Temperature Dependence of Exchange Bias and Coercivity in Ferromagnetic Layer Coupled with Polycrystalline Antiferromagnetic Layer

Transcription

1 Commun. Theor. Phys. (Beijing, China) 41 (2004) pp c International Academic Publishers Vol. 41, No. 4, April 15, 2004 Temperature Dependence of Exchange Bias and Coercivity in Ferromagnetic Layer Coupled with Polycrystalline Antiferromagnetic Layer ZHAO Jin-Wei, 1,3 HU Jing-Guo, 2, and CHEN Guang 1 1 Department of Materials Science & Engineering, Nanjing University of Science and Technology, Nanjing , China 2 College of Physics Science & Engineering, Yangzhou University, Yangzhou , and National Laboratory of Solid State Microstructures, Nanjing University, Nanjing , China 3 Jiangsu Entry-Exit Inspection and Quarantine Bureau, Nanjing , China (Received August 27, 2003) Abstract The temperature dependence of exchange bias and coercivity in a ferromagnetic layer coupled with an antiferromagnetic layer is discussed. In this model, the temperature dependence comes from the thermal instability of the system states and the temperature modulated relative magnetic parameters. Morever, the thermal fluctuation of orientations of easy axes of antiferromagnetic grains at preparing has been considered. From the present model, the experimental results can be illustrated qualitatively for available magnetic parameters. Based on our discussion, we can conclude that soft ferromagnetic layer coupled by hard antiferromagnetic layer may be very applicable to design magnetic devices. In special exchange coupling, we can get high exchange bias and low coercivity almost independent of temperature for proper temperature ranges. PACS numbers: Et, Ee, Cn Key words: ferromaagnetic layer, antiferromagnetic layer 1 Introduction The effect of exchange coupling, which arises from the interfacial exchange coupling between a ferromagnet and an antiferromagnet, significantly modifies some properties and phenomena of ferromagnetic (FM)/antiferromagnetic (AFM) bilayers. The most well-known effect is the shift of the hysteresis loop of the ferromagnet, called exchange bias, which was firstly discovered in partially oxidized Co particles more than 40 years ago. [1] Other important effects have also been observed, [2] such as almost all FM layers showing an increase in the coercivity, and the unusual shift in the ferromagnetic resonance when coupled to an AFM layer, even when samples are prepared in a situation that does not show an exchange bias. Recently, these effects have attracted much attention due to their application to giant magnetoresistive spin-valve heads for high-density recording systems. [2] Many experimental results have been reported that the characteristics of the exchange bias and the coercivity in FM/AFM bilayers depend on constituent materials, their thicknesses, the orientation of an applied field, and temperature. [3 8] As usual, this exchange coupling effect can be modeled as an exchange anisotropy field, which will add vectorially to the external field. Many theoretical results about thickness dependence of exchange bias and shift of ferromagnetic resonance have been reported. [3,9 11] However, the magnetic devices, such as read heads based on the above effects are usually required to operate in surroundings of varied temperature, so the temperature dependence of the exchange bias and the coercivity is quite important. Up to now, many experimental [5 8] results have presented that the temperature dependence of the exchange bias and the coercivity show, in general, similar behavior while the relative values are different. This behavior is that the exchange bias and the coercivity decrease with increasing temperature in the low temperature ranges. However, with further increasing temperature the exchange bias becomes small and vanish, in which the temperature is called blocking temperature while the coercivity reaches a peak. There are some model aiming to explain qualitatively the temperature dependence of the exchange bias and the coercivity. [5,12,13] However, the details of how the temperature dependence is associated with their magnetic parameters, such as interface exchange coupling, anisotropy of FM and AFM layer, and the size of AFM grains, still remain unclear. In this paper, our aim is, based on a Fulcomer and Charap model, [5] in which the ferromagnetic layer is considered perfect with uniaxial anisotropy while the antiferromagnetic layer is consisted by many independent antiferromagnetic grains with polycrystalline uniaxial anisotropy, to investigate the temperature dependence of the exchange bias and the coercivity as well as how the temperature dependence is associated with their magnetic parameters, and to find an optimal composition of The project supported by Natural Science Foundation of Educational Bureau of Jiangsu Province under Grant Nos. 01KJD and 03KJB140153, and National Natural Science Foundation of China under Grant No Eail: hujgyz@263.net

