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Key role in giant magnetoresistance of granular films: Single-domain ferromagnetic granules
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 305 (2006) 310–314 www.elsevier.com/locate/jmmm
Key role in giant magnetoresistance of granular films: Single-domain ferromagnetic granules Changzheng Wanga,, Yonghua Rongb, T.Y. Hsu (Xu Zuyao)b a
b
Department of Physics, Liaocheng University, Liaocheng City, 252059 Shandong Province, PR China School of Materials Science and Engineering, Shanghai Jiaotong University, Shanghai, 200030, PR China Received 18 June 2005 Available online 2 February 2006
Abstract The challenging problem on what kind of ferromagnetic granules plays a key role in giant magnetoresistance (GMR) was investigated. By analyzing the hysteresis curves and GMR of FeCo–Al2O3 films with different volume fraction of granules, we found that only the change of the fraction of single-domain granules over total ferromagnetic granules with the volume fraction of FeCo granules in FeCo–Al2O3 film is in agreement with that of GMR. This verifies the key role of single-domain granule in GMR. And it was also confirmed by our annealing experiments. However, the hysteresis curve of FeCo–Al2O3 film with low FeCo content exhibits superparamagnetic characteristic when it is measured at room temperature, which is attributed to the fact that the fraction of superparamagnetic granules is in majority. r 2006 Elsevier B.V. All rights reserved. PACS: 72.15.Gd; 75.47.m; 75.70.Cn Keywords: Giant magnetoresistance; Granular films; Single-domain ferromagnetic granules
1. Introduction Giant magnetoresistance (GMR) effect has been extensively investigated since it was discovered in Fe/Cr multilayers films in 1988 [1] and then in ferromagnetic metal–metal [2,3] and ferromagnetic metal–insulator granular films [4,5]. In granular films, all the granules can be divided into three categories by two critical sizes [6]: superparamagnetic, single-domain ferromagnetic and multi-domain ferromagnetic granules. Therefore, the problem on what kind of ferromagnetic granules play a key role in GMR strongly attracts investigators’ attention. Two important experiments supported the key role of superparamagnetic granules in GMR are that the hysteresis curve of granular films can be well described by Langivien function [3–5] and GMR is directly proportional to the reduced magnetization square based on superparamagnetic granules [2]. Nevertheless, our theories [7,8] verify the key Corresponding author. Tel.: +86 635 8258335; fax: +86 635 8231207.
E-mail address: [email protected] (C. Wang). 0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.01.016
role of single-domain granule in GMR, and are well consistent with experiments reported in literatures, including the dependence of GMR on the applied field, measuring temperature, the volume fraction of ferromagnetic granules or the granular size. Solving such a challenging problem will be the objective of the present investigation. In this paper we measured the dependence of GMR on the volume fraction of granules in FeCo–Al2O3 films, and further determined the size distribution of ferromagnetic granules in films with the largest GMR by transmission electron microscopy (TEM), which was verified to satisfy the log–normal distribution function. In addition, the hysteresis curves of films with various volume fractions were measured and were made a fitting by modification of Stearns’ equation [9]. By means of fitting the change of the fraction of a superparamagnetic, a singledomain or a multi-domain granules over total granules with the volume fraction of granules was obtained. Comparing the dependence of GMR on the volume fraction of granules with fitting result it indicates that only the change of fraction of single-domain granules with the
ARTICLE IN PRESS C. Wang et al. / Journal of Magnetism and Magnetic Materials 305 (2006) 310–314
volume fraction of FeCo granules are the same tendency as that of GMR, which reveals that single-domain granules play a key role in GMR. Moreover, the above conclusion was confirmed by our annealing experiments. In addition, the origin of the hysteresis curves of films with superparamagnetic feature was reasonably explained.
