Hysteresis and Avalanche in Different Dimensions

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1、精品论文Hysteresis and Avalanche in Different DimensionsXiang ChangshengSchool of Material Science and Engineering, Shandong University, Jinan, Shandong (250061)AbstractBecause the magnetic domains interact with each other, the relationships between the domains areimportant in determining the properties

2、 of magnetic materials. The shape of the hysteresis and the size of the avalanche vary obviously as the coupling between the domains changes. Special properties can be substantiated by comparing the hysteresis loops and the avalanches. Broad applications will be given in the design of the magnetic m

3、aterials according to these properties.Keywords: Hysteresis; Avalanche Random; Magnetic Materials1. IntroductionHysteresis phenomena occur in magnetic and ferromagnetic materials. The hysteresis loop is not as smooth as we imagined, since consecutive ultrasonic and high frequency impulse voltage is

4、emitted from the surface of the magnetic material due to the irreversible movement of the magnetic domain and magnetic domain wall displacement. This is the so called Barkhausen effect. 1, 2 In the field of magnetic material, a parameter called random(R) has been introduced to evaluate the coupling

5、relationship between magnetic domains. 3-5 Critical randomness (Rc) exists in each dimension, at which point the coupling and randomness is balanceable. 6,7 James P. Sethna, Olga Perkovic and Karin A. Dahmen have proven that if the randomness between the magnetic domains is weak compared to the coup

6、ling, the domains will cooperate with each other, which leads the avalanche to give a kick to its neighbor. As a result, a large avalanche will happen. On the contrary, if the randomness is strong, the domains will flip independently, leading to small avalanches 8, 9. In addition, R is also a parame

7、ter that plays a vital role in determining the shapes of hysteresis loops. Shapes change obviously when given a different R in the same system. 10-12In this paper, some deeper relations among these three factors are given. This study is very useful for a deeper understanding of the hysteresis phenom

8、ena.2. Modeling ProcessA Hysteresis Simulation software program is used to simulate the model. In the pictures of the avalanche, each color stands for a different size. The color also indicates the time of the appearing sequence. In general, the black color corresponds to spins that have not yet fli

9、pped, and each avalanche of flipped spins is given a different color 13. My simulation is based on two to four dimensions. In this paper, three kinds of simulations are used. The hysteresis loop in two dimensions is simulated while the random numbers are 0.9, 1.2, 1.5, 1.8 and 2.1, respectively. The

10、 simulating algorithm is bits with the parameter of a length of 1000.In dimensions higher than two, all avalanches are projected into two dimensions and the avalanches will overlap each other. 13 The hysteresis loop is simulated at different randomness： 2.16,2.5, 3, 4, and 5 in three dimensions. The

11、 simulating algorithm is bits with the parameter of a length of400.At last, hysteresis loops at Rc in two to four dimensions are simulated. The critical randomness of two to four dimensions is 0.9, 2.16 and 4.2, respectively. The simulating algorithm is bits with the parameter of a length of 100.3.

12、Results and DiscussionBy means of the Hysteresis Simulation software package, a series of hysteresis loops and avalanches with different parameters are obtained. By analyzing the pictures with different dimensions,- 7 -we can see obvious differences: The coercivity and remanence of the hysteresis lo

13、op varies greatly when R is different. There are avalanches of all sizes, with many small avalanches and a few large ones. The large avalanche happens at the point where magnetization changes suddenly.In two dimensions, the Rc is close to 0.9. 6, 7 Fig.1 shows the shapes of the hysteresis loops at t

14、he random numbers： 0.9, 1.2, 1.5, 1.8, and 2.1, respectively. As the randomness increases from 0.9 to2.1, the middle part of the hysteresis loop changes from vertical to tilted to the X axis. As a result, the coercivity and remanence of the loops becomes smaller as the R increases. The decreases in

15、the coercivity and remanence mean an inferior quality of memory. In Fig.2, we can see that the size of the avalanche becomes smaller as the R increases. Fig.3 shows that the sizes of the avalanches are limited at a small range when randomness is above 0.9. On the contrary, the distribution is close

16、to linear when R is at 0.9.Now we specify the terms of our discussion on three dimensions whose Rc is 2.16. 6, 7 Fig. 4 shows the hysteresis loops at different random numbers: 2.16, 2.5, 3, 4, and 5 in three dimensions while the length is 400. The middle part of the hysteresis loop curve at Rc is ve

