial distri- coercivity of this sample, by counting the cells having the bution map of the local coercivity variation of a sample, corresponding value of the local coercivity for every 3 Oe from directly analyzing the local hysteresis loops of every interval. Here, the distribution density is normalized by the local area simultaneously measured with an identical condi- total number of 8000 cells. The asymmetric shape might be tion. Figure 1 demonstrates the local coercivity distribution ascribed to the difference between the wall-pinning and HC(x,y) of the 2.5 Å Co/11 Å Pd)10 sample in gray level nucleation energy barrier distributions, where the lower onto the two-dimensional xy plane, where each map corre- bound of the coercivity distribution is governed by the wall- sponds to a sample surface area of 32.0 25.6 m2 and each pinning coercivity and the upper bound is determined by the pixel corresponds to an area of 320 320 nm2. The figure nucleation coercivity.18 It should be noticed that the distribu- vividly shows the spatial fluctuation of the local coercivity tion in magnitude is neither a Gaussian nor a Lorentzian as on submicrometer scale. The difference in the loop shape generally assumed in the most theoretical models.7,9 Surpris- and the coercivity is clearly seen between the plots in the left ingly, the distribution of our samples could be well fitted by and right side of the figures, which show the hysteresis loops the linear lines in exponential scale as shown by the solid measured at the unit pixels corresponding to two different lines in the figure. local spots designated by each arrow. The fluctuation of the It is very interesting to directly correlate the real distri- local coercivity is possibly ascribed to the structural irregu- bution of the local coercivity with the magnetization reversal larity due to the possible accumulation of the lattice misfits, dynamics. For this study, we have investigated the magneti- residual stress, and other defects, especially at the interfaces zation reversal dynamics of the Co/Pd multilayers at pre- during deposition process in high vacuum, since the coerciv- cisely the same position as the local coercivity measurement ity is a structure-sensitive magnetic property.17 Therefore, of the sample. It was done via the time-resolved domain one might expect a larger variation in the local coercivity observation utilizing the MOMM system by applying a con- with increasing the number of repeats; it was indeed ob- stant reversing magnetic field near the average coercivity af- served in our Co/Pd multilayer samples.15 ter saturating the sample.3 Figure 3 a shows the domain In Fig. 2 we plot the distribution density of the local evolution patterns for the 2.5 Å Co/11 Å Pd)10 sample, where the gray level in the figure designates the time (x,y) required for the corresponding region of the (x,y)th pixel to reverse. Most interestingly, one can notice that the reversal pattern in Fig. 3 a is truly coincident with the local coerciv- ity distribution in Fig. 1. This directly demonstrates the close correlation between the local coercivity distribution and do- main reversal pattern on the submicron scale. For a quantitative analysis of the correlation, we have measured the number of pixels N(HC , ) by counting the pixels having the values of the local coercivity HC(x,y) and the local reversal time (x,y) at the same (x,y)th pixel in the corresponding map. Figure 3 b illustrates the correlated FIG. 2. The distribution density in magnitude of the local coercivity of the distribution of the number of pixels N(HC , ) in logarithmic 2.5 Å Co/11 Å Pd)10 sample. The density was determined by counting the scale in HC coordinates. In the figure, it is very clearly number of cells having the corresponding magnitude of the local coercivity for every 3 Oe interval. The solid lines are the best fits for the linear depen- seen that the local reversal time is truly correlated with the dency of each bound. local coercivity, which implies that the local domain dynam- Downloaded 20 Mar 2001 to 148.6.169.65. Redistribution subject to AIP copyright, see http://ojps.aip.org/japo/japcpyrts.html 3098 J. Appl. Phys., Vol. 88, No. 5, 1 September 2000 S.-B. Choe and S.-C. Shin ics during magnetization reversal is directly governed by the the local coercivity distribution governs the domain reversal local coercivity. dynamics via a thermally activated relaxation process. The reversal mechanism taking into account the local coercivity distribution could be analyzed within the context This work was supported by the Creative Research Ini- of a thermally activated relaxation process. The half reversal tiatives of the Ministry of Science and Technology of Korea. time , the time needed to reverse half the volume of the sample, is known to be exponentially dependent on an ap- plied field H.4 By considering the local coercivity distribu- 1 J. Ferre´, J. P. Jamet, and P. Meyer, Phys. Status Solidi A 175, 213 1999 . 2 tion H B. Raquet, R. Mamy, and J. C. Ousset, Phys. Rev. B 54, 4128 1996 . C(x,y ), the half reversal time (x,y ) of the magneti- 3 S.-B. Choe and S.-C. Shin, Phys. Rev. B 57, 1085 1998 ; Appl. Phys. zation MS of a volume VA located at (x,y) is given by Lett. 70, 3612 1997 . 4 J. Pommier, P. Meyer, G. Po´nissard, J. Ferre´, P. Bruno, and D. Renard, x,y Phys. Rev. Lett. 65, 2054 1990 . 0 exp VAMA k 5 BT HC x,y H , 1 B. E. Bernacki, T.-H. Wu, and M. Mansuripur, J. Appl. Phys. 73, 6838 1993 . where 6 0 is the characteristic reversal time for H M. Speckmann, H. P. Oepen, and H. Ibach, Phys. Rev. Lett. 75, 2035 H 1995 . C(x,y ), kB is the Boltzmann's constant, and T is 7 temperature.4 It is clearly demonstrated that the correlated J. Ferre´, V. Grolier, P. Meyer, S. Lemerle, A. Maziewski, E. Stefanowicz, S. V. Tarasenko, V. V. Tarasenko, and M. Kisielewskis, Phys. Rev. B 55, distribution can be quantitatively characterized by Eq. 1 as 15092 1997 . shown by the solid line in Fig. 3 b . The activation volume 8 J.-P. Jamet, S. Lemerle, P. Meyer, J. Ferre´, B. Bartenlian, N. Bardou, C. V Chappert, P. Veiller, F. Rousseaux, D. Decanini, and H. Launois, Phys. A of the sample is determined to be 7.9 10 18 cc, which is almost identical to the previous value determined via the Rev. B 57, 14320 1998 . 9 P. Bruno, G. Bayreuther, P. Beauvillian, C. Chapert, G. Lugert, D. Re- field dependence of the half reversal time in the whole area nard, J. P. Renard, and J. Seiden, J. Appl. Phys. 68, 5759 1990 . of the sample.19 10 S. K. Han, S.-C. Yu, and K. V. Rao, J. Appl. Phys. 79, 4260 1996 . 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