7 6 5 GMR(%)
2. Experimental procedure All granular films were deposited on the substrate of glass (for GMR and magnetic measurements) or KCl (for TEM observation) with magnetron-controlled sputtering method. The volume fraction of granules in films was controlled by changing the sputtering power of target (FeCo, Al2O3) and was determined by means of energydispersive spectrum attached to scanning electron microscope. The film thickness was measured as about 300 nm by a a-step meter and all annealed samples were sealed in quartz tube filled with Ar gas. GMR was measured through conventional four probes method at room temperature in fields up to 12.5 K Oe and the magnetic property was measured with vibrated sample magnetometer (VSM) whose maximum field is 10 K Oe. 3. Results and discussion Fig. 1 shows the dependence of GMR on the volume fraction of granules in FeCo–Al2O3 films. It can be seen that GMR first increases and then decreases, reaching a maximum of 6.7% at about 32.8 vol% FeCo. In order to clarify what kinds of granules play a key role in GMR, it is vital to know the size distribution of granules. Figs. 2(a) and (b) show the dark field image using TEM and corresponding size distribution of magnetic granules in as-deposited FeCo (32.8 vol%)–Al2O3 films. It can be found that the size distribution of granules evaluated from dark field image satisfied approximately with log–normal function [7]. According to Refs.[7,8], the fraction of superparamagnetic, single-domain or multi-domain granules over total ones can be calculated as 65.7%, 31.6% or 2.7%, respectively. In addition, we will fit the hysteresis curves of FeCo–Al2O3 films to obtain the variation of three kinds of magnetic granules with the volume fraction of FeCo granules. Stearns [9] divided all magnetic granules in films into two categories: superparamagnetic and ferromagnetic granules and made a excellent fitting to the hysteresis curve with following formula " 1 # mH mH 2M SF pS ¯ ¯ 1 ðH H C tan M T ðTÞ ¼ tan þ N g m¯ coth , kT kT p HC 2
(1) where the first term is a function used to represent a ferromagnetic hysteresis curve. The second term is the usual expression for superparamagnetic component. M SF and M SSP ¼ N g m¯ are the saturated magnetization of the
311
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30
40
50 60 volume fraction (%)
70
80
Fig. 1. The dependence of GMR on the volume fraction of granules for FeCo–Al2O3 films. The solid lines are guides to the eyes.
ferromagnetic and superparamagnetic granules, respectively. S is the squareness of the ferromagnetic loop, i.e. the ratio of the remanent magnetization, MR, toM SF . m¯ and N g are the average moment per granule and the number of granule/cm3 in the superparamagnetic granules, respectively. On the other hand, Xu et al. [10] considered that the ferromagnetic granules could reach saturation easily when the applied field is larger than 1 T, therefore, the magnetization of ferromagnetic granules was assumed as a constant, M 0FM , and used following formula to make a fitting to the hysteresis curve of films when the applied field is larger than 1 T [10] 0 M ¼ M 0SP LðmH=k ¯ B TÞ þ M FM ,
(2)
where M 0SP and M 0FM are the saturated magnetization of the superparamagnetic and ferromagnetic components. By comparing Eq. (1) with Eq. (2), it is clear that the difference is only the expression of ferromagnetic component. Considering all granules in a given film can be divided into three categories [6], we assume that the hysteresis curve can be made a fitting with a function made up of superparamagnetic, single-domain and multi-domain components 2M SSF pS 1 H H C M T ðTÞ ¼ tan tan 2 p HC " 1 # mH mH ¯ ¯ þ N g m¯ coth ð3Þ M SMF , kT kT where M SSF and M SDF are the magnetization of singledomain and multi-domain component, respectively. Here, the magnetization of multi-domain component is also assumed as a constant according to Xu’s viewpoints [10]. According to Eq. (3), we made fittings to the hysteresis curves for a series of FeCo–Al2O3 films deposited at room
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Fig. 2. (a) Dark field image and (b) The size distribution of magnetic granules in as–deposited FeCo(32.8 vol%)–Al2O3 films The solid lines stands for log–normal curve.
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Fig. 3. Hysteresis curves and their corresponding fitting results for various volume fraction in FeCo–Al2O3 films: (a) 25.8%, (b) 32.8%, (c) 42.3%, and (d) the changes of fractions for three magnetic granule parts in various FeCo–Al2O3 films. Solid squares: experimental data; curve 1: calculated total magnetic granules; curve 2: calculated superparamagnetic granules; curve 3: calculated single-domain granules; curve 4: calculated multi-domain granules.
