NSTITUTE OF HYSICS UBLISHING OURNAL OF HYSICS D A PPLIED HYSICS J

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Phys D Appl Phys 34 2001 4853 wwwioporgJournalsjd PII S0022372701149752 Anomalous behaviour of minor magnetic hysteresis loops in garnet 64257lms GV ertesy and A Magni Hungarian Academy of Sciences Research Institute for Technical Physics and Materi ID: 29029 Download Pdf

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NSTITUTE OF HYSICS UBLISHING OURNAL OF HYSICS D A PPLIED HYSICS J

Phys D Appl Phys 34 2001 4853 wwwioporgJournalsjd PII S0022372701149752 Anomalous behaviour of minor magnetic hysteresis loops in garnet 64257lms GV ertesy and A Magni Hungarian Academy of Sciences Research Institute for Technical Physics and Materi

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NSTITUTE OF HYSICS UBLISHING OURNAL OF HYSICS D: A PPLIED HYSICS J. Phys. D: Appl. Phys. 34 (2001) 48–53 www.iop.org/Journals/jd PII: S0022-3727(01)14975-2 Anomalous behaviour of minor magnetic hysteresis loops in garnet films GV ertesy and A Magni Hungarian Academy of Sciences, Research Institute for Technical Physics and Materials Science, H-1525 Budapest, PO Box 49, Hungary IEN Galileo Ferraris, Corso M. d’Azeglio 42, I-10125 Torino, Italy E-mail: vertesyg@mfa.kfki.hu Received 27 June 2000 Abstract The widths of the minor hysteresis loops were investigated in

epitaxially grown uniaxial magnetic garnet films as a function of the maximal magnetic field at the end of the loops. An anomalous behaviour of the minor loops was observed in several samples: the width of a minor loop decreased with increasing maximal field. The phenomenon was interpreted on the basis of domain wall nucleation. Different coercive fields (the domain wall coercive field, cw , and the technical coercive field, ct ) and their relation were also discussed. 1. Introduction Coercive properties of materials are commonly considered to be one of the

most important parameters in applied magnetism. The coercive field—which is in close correlation to the hysteresis losses of the material—is determined from the width of the hysteresis loop. The technical coercivity, ct , is defined as the external magnetic field necessary to reduce the total magnetic moment of the sample to zero after having been previously saturated. ct is the half-width of the saturation- to-saturation or major hysteresis loop. It was shown [1] that another characteristic coercive parameter, the domain wall coercive field cw , could also be

determined from reproducible and well defined small minor hysteresis loops. The coercivity determined from the major hysteresis loop was found to be significantly higher than the domain wall coercivity [2]. This agrees very well with the usual experience on the great majority of magnetic materials, i.e. the width of the major hysteresis loop is larger than that any of the minor loops. However, in certain cases, measuring epitaxially grown magnetic garnet films—in contrast to the regular and expected case—the minor hysteresis loops were found to be wider than the major loop

[3]. The aim of the present work is to continue these investigations and to study the connection between the widths of series of minor loops obtained with increasing value of a magnetic field at the end of the minor loops. Epitaxial magnetic garnet films were chosen for the investigations. These films belong to the most perfect single- crystalline materials, as their growth by liquid-phase epitaxy (LPE) technology and the control of their magnetic properties are very well established processes. Due to the growing conditions they exhibit large uniaxial anisotropy which is

perpendicular to the film plane. The magnetization vector inside all domains is aligned perpendicular to the film plane and the domain structure is the well known stripe domain structure, with 180 Bloch domain walls. 2. Experimental details The epitaxial magnetic garnet films that were chosen for the investigations were grown on a (111) oriented gadolinium gallium garnet (GGG) substrate by LPE from a traditional PbO–B melt-solution system [4, 5]. We investigated three different samples, A, B and C, which show a variety of loop properties. Two of them (A and B) have the same

nominal chemical composition: 92 Sm Ca 98 Fe 02 Ge 98 12 . The nominal composition of sample C is Y 03 Ca 97 Fe 03 ,Ge 85 ,Co 12 12 . In spite of the fact that samples A and B have the same chemical composition, their magnetic parameters are different, which is a result of the differences in the growth parameters used during the growth of the samples. Sample A represents the standard garnet samples; its behaviour is typical to the great the majority of samples, while samples B and C are more anomalous. Two pieces of sample B, a large one (about 2000 mm ) and a small one (40 mm ), were

