IEEE TRANSACTIONS ON MAGNETICS, VOL. 41, NO. 10, OCTOBER 2005 2845
On the Study of Coercivity and Interaction FieldDistributions From Microhysteresis Loops
L. X. Ye, J. M. Lee, and T.-H. Wu
Taiwan SPIN Research Center and Graduate School of Engineering Science and Technology, National Yunlin University ofScience and Technology, Yunlin 640, Taiwan, R.O.C.
We report direct measurement of the asymmetrical behaviors of microhysteresis loops within an area element at submicron scale onmagnetic thin-film material. We have investigated the effect of asymmetrical behaviors created by the neighboring magnetic elementsboth at micron scale and submicron scale. Our studies provide evidence of the asymmetrical behaviors of microhysteresis due to theinteraction field of nearby magnetic elements. Moreover, we have found that the discrepancy between and is larger for smallermeasured areas.
Index Terms—Coercivity, interaction field, microhysteresis, Preisach diagrams.
I. INTRODUCTION
WHEN AN external magnetic field is applied to a partic-ular magnetic media, each element feels not only this
field but also the field created by the neighboring magnetic el-ements [1]. Thus, the symmetry about an elementary loop ofthe magnetic moment reversal can be destroyed by the pres-ence of the interaction field [2], [3] created by other nearby el-ements. The magnetic domain reversal uniformity is influencedby asymmetrical behaviors. In this paper, direct measurementof interaction field distribution for a magnetic material with per-pendicular anisotropy has been studied using a Kerr microscope.Our results show that the asymmetrical behaviors at the sub-micron scale are prominent compared with those at the micro-scopic scale.
II. EXPERIMENTAL METHODS
The sample was prepared by cosputtering the Tb and FeCoonto an SiN-coated silicon substrate [4]. The layer structurewas silicon/SiN(25 nm)/TbFeCo(20 nm)/SiN (10 nm). Mea-surements were performed under a modified Kerr microscope aspreviously described [5]. Several magnetic fields were appliedperpendicularly to the film plane, and video images of magneticdomain wall motion with a speed of 30 frames/s were recorded.
Normalized gray-scale levels on pixels from the video imageswere then plotted against the applied magnetic fields to obtainthe microhysteresis loops [6] and coercivity values.
III. RESULTS AND DISCUSSIONS
Fig. 1 shows a typical microhysteresis loop for a measuredarea element 0.33 0.33 m. Normalized gray-scale levelstaken from the domain images are plotted versus the appliedfield (HA). We can see from the microhysteresis loop in Fig. 1that is 1259 Oe and is 1000 Oe, i.e., the coercivityvalue on the right side is larger than on the left side and the
Digital Object Identifier 10.1109/TMAG.2005.854675
Fig. 1. Microhysteresis loop within 0.33� 0.33 �m area.
difference of and is 259 Oe (Table I). In Fig. 1, theloop is displaced towards positive values of HA. The shiftdownward is due to the Faraday effect. The gray-scale levelsmeasured were dependent on the intensity of the light sourceand other noise. In this paper, we used digital image processing[7] to normalize gray-scale levels. Thus, the value of gray-scalelevels did not effect the estimation of and values.is the coercivity on the right side and is the coercivity onthe left side of the loop. is the arithmetic mean such that
. is the interaction field and iscalculated from .
In order to further understand the variations of interactionfield from each microhysteresis loop, we calculated the statis-tical incidences (the total number of pixels with any given gray-scale level) of various coercivity strengths and plotted coercivitydistribution of and values and versus on a
plane. Fig. 2(a) shows the incidence of various co-ercivity strengths of and from 90 000 microhysteresisloops, where each area of microhysteresis is 3.3 3.3 m. Thesolid line is the coercivity spectrum of , while the dashedline is the coercivity spectrum of . We can see from Fig. 2(a)that the coercivity peak of lies at 1286 Oe and the coercivitypeak of is at 1232 Oe. Comparing the solid line and dashedline curves from Fig. 2(a), three things can be seen. Firstly, the
2846 IEEE TRANSACTIONS ON MAGNETICS, VOL. 41, NO. 10, OCTOBER 2005
TABLE IH ;H ;H , AND 2H VALUES FROM Fig. 1
Fig. 2(a) Statistical numbers of various coercivity strengths of H and H .(b) Scatter plot of the coercivity values of H versus H .
ranges of coercivity strengths for and both lie between1100–1800 Oe.
Secondly, we can see that each of the coercivity spectra(solid line) and (dashed line) approximates a Gaussian dis-tribution, but in both cases the distribution is positively skewedtoward higher values of .
Thirdly, the peak height of and are similar, but thevalue of coercivity strength has shifted. This demonstrates asmall influence of interaction fields created by the neighboringmagnetic elements.
Fig. 2(b) shows a scatter plot of the coercivity values ofand . For an value of about 1200 Oe, the distributionof ranges from approximately 1150–1600 Oe. Fig. 2(b)demonstrates the variations of asymmetrical behavior veryclearly but does not show how many microhysteresis loopsdemonstrate asymmetrical behavior or the maximum variationsof interaction field.