temperature. Figs. 3(a–c) are the hysteresis curves and their corresponding fittings of films with the volume fraction 25.8%, 32.8%, 42.3% of FeCo granules using Eq. (3), respectively. Based on Stearns’ method [10] the fraction of superparamagnetic, single-domain or multi-domain granules over total ones was determined by M SSP =M ST , M SSF =M ST
or M SDF =M ST , respectively, where M ST ¼ M SSP þ M SSF þ M SDF . It is clear from fitting results that all granules in films are only composed of superparamagnetic and singledomain granules when the volume fraction of FeCo granules is low (such as 25.8% FeCo). With increasing the volume fraction of FeCo granules, as seen in Fig. 3(d),
ARTICLE IN PRESS C. Wang et al. / Journal of Magnetism and Magnetic Materials 305 (2006) 310–314
25.8% FeCo 32.8% FeCo 42.3% FeCo
6
GMR(%)
the fraction of superparamagnetic granule decreases monotonically, while the fraction of multi-domain increases monotonically. In contrast with both, the fraction of single-domain granules increases first and then decreases, reaching a maximum of 28.6% at 32.8 vol% FeCo. This changing tendency is in agreement with that of GMR with the volume fraction of granules in Fig. 1. This verifies the key role of single-domain granule in GMR, which supports our theoretical results [7,8]. As discussed in Refs. [7,8], if the volume fraction of FeCo granules in films is low, FeCo granule size will be small, leading to that most of FeCo granules behave as superparamagnetic nature unfavorable for GMR. With increasing the volume fraction of FeCo granules, FeCo granule size also increases, which results in that the fraction of superparamagnetic granules decreases and the fractions of single-domain and multidomain increases. When the fraction of single-domain granules reaches a maximum, the GMR of film will exhibit a maximum, as shown in Figs. 1 and 3(d). With further increasing the volume fraction of FeCo granules the granule size will increase, accordingly, most granules become multi-domain granules that have no effect on GMR [11] and result in the drop of GMR or even vanish of GMR. Annealing treatment can markedly change the sizes of granules accompanying the elevation of annealing temperature for a given film, accordingly, it can be expected that GMR of FeCo–Al2O3 film will exhibit peak value with the elevation of annealing temperature accompanying the volume fraction change of three kinds of ferromagnetic granules, which is verified by our experiments, as seen in Fig. 4. Moreover, it is clear that with increasing annealing temperature, the GMR of films with lower volume fraction reaches a peak value at certain annealing temperature. While for films with higher volume fraction, the GMR has almost no changes at first, and then decreases with increasing annealing temperature. This also can be explained according to above viewpoint that single-domain granules play a key role in GMR. For granular films with lower volume fraction, granule size is smaller and most granules exhibit superparamagnetic nature in as-deposited films, resulting in low GMR. With the elevation of annealing temperature, granules grow to be larger, resulting in the increase of volume fraction of single-domain granules, and then GMR improves. With further increasing annealing temperature, most granules can become multidomain ones, leading to the drop of GMR. While for films with higher volume fraction, since single-domain granules have reached a larger volume fraction in as-deposited films, during annealing, the granules will grow or connect so that partial granules become multi-domain ones, causing the monotonically decrease of the fraction of single-domain granules and then GMR. It is worthy to emphasize that the fraction (about 31.6%) of single-domain granules obtained by TEM observation approximately approaches to that (28.6%) by VSM measurement in FeCo(32.8 vol%)–Al2O3 films (correspond-
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Fig. 4. The dependence of longitudinal GMR effect on annealing temperature for FeCo–Al2O3 films with various volume fractions.
ing to the largest GMR), which indicate that the fractions of ferromagnetic granule determined indirectly by VSM are reliable. The measuring result indicates that the fraction of single-domain granules is far smaller than that (69.8%)of superparamagnetic granules in FeCo(32.8 vol%)–Al2O3 films, as a consequence, the hysteresis curve of the film exhibits the superparamagnetic nature. For as-deposited or annealing films, the fraction of single-domain granules exceeds hardly 50% because of the existence of the size distribution of granules in films, in other words, the superparamagnetic granules always occupy majority in the ferromagnetic granules in films. However, when the hysteresis curve of a granular film is measured under low temperature, the fraction of single-domain granules can predominate in ferromagnetic granules for this film although the size of every granule is unchanged. Based on the formulas of two critical sizes distinguishing three kinds of ferromagnetic granules [7,8], it can be found that with lowering measuring temperature, the fraction of singledomain granules increases. For example, the critical size of Co granules distinguishing superparamagnetic from singledomain granules decreases rapidly from 7.6 nm at room temperature to 1.8 nm at 4 K and the critical size of Fe granules does from 16 to 3.6 nm while the critical size distinguishing single domain from multi-domain granules has almost no change [7,8]. As a result, GMR significantly increases with lowering measuring temperature accompanying the increase of the fraction of single-domain granules, which is supported by some experiments [12,13]. This fact strongly confirms our conclusion on the key role of singledomain granules in GMR. Moreover, it can be deduced that for a given film the nature of its hysteresis curve will gradually transform from the superparamagnetic to singledomain characteristic (that is, the coercive force gradually increases) when the measuring temperature gradually lowers from room temperature to liquid helium temperature, which is verified by Wang et al’s experiment [14].