measured. (The sizes of the samples A and C were about the same, approximately 60 mm .) Square samples were measured. The measurements were performed in the middle of the samples, the measured area of the film being a circle of about 3 mm in diameter. The dc bias field for magnetizing the sample was produced by a Helmholtz pair of solenoids. The Helmholtz coils were 0022-3727/01/010048+06$30.00  2001 IOP Publishing Ltd Printed in the UK 48
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Anomalous behaviour of minor hysteresis loops (a) -1000 -500 0 500 1000 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 M / M H

[A/m] (b) Figure 1. Major and minor hysteresis loops of sample A (the minor loops are very narrow and they are inside the major loop, so they are not available in (a)). (b) shows the magni ed central part of (a). able to produce a eld perpendicular to the sample, with max 10 Am . The homogeneity of the eld was better than 98% in the middle of the coil system (about 30 mm 2 mm in volume). The uniformity of the applied magnetic eld was also experimentally checked. An optical interference method was used for the determination of the lms thicknesses. The zero eld stripe domain period was measured

in a polarizing microscope. The saturation magnetization and the uniaxial anisotropy eld were measured in a vibrating sample magnetometer, PAR model 155. The magnetic contribution of the paramagnetic GGG substrate was always subtracted from the measured magnetic moment. The saturation magnetization, ,was determined from the saturation-to-saturation hysteresis loops measured with the external eld applied along the easy axis, i.e. perpendicular to the surface of the lm. The uniaxial anisotropy eld, , was determined from the saturation-to- saturation hysteresis loops measured with the external

eld applied normal to the easy axis, i.e. in the plane of the sample. A magneto-optical set-up utilizing the Faraday effect was used for measuring the hysteresis loops. A halogen lamp was the light source, the light beam passed through a polarizer; it was focused onto the sample surface and perpendicularly traversed the sample. The light beam then went through, in sequence, the objective, a second polarizer, the ocular and a photodiode. The signal reported by the photodiode is proportional to the light intensity, which is linked to the sample magnetization. This is due to the fact that,

although the Faraday rotation depends upon the wavelength of the light, in white light one can, nevertheless, correlate changes in magnetization with light variations. As shown for example in [6], a relationship exists between the light intensity and the corresponding sample relative magnetization M/M , depending upon two factors: the angle ( π/ ) between the analyser and the polarizer and the total Faraday rotation of the sample .As it is often dif cult to know, with any great precision, the values of and , it is possible to derive a relationship for M/M f(L ,L ,L , where and are the 49


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GV ertesy and A Magni Table 1. Measured parameters of the samples. ( is the lm thickness, is the saturation magnetization, is the uniaxial anisotropy eld and is the zero eld stripe domain period.) Sample m) (mT) (A m m) A 8.4 16.2 64 000 13.0 B 12.6 5.2 233 500 165.0 C 11.8 16.3 140 400 56.0 light intensities at the positive saturation, negative saturation and remanence, respectively. On our optical bench this relationship is automatically applied, the result being the loop H(A/m), M(T) , where is obtained by M/M and the knowledge of by vibrating scanning magnetometry (VSM)

measurements. The widths of the hysteresis loops were determined from the measured loops. For the characterization of the width of the actual loop, the half-widths of the loops measured around zero external eld were used. The minor loops were always recorded after the demagnetization of the sample by a perpendicular ac magnetic eld with its amplitude decreasing to zero. This procedure was to ensure that we always started from the domain structure with the lowest energy: the anhysteretic equilibrium period, can be determined with an accuracy of 30 A m . The widths of the minor hysteresis loops

were investigated by increasing the eld loop by loop as a function of the maximum external applied eld at the end of the loop ( peak ). The rst minor loop, starting from the equilibrium, demagnetized state is the beginning of the initial magnetization curve. The uniformity of the magnetic properties of the lms used which is a crucial question for the interpretation of the results, because measurements were performed on different pieces cut from the same wafer were carefully checked. The basic magnetic parameters (saturation magnetization, uniaxial anisotropy, stripe domain width, domain wall