If we plot versus with the statistical incidence asthe axis, then a 3-D picture emerges that combines Fig. 2(a)and (b). Fig. 2(c) shows such a plot, whereas Fig. 2(d) shows asimilar plot of versus . From Fig. 2(c) it is clearly seenthat the variations in asymmetrical behavior are real, but very
Fig. 2(c) 3-D diagram of numerical values of H and H versus H -Hplane. (d) 3-D diagram of numerical values of H and H versus H -Hplane. Each area of microhysteresis is 3.3� 3.3 �m.
small. In addition, the majority of pixel elements lie in the re-gion where the coercivity strength of approximates the coer-civity strength of . From Fig. 2(d), we see that the valueis between 80 and 100 Oe and ranges from 1050–1200Oe. Comparing Fig. 2(a) and (d), we see that the range of isnarrower than the range in variation in and . It indicatesthat some of the microhysteresis loops have larger variations of
and . That also means that some of the magnetic mo-ments have a strong interaction field.
Fig. 3(a) shows the statistical incidences of various coercivitystrengths of and from 90 000 microhysteresis loops,where each area of microhysteresis is 0.33 0.33 m Com-paring the solid line and dashed line from Fig. 3(a), three thingscan also be seen.
Firstly, the ranges of coercivity strengths from andare similar between 800 and 1700 Oe.
Secondly, we can see that the coercivity spectrum of(solid line) is a short and wide Gaussian-like spectrum com-pared to the spectrum for (dashed line).
Thirdly, the peak value of for and are dissimilar,and the peak of coercivity strength has shifted.
Comparing Figs. 2(a) and 3(a), we see that as the measuredarea becomes smaller (i.e., as the optical resolution increasesand the measured areas of microhysteresis loops decrease), thedifferences between and become clearer. The improvedmeasurement resolution reveals that there is a clear differencein magnitude in the and coercivity peaks, which alsobecame broader as the measured area is reduced. We can seefrom Fig. 3(a) that the coercivity peak of is 1152 Oe andthe coercivity peak of is 1099 Oe. Fig. 3(b) shows a scatterplot of the coercivity values of versus . The majorityof values are distributed between 900–1400 Oe, and
YE et al.: COERCIVITY AND INTERACTION FIELD DISTRIBUTIONS FROM MICROHYSTERESIS LOOPS 2847
Fig. 3. (a) Statistical numbers of various coercivity strengths of H andH . (b) Scatter plot of the coercivity values of H versus H . (c) 3-Ddiagram of numerical values of H and H versus H � H . (d) 3-Ddiagram of numerical values of H and H versus H -H plane. Each areaof microhysteresis is 0.33� 0.33 �m.
distribution is 900–1500 Oe. When is about 1200 Oe, therange in is 900–1500 Oe.
Fig. 3(c) shows the 3-D diagram of statistical incidencesof and plotted against the - plane. ComparingFigs. 2(c) and 3(c), we can see how the asymmetrical behaviorvaries with the reduction in measured area. The asymmetricalbehavior becomes more obvious. Fig. 3(d) shows the 3-Ddiagrams of statistical incidences of and plotted againstthe - plane. From this figure, we can see that thevalues lie between 200 and 150 Oe, and ranges 950–1300Oe.
The ranges of values and values have expandedcompared to the larger measured area in Fig. 2(c). Comparing
Fig. 3(a) and (d), we find that although the range of issimilar to that of and , the range of is broader, i.e.,most of the microhysteresis loops have larger variations ofand . We conjecture that the reason for this is that the largermeasured area feels a smaller force of interaction field, due toa cancellation of the interaction field by other nearby magneticelements. Thus, the integrated coercivity and interaction fielddistributions were seen to be reduced in the larger measuredarea.
IV. CONCLUSION
This paper has successfully demonstrated the simultaneousmeasurement of the interaction field from 90 000 micro-hysteresis loops. In this paper, in order to reduce the influence ofnoise when measuring the microhysteresis loops, we employeda spatial filter when image processing. Thus, the gray level ofeach pixel was replaced by the mean of the gray levels of a 3 3mask [7], centered on the measured pixel. Since the spatial res-olution was 1.1 1.1 m per pixel, the area of each “micro-hysteresis loop” was 3.3 3.3 m. Thus, a measured area of330 330 m contained 90 000 loops. Also, the spatial resolu-tion was 0.11 0.11 m per pixel, and the area of each “micro-hysteresis loop” was 0.33 0.33 m. Thus, a measured area of33 33 m containing 90 000 loops is achieved.
We have measured the discrepancies between the left sideand the right side coercivity. We have provided the
direct measurement tool of the interaction field of nearby mag-netic elements. For various microhysteresis loop scales, we havefound that the discrepancy is larger for smaller measured areas.
ACKNOWLEDGMENT
This work was supported in part by the National ScienceCouncil, R.O.C., under Contract NSC 92-2112-M-224-001 andby the Department of Industrial Technology, Ministry of Eco-nomic Affairs, R.O.C., under Contract 92-EC-17-A-01-S1-026.The authors would like to thank G. Turner-Walker for commentson earlier drafts of this paper.
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