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4. Conclusions
References
In summary, using VSM method, we measured the hysteresis curves of films with various volume fractions of FeCo granules and made excellent fittings with a function made up of superparamagnetic, single-domain and multidomain components. The fitting results indicated that the change of the fraction of single-domain granules with the volume fraction of FeCo granules was in agreement with that of GMR of films, verifying that single-domain granules play a key role in GMR, which is confirmed by most experiments including the change of GMR with the volume fraction of granules, annealing temperature or measuring temperature.
[1] M.N. Baibich, J.M. Broto, A. Fert, et al., Phys. Rev. Lett. 61 (1988) 2472. [2] J.Q. Xiao, J.S. Jiang, C.L. Chien, Phys. Rev. Lett. 68 (1992) 3749. [3] S. Honda, M. Nawate, M. Tanaka, et al., J. Appl. Phys. 82 (1997) 764. [4] S. Honda, T. Okada, M. Nawate, Phys. Rev. B 56 (1997) 14566. [5] H. Fujimori, S. Mitati, S. Ohnuma, Mater. Sci. Eng. B 31 (1995) 219. [6] B.D. Cullity, Introduction to Magnetic Materials, Addison-Wesley, London, 1972, p. 383. [7] C.Z. Wang, Z.H. Guo, Y.H. Rong, T.Y. Hsu (Xu Zuyao), J. Magn. Magn. Mater. 277 (2004) 273. [8] C.Z. Wang, Z.H. Guo, Y.H. Rong, T.Y. Hsu (Xu Zuyao), Phys. Lett. A 329 (2004) 236. [9] M.B. Stearns, Y. Cheng, J. Appl. Phys. 75 (1994) 6894. [10] J. Xu, B.J. Hickey, M.A. Howson, et al., Phys. Rev. B 56 (1997) 14602. [11] A. Hu¨tten, J. Bernardi, C. Nelson, et al., Phys. Status. Solidi(a) 150 (1995) 171. [12] S. Mitani, S. Takahashi, K. Takanashi, et al., Phys. Rev. Lett. 81 (1998) 2799. [13] T. Zhu, Y.J. Wang, Phys. Rev. B 60 (1999) 11918. [14] J.-Q. Wang, G. Xiao, Phys. Rev. B 50 (1994) 3423.
Acknowledgments The present work is financially supported by the National Nature Science Foundation of China under Grant no. 50071033 and Hi-Tech Research and development Program of China under Grant no. 2004AA32G090.
Journal of Magnetism and Magnetic Materials 305 (2006) 310–314 www.elsevier.com/locate/jmmm
Key role in giant magnetoresistance of granular films: Single-domain ferromagnetic granules Changzheng Wanga,, Yonghua Rongb, T.Y. Hsu (Xu Zuyao)b a
b
Department of Physics, Liaocheng University, Liaocheng City, 252059 Shandong Province, PR China School of Materials Science and Engineering, Shanghai Jiaotong University, Shanghai, 200030, PR China Received 18 June 2005 Available online 2 February 2006
Abstract The challenging problem on what kind of ferromagnetic granules plays a key role in giant magnetoresistance (GMR) was investigated. By analyzing the hysteresis curves and GMR of FeCo–Al2O3 films with different volume fraction of granules, we found that only the change of the fraction of single-domain granules over total ferromagnetic granules with the volume fraction of FeCo granules in FeCo–Al2O3 film is in agreement with that of GMR. This verifies the key role of single-domain granule in GMR. And it was also confirmed by our annealing experiments. However, the hysteresis curve of FeCo–Al2O3 film with low FeCo content exhibits superparamagnetic characteristic when it is measured at room temperature, which is attributed to the fact that the fraction of superparamagnetic granules is in majority. r 2006 Elsevier B.V. All rights reserved. PACS: 72.15.Gd; 75.47.m; 75.70.Cn Keywords: Giant magnetoresistance; Granular films; Single-domain ferromagnetic granules
1. Introduction Giant magnetoresistance (GMR) effect has been extensively investigated since it was discovered in Fe/Cr multilayers films in 1988 [1] and then in ferromagnetic metal–metal [2,3] and ferromagnetic metal–insulator granular films [4,5]. In granular films, all the granules can be divided into three categories by two critical sizes [6]: superparamagnetic, single-domain ferromagnetic and multi-domain ferromagnetic granules. Therefore, the problem on what kind of ferromagnetic granules play a key role in GMR strongly attracts investigators’ attention. Two important experiments supported the key role of superparamagnetic granules in GMR are that the hysteresis curve of granular films can be well described by Langivien function [3–5] and GMR is directly proportional to the reduced magnetization square based on superparamagnetic granules [2]. Nevertheless, our theories [7,8] verify the key Corresponding author. Tel.: +86 635 8258335; fax: +86 635 8231207.
