VOLUME 84, NUMBER 23 P H Y S I C A L R E V I E W L E T T E R S 5 JUNE 2000 Statistical Properties of Barkhausen Noise in Thin Fe Films Ezio Puppin* Istituto Nazionale per la Fisica della Materia, Dipartimento di Fisica, Politecnico di Milano, P.za L. da Vinci 32-20133 Milano, Italy (Received 7 December 1999) The statistical properties of Barkhausen noise in an epitaxial Fe film grown on MgO have been charac- terized with magneto-optical Kerr effect measurements. The data reveal that magnetization reversal takes place via sudden jumps between a discrete number of randomly distributed magnetic configurations. The smallest jumps occur on a scale length of 10 mm and their amplitude distribution can be fitted with a power law: P DM DM2a with a 1.1 and DM spanning over several decades. PACS numbers: 75.60.Ej Magnetization reversal in ferromagnetic solids takes In this paper, data collected with a recently developed place via discrete jumps. If, during this process, a pickup experimental technique will be presented. This technique coil is placed near the sample a characteristic noise is overcomes the major limitations of the standard pickup coil induced in the coil by the random changes of the magnetic since it is space resolved an sufficiently sensitive for thin flux. This noise is called Barkhausen noise (BN) from the films. The basic layout of the apparatus is shown in Fig. 1. name of the scientist who made its first observation [1], Briefly, a conventional ellipsometer for magneto-optical whereas the individual jumps are known as Barkhausen Kerr effect measurements (MOKE) has been modified by jumps (BJ). Generally speaking, a magnetic solid under introducing a focusing optics which allows one to vary the the action of an external field belongs to a larger class size of the laser beam onto the sample from 10 mm to sev- of physical systems whose common feature is a strongly eral mm [12]. The high noise rejection of the system allows nonlinear and dissipative behavior in the presence of a the measurement of individual hysteresis loops in 1 s or structural disorder. Among the numerous examples, it is less with a good signal-to-noise ratio. A typical data acqui- worth mentioning flux lines in type-II superconductors sition consists of a series of 1000 loops measured one after [2], microfractures [3], earthquakes [4], and liquid crystals the other at a frequency of 1 Hz. The sample [13] is an epi- in porous media [5]. Even though a unifying theory for taxial Fe film having a thickness of 900 Å. The substrate this class of physical systems is far from being formulated, is a single crystal of MgO (001) heat treated in vacuum a distinctive feature is always observed: the presence of in order to observe a sharp 1 3 1 LEED pattern charac- scaling behavior for certain measurable quantities. In the teristic of the bulk-terminated lattice. The Fe evaporation case of BN, scaling is shown by the probability amplitude has been performed in a vacuum chamber with a base pres- of the jumps that appear to be linear in a log-log plot over sure of 5 3 10211 Torr at a rate of 10 Å min. The films' several decades. The presence of scaling in BN attracted thickness has been measured with a quartz microbalance, the interest of statistical physicists, and several models and purity has been checked with x-ray photoelectron spec- have been proposed with different underlying physical troscopy and Auger spectroscopy. Magnetization is in the assumptions and varying fortune in explaining the experi- mental observations [6­10] (for a more complete review, see Ref. [6] and references quoted therein). The experimental technique normally adopted in BN measurements is based on the same principle of the original work of Barkhausen, i.e., magnetic flux variations connected with BJ are detected with an inductive pickup coil wound around the sample. The voltage signal across the coil consists of a series of peaks having random amplitude and duration. Modern electronics and computer driven data acquisition allowed the collection of a larger amount of high quality data, thereby making possible a systematic investigation of the statistical properties of this phenomenon. A drawback to the inductive technique is that it is intrinsically unable to assign a precise spatial loca- tion to each pulse. Another limitation is the relatively low sensitivity of the inductive technique, which prevented its systematic application to thin films and magnetic mi- FIG. 1. Optical setup. The field generated with two coils in crostructures with only a few exceptions [11]. air is measured with a Hall probe (not shown). 0031-9007 00 84(23) 5415(4)$15.00 © 2000 The American Physical Society 5415 VOLUME 84, NUMBER 23 P H Y S I C A L R E V I E W L E T T E R S 5 JUNE 2000 plane of the film, and the loops have been measured with in-plane magnetization have been investigated. In par- the external field parallel to the sample surface. A selec- ticular, Ref. [15] describes sudden magnetization reversals tion of four loops, measured one after the other with a spot observed in the Kerr signal during magnetic relaxation. size of 100 mm, is shown in Fig. 2. The values of magne- From a series of 1000 loops, such as those shown in tization at saturation have been arbitrarily set equal to 250 Fig. 2, it is possible to extract the probability distribution and 50 (arbitrary units) and therefore the overall magneti- that a jump with a certain amplitude will occur. The