coercive eld) were measured at different positions of the wafer and the scatter of the magnetic parameters as a function of the different positions of the wafer were never found to be larger than a few per cent. 3. Results The measured parameters of the investigated samples are given in table 1. The saturation-to-saturation hysteresis loop measured on sample A is shown in gure 1, together with the minor hysteresis loops (in the middle of the curve). The widths of minor loops are smaller than that of the major loop; however, in the gure where the whole major loop is shown gure 1(a)), this is

not clear because of the narrow loops. Figure 1(b) shows the central area of gure 1(a), where the above-mentioned correlation can be easily recognized. Sample C and the large piece of sample B show anomalous behaviour from the point of view of the ratio of the widths of the major and minor hysteresis loops. The minor hysteresis loops, measured around the zero net magnetization, are de nitely wider than the major loop at M/M 0. The hysteresis loops of samples B and C are shown in gures 2 and 3, respectively. A series of minor loops were recorded, with increasing external magnetic eld. The

widths of the minor hysteresis Figure 2. Major and minor hysteresis loops of sample B, measured on the large piece of the specimen. Figure 3. Major and minor hysteresis loops of sample C. loops ( ) were determined by increasing the eld loop by loop, as a function of the maximum external applied eld at the end of the actual loop ( peak ). The results can be seen for the three samples in gures 4 6. The case illustrated in gure 4 can be considered to be the typical behaviour of loops, which can usually be measured on regular samples. In this case (H )>H (H if >H , for external eld values less

than 40 000 A m . Over this value the width of the loops goes to saturation. Obviously, in this case ct >H cw . (In this work the term is generally used for characterizing the widths of the hysteresis loops. At the initial range of the external eld, where the domain wall movement is reversible, cw .At very high elds, where is going to saturation, ct .) Samples B and C show irregular behaviour over a wide range of magnetic eld: the widths of the loops decreases with increasing peak (H ) (H if >H . After reaching a critical value of the eld, however, the widths of the loops suddenly increase,

and a large eld is necessary to maximize the widths of the loops. The saturation value of in such cases seems to have the same value as that of at small elds, so that ct cw The hysteresis measurements were also performed on the small piece of sample B. The results are shown in gures 7 and 8. It is seen that the correlation of the widths of the minor and major loops was reversed by cutting the sample, and the (H peak function also became different; it became similar 50
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Anomalous behaviour of minor hysteresis loops Figure 4. The width of minor loops as a function of the maximal

eld, peak , at the end of the loop, measured on sample A. (The broken line indicates the apparent value of the saturating eld.) 0 1000 2000 3000 4000 20 40 60 80 100 120 140 [A/m] peak [A/m] Figure 5. The width of minor loops as a function of the maximal eld, peak , at the end of the loop, measured on a large piece of sample B. (The broken line indicates the apparent value of the saturating eld.) Figure 6. The width of minor loops, as a function of the maximal eld, peak , at the end of the loop, measured on sample C. (The broken line indicates the apparent value of the saturating eld.) to the

regular case. The value of cw is the same in both the large and small pieces of the sample ( cw 135Am ), while Figure 7. Major and minor hysteresis loops of sample B, measured on a small piece of the specimen. 0 1000 2000 3000 4000 50 100 150 200 250 300 [A/m] peak [A/m] Figure 8. The width of minor loops as a function of the maximal eld, peak , at the end of the loop, measured on a small piece of sample B. (The broken line indicates the apparent value of the saturating eld.) there is a signi cant difference in the value of ct (310 A m for the small piece and 135 A m for the large piece). 4.