17、rtical to the X axis which makes the loop close to a rectangular shape. This property would support the memory quality to the greatest extent. When R is above 2.16, the loops become tilted to the X axis, just as the same as in two dimensions. The avalanches are infinite and large when RRc, avalanche

18、s seem not to have a good correlation with each other; therefore, the avalanches are finite and small. We can see in Fig.5 that the bigger the R is, the smaller the avalanches are. The avalanche size distributions in three dimensions are shown in the log-log coordination in Fig. 6. We can see from t

19、he figure, as the size grows, the range of the avalanches becomes small. Curves with a larger R are cutoff at a smaller size. Yet, the line at R=2.16 covers all the sizes from 1 to 5 decades. The distribution is in good agreement with the simulations in Fig.5.After analyzing the properties in two an

20、d three dimensions, we suggest that our argument be applied to higher dimensions. In Fig.7, we see the hysteresis loops at critical disorders from two to four dimensions. All the middle parts of the loops are vertical to the X axis, so that they almost overlap each other. The simulations of the aval

21、anches are shown in Fig.8 according to the information in Fig.7. Big avalanches and the small ones are all presented at Rc, which is quite different from avalanches at other random parameters in the same dimension. Avalanche size distribution is also simulated in Fig.9. We can see another shared fea

22、ture that all the size distribution lines are nearly linear which covers the size from one to five decades.4. ConclusionThe relationships among R, the shape of the hysteresis and the size of the avalanche have been presented. Given the amount of the parameter R and its dimensions, the magnetic prope

23、rties of a material can be estimated for the aspects of hysteresis and avalanche. After analyzing the properties of the magnetic material, we draw the conclusion that the properties of material at critical randomness would have the best memory effect, since the shape of the hysteresis is close to a

24、rectangle under this condition. Furthermore, the range of avalanche size is from one to five decades when R is close to critical randomness. The existence of large sized avalanche is a criterion of good memory quality and a large avalanche indicates that the movement of magnetic domains is relativel

25、y strong; as a result, the magnetic material is easily magnetized. Interestingly, the larger the size of the avalanche, the faster the change of magnetization, which makes the middle part of the hysteresis loop vertical to the X axis. The above analysis gives us a better understanding of the memory

26、qualities of the magnetic materials.AcknowledgeWe would like to acknowledge the support from the New Century Excellent Talent Program of theMinistry of Education of the Government of the Peoples Republic of China in the form of Grant No.NCET-05-0599. The work was also supported by Grant No.50571093

27、from the National Natural Science Foundation of China and a grant from National Science Fund for Distinguished Young Scholars (No. 50625101) and Scientific Research Foundation for Returned Scholars (JIAO WAI SI LIU20071108), Ministry of Education of China. We also thank the Scientific Research Found

28、ation of Shandong University project No. 10000067950014 and a City University of Hong Kong Strategic Research Grant Project No. 7002204.References1 Matthew C. Kuntz, Olga Perkovic, Karin A. Dahmen, Bruce W. Roberts, James P. Sethna, Computing inScience and Engineering. 1, 4 (1999).2 O. Perkovic K.A.

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31、. Shore, Phys. Rev. Lett.70, 3347 (1993).11 O. Perkovic K.A. Dahmen and J.P. Sethna, Phys. Rev. Lett. 75, 24 (1995).12 J. P. Sethna, K.Dahmen, S. Kartha, J. A. Krumhansl, O. Perkovic, B. W. Roberts, andJ. D. Shore (reply), Phys. Rev. Lett. 72, 947 (1994).13 The simulations were performed using the H

32、ysteresis Simulation program as a module in The Windowsinterface.14 K Dahmen, JP Sethna, Phys. Rev. B 53, 14872 - 14905 (1996).CaptionsFigure 1. The hysteresis loops in two dimensions at random numbers 0.9, 1.2, 1.5, 1.8, and 2.1, respectively.Figure 2. The simulations of avalanches correspond to Fi

33、gure 1.Figure 3. The avalanche size distribution corresponds to Figure 1 in the log-log coordinate.Figure 4. The hysteresis loops in 3 dimensions while at random numbers 2.16, 2.5, 3, 4 and 5, respectively.Figure 5.The simulations of avalanches correspond to Figure 4.Figure 6. The avalanche size dis

34、tribution corresponds to Figure 4 in the log-log coordinate.Figure 7. The hysteresis loops of at critical randomness in two to four dimensions.Two DThree DFour DFigure 8. The simulations of avalanches correspond to the Figure 7.Figure 9. The avalanche size distribution corresponds to Figure 7 in the log-log coordinate.