am- zation reversal in a single loop is, by definition, equal to plitude DM of a single jump is simply defined, as shown 100. The most visible characteristic of these loops is the in Fig. 2. In a series of 1000 loops several thousand jumps presence of steps whose amplitude and field position ran- are observed and the histogram of their amplitudes can be domly fluctuate by repeating the cycle measurement: It drawn. This process has been repeated for different values is obvious to relate these jumps to the usual Barkhausen of the spot size, and the corresponding distributions are jumps. The presence of sudden magnetization reversals shown in Fig. 3. The vertical axis of each curve is simply has already been pointed out in magneto-optical experi- ments. In one of these works, BJ during domain wall motion in thin films with perpendicular anisotropy are described [14] and information is extracted on the spatial distribution of the wall pinning sites and their correspond- ing pinning times. In another paper [15] the wall dy- namics and the pinning mechanisms in thin Fe films with FIG. 2. A series of 4 loops taken in close succession at a FIG. 3. Statistical distributions of the jump amplitudes for dif- frequency of 1 Hz. ferent values of the spot size. 5416 VOLUME 84, NUMBER 23 P H Y S I C A L R E V I E W L E T T E R S 5 JUNE 2000 the histogram of the experimental data without any nor- malization. By reducing the spot size, and therefore the sampled area on the sample surface, the distribution ceases to be a smooth curve and sharp peaks appear. It is impor- tant to note that the statistical weight of the various dis- tributions in Fig. 3 is always the same and therefore the structures observed cannot be considered as a noise des- tined to be wiped out by increasing the number of loops in the series. These structures represent a true physical effect and this is more clearly observed in the lower part of Fig. 3, where the distribution for a spot size of 20 mm is shown. In this case the peaks are well separated and the distribution is truly equal to zero in between. For this reason the distribution has been drawn in a linear-log plot instead of the log-log plot of the other curves in Fig. 3. In order to explain the presence of sharp peaks in the amplitude distribution another related distribution must be taken into account, i.e., the probability distribution of the values assumed by magnetization in the flat portions of the loops and indicated by M in Fig. 2. When magneti- zation takes one of these values it remains nearly constant by changing the external field H until a new jump occurs. In other words, these particular values can be regarded as "stable" configurations of the systems, being stability de- fined as a relatively low sensibility to variations of the ex- ternal field. By considering the possible values taken by M in a series of 1000 loops with a spot size of 20 mm, the distribution shown in the upper part of Fig. 4 is observed. Also in this case sharp peaks are observed and this indi- cates that only a discrete number of magnetization values FIG. 4. Lower panel: probability distribution for a spot size are allowed during magnetization reversal within the area of 20 mm. Upper panel: probability distribution of M extracted sampled by the laser beam. This experimental observation from the same set of data. indicates that BJ are taking place between a discrete set of possible states characterized by a particular value of M. transition between two states, each identified by a particu- The physical origin of these states has to be found in the lar value of M. This correspondence will be investigated random distribution of magnetic pinning sites. This inter- in more detail in successive papers [16]. pretation is confirmed by repeating the same set of mea- Returning to the distributions of Fig. 3, it will now be surements with a spot diameter of 20 mm in a different considered how they can be assembled in a unique plot by location of the sample surface: The distribution is always rescaling the horizontal and the vertical axis in a simple peaked but the number, position, and relative intensity of way by taking into account only the spot size. In this the peaks randomly changes. In this energy landscape the way a distribution is obtained which spans over several system can only be found, during its magnetization re- decades such as those already published in literature and versal, in a numerable set of metastable states, and each obtained with the inductive technique [17]. Let us first individual jump corresponds to a transition between two consider the horizontal axis in two arbitrary distributions of these states. Within this picture jumps will occur only taken with two different spot sizes, D1 , D2. A jump between M values corresponding to the peaks in P M . DM1 in the first distribution represents the percentage vari- The correspondence between allowed M values and jump ation of magnetization within an area proportional to D21. amplitude is better understood by considering the lower The same percentage variation observed in the second dis- part of Fig. 4, where P DM is shown (this is the same tribution, where the sampled area is proportional to D21, curve as in the lower part of Fig. 3). The various peaks will correspond to a real magnetization variation larger are labeled with letters and their DM value is indicated. by a factor R D22 D21. This correction factor, sim- The transitions from