E-mail address: [email protected] (C. Wang). 0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.01.016
role of single-domain granule in GMR, and are well consistent with experiments reported in literatures, including the dependence of GMR on the applied field, measuring temperature, the volume fraction of ferromagnetic granules or the granular size. Solving such a challenging problem will be the objective of the present investigation. In this paper we measured the dependence of GMR on the volume fraction of granules in FeCo–Al2O3 films, and further determined the size distribution of ferromagnetic granules in films with the largest GMR by transmission electron microscopy (TEM), which was verified to satisfy the log–normal distribution function. In addition, the hysteresis curves of films with various volume fractions were measured and were made a fitting by modification of Stearns’ equation [9]. By means of fitting the change of the fraction of a superparamagnetic, a singledomain or a multi-domain granules over total granules with the volume fraction of granules was obtained. Comparing the dependence of GMR on the volume fraction of granules with fitting result it indicates that only the change of fraction of single-domain granules with the
ARTICLE IN PRESS C. Wang et al. / Journal of Magnetism and Magnetic Materials 305 (2006) 310–314
volume fraction of FeCo granules are the same tendency as that of GMR, which reveals that single-domain granules play a key role in GMR. Moreover, the above conclusion was confirmed by our annealing experiments. In addition, the origin of the hysteresis curves of films with superparamagnetic feature was reasonably explained.
7 6 5 GMR(%)
2. Experimental procedure All granular films were deposited on the substrate of glass (for GMR and magnetic measurements) or KCl (for TEM observation) with magnetron-controlled sputtering method. The volume fraction of granules in films was controlled by changing the sputtering power of target (FeCo, Al2O3) and was determined by means of energydispersive spectrum attached to scanning electron microscope. The film thickness was measured as about 300 nm by a a-step meter and all annealed samples were sealed in quartz tube filled with Ar gas. GMR was measured through conventional four probes method at room temperature in fields up to 12.5 K Oe and the magnetic property was measured with vibrated sample magnetometer (VSM) whose maximum field is 10 K Oe. 3. Results and discussion Fig. 1 shows the dependence of GMR on the volume fraction of granules in FeCo–Al2O3 films. It can be seen that GMR first increases and then decreases, reaching a maximum of 6.7% at about 32.8 vol% FeCo. In order to clarify what kinds of granules play a key role in GMR, it is vital to know the size distribution of granules. Figs. 2(a) and (b) show the dark field image using TEM and corresponding size distribution of magnetic granules in as-deposited FeCo (32.8 vol%)–Al2O3 films. It can be found that the size distribution of granules evaluated from dark field image satisfied approximately with log–normal function [7]. According to Refs.[7,8], the fraction of superparamagnetic, single-domain or multi-domain granules over total ones can be calculated as 65.7%, 31.6% or 2.7%, respectively. In addition, we will fit the hysteresis curves of FeCo–Al2O3 films to obtain the variation of three kinds of magnetic granules with the volume fraction of FeCo granules. Stearns [9] divided all magnetic granules in films into two categories: superparamagnetic and ferromagnetic granules and made a excellent fitting to the hysteresis curve with following formula " 1 # mH mH 2M SF pS ¯ ¯ 1 ðH H C tan M T ðTÞ ¼ tan þ N g m¯ coth , kT kT p HC 2
(1) where the first term is a function used to represent a ferromagnetic hysteresis curve. The second term is the usual expression for superparamagnetic component. M SF and M SSP ¼ N g m¯ are the saturated magnetization of the
311
4 3 2 1 0 -1 20
30
40
50 60 volume fraction (%)
70
80
Fig. 1. The dependence of GMR on the volume fraction of granules for FeCo–Al2O3 films. The solid lines are guides to the eyes.