Discussion From measuring the magnetic hysteresis loops two characteris- tic parameters can be determined from the widths of the loops, each characterizing different properties of the measured spec- imen. One of them, the so-called coercive force, or technical coercivity ( ct ), i.e. the width of the saturation-to-saturation hysteresis loop, is one of the most frequently used parameters for the characterization of magnetic materials. However, as is seen from the experiments, it is not easy to determine its correct value. The magnetization of the samples seems to be saturated at relatively low

values of the external eld: the mag- netic moment of the sample no longer increases with increas- ing eld. This can be seen very well in gures 1(a), 2 and 3. This apparent saturation is observed not only by magneto-optic measurements; measuring the same samples by methods other than magneto-optics, for example by VSM, the same apparent saturation is obtained. The value of this apparent saturation is indicated by the vertical, broken lines in gures 4 6 and 8. The 51
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GV ertesy and A Magni observation of the domain structure reveals a saturated single- domain structure above this

value of the external normal eld. The explanation of this phenomenon, i.e. why does change so much if the sample is saturated, cannot be given on the ba- sis of the available data. The reason could be the existence of too small, invisible, reversed domains, or a not exactly perpen- dicular magnetization, which slowly rotates towards the exact perpendicular. As it is seen in gures 4 6, the value of depends signi cantly on the value of the saturating eld, and rather a high value of the external eld is necessary to saturate If we want to obtain a characteristic value of ct ,wehaveto nd the

saturation of the (H peak function. This also shows that the use of the terms minor and major loops in the above considerations is not de nite. From this point of view the loops which were called the major loops in gures 1 3 are not the real saturation-to-saturation loops. The other characteristic parameter of a hysteresis loop is the domain wall coercive eld, cw , which characterizes the interaction between the translating domain walls and the actual structure of the material [2, 7, 8]. It is de ned as the minimum mean external magnetic eld necessary to irreversibly move the walls in the

sample. This parameter properly describes the interaction between the moving domain walls and material defect structure, and for a given sample it is a very stable quantity. However, cw can be measured only in certain cases, where the change of magnetization takes place only by domain wall displacement. Uniaxial epitaxial magnetic garnets are a very good model material in which to study this parameter. ct is the most important parameter in technical applications, but it is generally dif cult to nd its direct link with the individual micromagnetic processes which take place in the material

during the complete change of the magnetic state of the sample. These processes can include the rotation of the vector of magnetization, the nucleation of magnetic domains and the translation of domain walls within the bulk of the material. Usually ct is larger than cw and wider and wider hysteresis loops are measured if the external eld is increasing. This is generally well known and can be found in basic handbooks dealing with magnetic phenomena. The same general relationship was previously also found in the case of epitaxial magnetic garnet lms, when systematically investigating and

comparing the results of different methods for coercivity measurement [2]. It was also experienced for the regular garnet sample of the present work (see gure 4). However, in certain cases, which are represented by samples B and C, the opposite relationship can exist between the hysteresis loops (see gures 2 and 3). The cw >H relationship was reproducibly found on these samples over a wide range of the external magnetic eld. The reason could originate in the extraordinary magnetic parameters of these samples, compared with the standard samples (see table 1). It is thought that the shape of the

major hysteresis loop is determined mainly in the epitaxially grown magnetic garnet lms by the domain wall nucleation. The saturation magnetization of samples B and C is small, compared with the uniaxial anisotropy eld. The nucleation of the domain walls is dif cult in the previously saturated sample because the nucleation is poorly assisted by the low value of the saturation magnetization (low value of the demagnetization energy) and at the same time it is strongly opposed by the large value of the domain wall energy density, (AK where is the exchange constant and is the uniaxial anisotropy

constant. If a thin lm of thickness is considered, with a large uniaxial anisotropy perpendicular to the lm plane, the nucleation eld can be expressed by the following formula, by applying the dipolar-random eld Ising model to the garnet lms [9]. Here is the cell size of the magnetically saturated area and the magnetic moment of a single cell is hI / DW (1) The difference in the parenthesis of the nucleation eld formula has been shown as an important parameter in [7]. It has been veri ed that for non-standard samples (such as B and C) w> 0, while w< 0 for standard samples. depends just on

physical quantities, while is the lattice cell size we choose. The nucleation eld goes to zero with from negative values (standard) or from positive values (non-standard). It was also shown that ct (or , where is the width of the hysteresis loops between the low and large external eld regions) and cw can be modi ed independently. In an irregular sample (sample B) the originally existing /H cw 1 relationship can be reversed into /H cw 1 by cutting the sample into a small piece. The modi cation of the size of the sample has no in uence on any basic magnetic material parameter, which determines