which these peaks are generated are ply representing the ratio of the sampled area, must be shown in the upper part of Fig. 4 and labeled with the same applied to the various distributions. More precisely, the letters used for the peaks. Clearly, all of the peaks in the horizontal coordinates must be multiplied times R. On the amplitude distribution have a counterpart in the magnetiza- other hand, let us consider the vertical axis. The number tion distribution and each of them can be associated with a of jumps occurring within a certain area of the sample is 5417 VOLUME 84, NUMBER 23 P H Y S I C A L R E V I E W L E T T E R S 5 JUNE 2000 [1] H. Barkhausen, Z. Phys. 20, 401 (1919). [2] S. Field, J. Witt, F. Nori, and Xinsheng Ling, Phys. Rev. Lett. 74, 1206 (1995). [3] S. Zapperi, A. Vespignani, and H. E. Stanley, Nature (Lon- don) 388, 658 (1997). [4] J. M. Carlson and J. S. Langer, Phys. Rev. Lett. 62, 2632 (1989). [5] T. Bellini, N. A. Clark, C. D. Muzny, Wu Lei, C. W. Garland, D. W. Schaefer, and B. J. Oliver, Phys. Rev. Lett. 69, 788 (1992). [6] S. Zapperi, P. Cizeau, G. Durin, and H. E. Stanley, Phys. Rev. B 58, 6353 (1998). [7] D, Spasojevic´, S. Bikvic´, S. Milo sevic´, and H. E. Stanley, Phys. Rev. E 54, 2531 (1996). FIG. 5. Overall distribution of the jump amplitudes. This [8] J. S. Urbach, R. C. Madison, and J. T. Markert, Phys. Rev. curve is obtained from the data of Fig. 3 by rescaling both the Lett. 75, 276 (1995); J. S. Urbach, R. C. Madison, and horizontal and the vertical axis (see text). J. T. Markert, Phys. Rev. Lett. 75, 4694 (1995). [9] K. P. O'Brien and M. B. Weissman, Phys. Rev. E 50, 3446 proportional to the area itself. This trivial observation ne- (1994). cessitates that one must correct the probability distribution, [10] P. J. Cote and L. V. Meisel, Phys. Rev. Lett. 67, 1334 actually extracted from the experimental data by making a (1991). frequency count, by the same ratio used for the horizontal [11] N. J. Wiegman, Appl. Phys. 12, 157 (1977); N. J. Wiegman axis. In this case, R must divide the vertical coordinates and R. ter Stege, Appl. Phys. 16, 167 (1978); R. ter Stege of each distribution. and N. J. Wiegman, J. Phys. E 11, 791 (1978). [12] The laser beam is Gaussian and the spot size is defined The final result of this rescaling is shown in Fig. 5. as the FWHM of the intensity profile. Since the beam Here The different distributions of Fig. 3 are now plotted impinges on the sample at 45± as shown in Fig. 1, the spot in a single diagram. The normalization according to the on the beam is nearly elliptical with a major axis larger, above discussion has been performed by arbitrarily assum- with respect to the beam size, by a 1.414 factor. ing D1 1 for the distribution measured with a spot size [13] R. Bertacco, S. De Rossi, and F. Ciccacci, J. Vac. Sci. of 20 mm. The resulting distribution is equivalent to the Technol. A 16, 2277 (1998). other already published, where the peak amplitude is de- [14] S. Gadetsky and M. Mansuripur, J. Appl. Phys. 79, 5667 fined as the integral over time of the pulse shape measured (1996). with the inductive pickup coil. The normalization opera- [15] R. P. Cowburn, J. Ferré, S. J. Gray, and J. A. C. Bland, tion, based only on the spot size without any attempt to fit Phys. Rev. B 58, 11 507 (1998). the various data, brings a series of curves whose envelope, [16] Also the saturation region of the loop is flat but this can- not be regarded as a metastable state of the system in in the log-log plot, defines a rather well-defined straight the sense used here. For this reason the data shown in line whose linearity spans over several decades. The as- Fig. 4 have been filtered in order to eliminate all of those sociated power law P DM DM2a is best fitted with jumps starting or ending in a saturated state. This point a 1.1 6 0.05. Data taken with the inductive technique must be stressed, otherwise some paradox will emerge from ribbon shaped samples with a thickness of more than from Fig. 4. For instance, the magnetization state cor- 10 mm indicate a value of the coefficient ranging from 1.3 responding to M 211 would trap the system indefi- [6,8] to 1.77 [7]. The only available thin film data [11] in- nitely since no jumps are starting from there. In reality, dicate that NiFe with a thickness comparable to our sample from this state, jumps reaching M 50 (saturation) are follows a power law with a around 1.6. In the future it will observed. be interesting to verify if the existing models, successfully [17] Since the laser spot has a Gaussian profile, a magnetic re- applied to bulk samples, can be modified for two-dimen- versal having a real value DMr (in magnetic units) will produce a measured value DM dependent on the location sional systems in order to explain the experimental data of this reversal on the sample surface. This effect will described here. produce a distortion in the probability distribution P DM . I kindly acknowledge Stefano Zapperi and Gianfranco For this reason the shape of each individual distribution Durin for helpful discussions, and Stefano De Rossi for of Fig. 3 is not discussed in detail in this paper. Here the sample preparation. discussion is based on the overall distribution obtained by considering the envelope of the various curves of Fig. 3 and shown in Fig. 5. This approach allows one to ne- glect the distortion effect related to the Gaussian profile of *Email address: ezio.puppin@polimi.it the beam. 5418