ferromagnetic and superparamagnetic granules, respectively. S is the squareness of the ferromagnetic loop, i.e. the ratio of the remanent magnetization, MR, toM SF . m¯ and N g are the average moment per granule and the number of granule/cm3 in the superparamagnetic granules, respectively. On the other hand, Xu et al. [10] considered that the ferromagnetic granules could reach saturation easily when the applied field is larger than 1 T, therefore, the magnetization of ferromagnetic granules was assumed as a constant, M 0FM , and used following formula to make a fitting to the hysteresis curve of films when the applied field is larger than 1 T [10] 0 M ¼ M 0SP LðmH=k ¯ B TÞ þ M FM ,
(2)
where M 0SP and M 0FM are the saturated magnetization of the superparamagnetic and ferromagnetic components. By comparing Eq. (1) with Eq. (2), it is clear that the difference is only the expression of ferromagnetic component. Considering all granules in a given film can be divided into three categories [6], we assume that the hysteresis curve can be made a fitting with a function made up of superparamagnetic, single-domain and multi-domain components 2M SSF pS 1 H H C M T ðTÞ ¼ tan tan 2 p HC " 1 # mH mH ¯ ¯ þ N g m¯ coth ð3Þ M SMF , kT kT where M SSF and M SDF are the magnetization of singledomain and multi-domain component, respectively. Here, the magnetization of multi-domain component is also assumed as a constant according to Xu’s viewpoints [10]. According to Eq. (3), we made fittings to the hysteresis curves for a series of FeCo–Al2O3 films deposited at room
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Fig. 2. (a) Dark field image and (b) The size distribution of magnetic granules in as–deposited FeCo(32.8 vol%)–Al2O3 films The solid lines stands for log–normal curve.
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Fig. 3. Hysteresis curves and their corresponding fitting results for various volume fraction in FeCo–Al2O3 films: (a) 25.8%, (b) 32.8%, (c) 42.3%, and (d) the changes of fractions for three magnetic granule parts in various FeCo–Al2O3 films. Solid squares: experimental data; curve 1: calculated total magnetic granules; curve 2: calculated superparamagnetic granules; curve 3: calculated single-domain granules; curve 4: calculated multi-domain granules.
temperature. Figs. 3(a–c) are the hysteresis curves and their corresponding fittings of films with the volume fraction 25.8%, 32.8%, 42.3% of FeCo granules using Eq. (3), respectively. Based on Stearns’ method [10] the fraction of superparamagnetic, single-domain or multi-domain granules over total ones was determined by M SSP =M ST , M SSF =M ST
or M SDF =M ST , respectively, where M ST ¼ M SSP þ M SSF þ M SDF . It is clear from fitting results that all granules in films are only composed of superparamagnetic and singledomain granules when the volume fraction of FeCo granules is low (such as 25.8% FeCo). With increasing the volume fraction of FeCo granules, as seen in Fig. 3(d),
ARTICLE IN PRESS C. Wang et al. / Journal of Magnetism and Magnetic Materials 305 (2006) 310–314
25.8% FeCo 32.8% FeCo 42.3% FeCo
6
GMR(%)
the fraction of superparamagnetic granule decreases monotonically, while the fraction of multi-domain increases monotonically. In contrast with both, the fraction of single-domain granules increases first and then decreases, reaching a maximum of 28.6% at 32.8 vol% FeCo. This changing tendency is in agreement with that of GMR with the volume fraction of granules in Fig. 1. This verifies the key role of single-domain granule in GMR, which supports our theoretical results [7,8]. As discussed in Refs. [7,8], if the volume fraction of FeCo granules in films is low, FeCo granule size will be small, leading to that most of FeCo granules behave as superparamagnetic nature unfavorable for GMR. With increasing the volume fraction of FeCo granules, FeCo granule size also increases, which results in that the fraction of superparamagnetic granules decreases and the fractions of single-domain and multidomain increases. When the fraction of single-domain granules reaches a maximum, the GMR of film will exhibit a maximum, as shown in Figs. 1 and 3(d). With further increasing the volume fraction of FeCo granules the granule size will increase, accordingly, most granules become multi-domain granules that have no effect on GMR [11] and result in the drop of GMR or even vanish of GMR. Annealing treatment can markedly change the sizes of granules accompanying the elevation of annealing temperature for a given film, accordingly, it can be expected that GMR of FeCo–Al2O3 film will exhibit peak value with the elevation of annealing temperature accompanying the volume fraction change of three kinds of ferromagnetic