the behaviour of the domain walls through the domain wall energy density and domain wall thickness. Cutting of the sample into smaller pieces also has no in uence on the originally existing defect structure of the material. Because of this, no change in cw can be expected due to cutting a sample, in good agreement with the experiments. On the other hand, the nucleation of the domain wall becomes even more dif cult if the sample size is decreased, because of the change of the demagnetizing eld. The magnetostatic term in the expression of , see for example [10], eff (2) makes it clear that

magnetostatic effects give a signi cant contribution to the coercivity. (Here is a phenomenological parameter and eff is the effective demagnetizing factor.) This is the reason why the modi cation of the demagnetizing eld by cutting the sample can have such a large in uence on the actual value ct Starting from the demagnetized state and measuring the minor loops at higher and higher maximum elds, an increasing value of the width of minor loops was found in the case of the standard sample ( gure 4). This relationship is typical for the great majority of magnetic materials. In the non-regular

samples an anomalous, opposite dependence was found: the width of minor loops decrease if the eld was increasing ( gures 5 and 6). This anomalous (H peak dependence correlates very well with the previously observed anomalous relation between the widths of minor and major 52
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Anomalous behaviour of minor hysteresis loops loops, and the slope of the (H peak function can be turned from negative to positive even in the same sample by reducing its size (sample B). The reason of this phenomenon could also originate in the extraordinary magnetic parameters of these samples, compared

with the standard samples, as discussed above. 5. Conclusions The widths of the series of hysteresis loops were investigated in epitaxially grown uniaxial magnetic garnet lms. It was shown that in certain, anomalous, cases the minor loops become narrower and narrower as the maximal value of the external, normal magnetic eld is increased to a critical value of the eld. This behaviour was observed in garnet lms with extraordinary high uniaxial anisotropy and low saturation magnetization, and it was interpreted on the base of the domain nucleation. The results revealed the different characters of

the macroscopic coercive eld, determined from the saturation loop, and of the domain wall coercive eld, determined from minor loops, close to zero magnetization. ct was found rather to be a sample parameter while cw was a material parameter. ct depends very much on the actual size of the sample and it also depends on the magnetic prehistory of the sample. The regular samples are characterized by the cw ct relationship, while in anomalous samples cw ct . The ratio of the widths of the major and minor loops, as well as the slope of the (H peak function can be reversed within the same sample by

cutting the sample into smaller pieces. The high sensitivity of the widths of the hysteresis loops on the maximal value of the magnetic eld was also shown. Unexpectedly large values of the magnetic eld are necessary to saturate the widths of the hysteresis loops. This result can be important for determining the exact value of ct in the materials, and, on the other hand, calls attention to the need for exact terminology, i.e. what can be called a major loop. Acknowledgments The authors are indebted to the Magnetic Department of Institute of Physics (Prague), Academy of Sciences of the Czech

Republic, for the opportunity to use VSM for the measurements. The work was partially supported by Hungarian Scienti c Research Fund (T-026153). References [1] V ertesy G, Pust L, Tom s I and Pa ces J 1991 J. Phys. D: Appl. Phys. 24 1482 [2] V ertesy G, Pardavi-Horv ath M, B odis L and Pint er I 1988 J. Magn. Magn. Mater. 75 389 [3] V ertesy G and Magni A 2000 Physica 275 133 [4] Gies s E A 1975 J. Cryst. Growth. 31 358 [5] G ornert P, Hergt R, Sinn E, Wendt M, Keszei B and Vandlik J 1988 J. Cryst. Growth 87 331 [6] Tom sI, Siroky P, Gemperle R and V ertesy G 1986 J. Magn. Magn. Mater. 58 347

[7] Krause H, Theile J, Dahlbeck R and Engemann J 1991 J. Magn. Magn. Mater. 95 95 [8] Grigorenko A N, Mishi n S A and Rudashevski i E G 1988 Fiz. Tver. Tela 30 2948 [9] Magni A and V ertesy G 2000 Phys. Rev. 61 3203 [10] Bertotti G 1998 Hysteresis in Magnetism (New York: Academic) 53