granules, which is verified by our experiments, as seen in Fig. 4. Moreover, it is clear that with increasing annealing temperature, the GMR of films with lower volume fraction reaches a peak value at certain annealing temperature. While for films with higher volume fraction, the GMR has almost no changes at first, and then decreases with increasing annealing temperature. This also can be explained according to above viewpoint that single-domain granules play a key role in GMR. For granular films with lower volume fraction, granule size is smaller and most granules exhibit superparamagnetic nature in as-deposited films, resulting in low GMR. With the elevation of annealing temperature, granules grow to be larger, resulting in the increase of volume fraction of single-domain granules, and then GMR improves. With further increasing annealing temperature, most granules can become multidomain ones, leading to the drop of GMR. While for films with higher volume fraction, since single-domain granules have reached a larger volume fraction in as-deposited films, during annealing, the granules will grow or connect so that partial granules become multi-domain ones, causing the monotonically decrease of the fraction of single-domain granules and then GMR. It is worthy to emphasize that the fraction (about 31.6%) of single-domain granules obtained by TEM observation approximately approaches to that (28.6%) by VSM measurement in FeCo(32.8 vol%)–Al2O3 films (correspond-
313
4
2
0 300
400
500 600 700 Annealing Temperature (K)
800
Fig. 4. The dependence of longitudinal GMR effect on annealing temperature for FeCo–Al2O3 films with various volume fractions.
ing to the largest GMR), which indicate that the fractions of ferromagnetic granule determined indirectly by VSM are reliable. The measuring result indicates that the fraction of single-domain granules is far smaller than that (69.8%)of superparamagnetic granules in FeCo(32.8 vol%)–Al2O3 films, as a consequence, the hysteresis curve of the film exhibits the superparamagnetic nature. For as-deposited or annealing films, the fraction of single-domain granules exceeds hardly 50% because of the existence of the size distribution of granules in films, in other words, the superparamagnetic granules always occupy majority in the ferromagnetic granules in films. However, when the hysteresis curve of a granular film is measured under low temperature, the fraction of single-domain granules can predominate in ferromagnetic granules for this film although the size of every granule is unchanged. Based on the formulas of two critical sizes distinguishing three kinds of ferromagnetic granules [7,8], it can be found that with lowering measuring temperature, the fraction of singledomain granules increases. For example, the critical size of Co granules distinguishing superparamagnetic from singledomain granules decreases rapidly from 7.6 nm at room temperature to 1.8 nm at 4 K and the critical size of Fe granules does from 16 to 3.6 nm while the critical size distinguishing single domain from multi-domain granules has almost no change [7,8]. As a result, GMR significantly increases with lowering measuring temperature accompanying the increase of the fraction of single-domain granules, which is supported by some experiments [12,13]. This fact strongly confirms our conclusion on the key role of singledomain granules in GMR. Moreover, it can be deduced that for a given film the nature of its hysteresis curve will gradually transform from the superparamagnetic to singledomain characteristic (that is, the coercive force gradually increases) when the measuring temperature gradually lowers from room temperature to liquid helium temperature, which is verified by Wang et al’s experiment [14].
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4. Conclusions
References
In summary, using VSM method, we measured the hysteresis curves of films with various volume fractions of FeCo granules and made excellent fittings with a function made up of superparamagnetic, single-domain and multidomain components. The fitting results indicated that the change of the fraction of single-domain granules with the volume fraction of FeCo granules was in agreement with that of GMR of films, verifying that single-domain granules play a key role in GMR, which is confirmed by most experiments including the change of GMR with the volume fraction of granules, annealing temperature or measuring temperature.
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Acknowledgments The present work is financially supported by the National Nature Science Foundation of China under Grant no. 50071033 and Hi-Tech Research and development Program of China under Grant no. 2004AA32G090.