2 624 ZHAO Jin-Wei, HU Jing-Guo, and CHEN Guang Vol. 41 FM/AFM bilayers in order to improve their performance. In this model, the source of temperature dependence results from thermal instabilities of the system state and temperature dependence of relative magnetic parameters. Meanwhile, thermal frustration of orientations of easy axes of antiferromagnetic grains at preparing has been considered. These results show that in general, at low temperatures, the exchange bias and the coercivity decrease with increasing temperature, but the exchange bias always becomes small while the coercivity firstly increases, then reaches a peak, and finally decreases at higher temperatures. Moreover, their behavior will be effectively modified by selecting properly relative magnetic parameters. Based on the above model, we can well illustrate some recent experimental results, and give some suggestion. The paper is organized as follows. Section 2 is devoted to the model for individual independent AFM grains coupled to an FM layer. In Sec. 3 the numerical results about the dependence of the exchange bias and the coercivity on the temperature and on the other magnetic parameters are obtained and discussed. Finally, a main conclusion is given in Sec. 4. coherently due to the fact that the AFM grains are so small enough that they are a single domain. For simplicity, it is assumed that there is no interaction between the AFM grains, but an exchange coupling exists between the FM layer and AFM grains. This behavior of AFM grains is closely related to that of superparamagnetism in small AFM particles. Furthermore, it is assumed that both the FM layer and the AFM grains have only uniaxial magnetic anisotropies. 2 Model To derive the dependences of the exchange bias and coercivity on temperature and on magnetic parameters for the exchanged-coupled FM and AFM bilayers, a model is presented, in which the FM magnetization and AFM net sublattice magnetization are considered to be uniform due to the fact that almost all experiments have been done in magnetic fields high enough to saturate the FM and AFM magnetization. As shown in Fig. 1, the interface is arranged to lie in the x-y plane with the z axis normal to the interface, and the FM/AFM system consists of one perfect FM layer coupled to N AFM grains (N = 10 5 ). The thickness of the FM layer, d, is thin enough that there is no domain wall inside the ferromagnet. In fact, many experiments have confirmed that there is no helical structure along the z axis in a thin FM layer. For example, Parkin et al. [14] have observed that a uniform magnetization distributed throughout the thickness of a 400 Å of Ni 80 Fe 20 layer coupled with an Fe 50 Mn 50 layer. All AFM grains have the same height D but different interface areas A i. All spins in each grain are assumed to behave E = K FM A FM d sin 2 θ HM FM A FM d cos θ + i Fig. 1 A schematic model of the FM/AFM bilayer for calculation. Uniaxial anisotropy is assumed in the FM layer and AFM grains. The grain size distribution of AFM layer is taken into consideration. Based on the above assumption, the total energy of an exchange coupled FM/AFM bilayer in the presence of an applied field H is given by { } K AFM A i D sin 2 φ i f(α i )J E1 A i cos[θ (α i + φ i )], (1) where K FM and K AFM are the uniaxial anisotropy constants of FM layer and AFM grains, respectively; θ, φ, and α i are the angles between the FM magnetization and the FM anisotropy axis, the AFM sublattice magnetization and the AFM anisotropy axis, and the i-th AFM grain anisotropy axis and the applied field, with the subscript i representing all the possible distributions of each parameter. For simplicity, we assume that the FM easy axis is collinear to the direction of external field, but the i-th AFM easy axis departs from the external field denoted by

3 No. 4 Temperature Dependence of Exchange Bias and Coercivity in Ferromagnetic Layer Coupled 625 α i, and f(α i ) is the occupational distribution function of all AFM grain easy axis which depends on the sample s preparation, the history of magnetization processes, and the temperature variation of surroundings. M FM is the saturated magnetization of the FM layer with its volume A FM d. Here, A FM = i A i. The first term in Eq. (1) is the uniaxial anisotropy energy of the FM layer while the second term is the Zeeman energy. In the big brackets of Eq. (1), the first term is the uniaxial anisotropy energy of the AFM grains, and the second term is the direct unidirectional coupling energy with bilinear coupling constants J E1. At equilibrium, the first derivatives of the energy E denoted by Eq. (1) with respect to the angle φ must be equal to zero. From the partial derivation of Eq. (1) with φ, we can obtain the energy minimum equations, which determine the angle φ under certain values of θ and {α i }. By calculation, we can see two values of φ for certain values of θ and {α i } which satisfy the energy minimum equations. This means that when the FM layer magnetization rotates, the AFM grain has two stable states concerning the direction of the AFM magnetization. Hereafter, we call these stable states state 1 and state 2, respectively. In order to calculate the energy of the system for certain value of θ and {α i }, we should know the populations of both the state 1 and state 2 of all the AFM magnetizations. By using the energy E 1(2)i corresponding to the state 1 (2) of the i-th AFM grain, we can get the population of the state 1 of the i-th AFM magnetization as p 1i = {1 + exp[(e 2i E 1i )/k B T ]} 1. (2) Taking into account p 1i + p 2i = 1, we obtain the population of the state 2 of the i-th AFM magnetization. For certain value of θ and {α i }, the energy of the system can be obtained by E i (θ, α i ) = p 1i E 1i + p 2i E 2i. (3) where α i is defined to be distributed randomly in the range from π/2 to π/2. The total energy of the system is obtained by taking into account the distribution of the anisotropy axes of all AFM grain f(α i ), E(θ) = i π/2 π/2 E i (θ, α i )f(α i )dα i. (4) In the present model, the total energy E(θ) is the function of strength and orientation of external applied field. The direction of the FM magnetization θ is determined numerically by minimizing Eq. (4) for the certain value of external field, from which we can calculate the system s magnetization processes. Then from magnetic curve we can get the exchange bias and coercivity. [15] In the process of calculation, energy is scaled by A FM, but exchange bias and coercivity scaled by K FM A FM t FM. However, for an actual sample, the AFM grains have a rather continuous distribution in their sizes over some ranges, resulting in a continuous distribution in the exchange coupling strength, when the exchange coupling strength of each AFM grain is assumed to be inversely proportional to the square root of the interface area of the AFM grain. As generally accepted, [16] the sizes of AFM grains shown in Fig. 1 exhibits log-normal distribution, { 1 2/2σ P = exp [ 2 ln(a 2 i/a mean )] }, (5) where A mean = 16 nm 2 and σ = [16] There are three advantages of our model compared to the previous one. [5,12,13] Firstly, the size of AFM grains have considered to be continuous log-normal distribution, and the exchange coupling strength of each AFM grain is assumed to be related to the interface area of AFM grains. Secondly, the temperature dependence comes from the thermal instability of the system states, including the temperature modulated relative magnetic parameters. Thirdly, the thermal fluctuation of orientations of easy axes of antiferromagnetic grains at preparing has been considered, and the distribution function of the AFM easy axis denoted by f(α) is determined by the Boltzmann distribution relative surroundings of prepared temperature. 3 Analysis and Discussion We consider an FM/AFM system in which the Curie temperature of the ferromagnet is much greater than the Néel temperature of the antiferromagnet, which is usually the case based on Refs. [6] and [13]. Thus, we study the properties of the system near Néel temperature and assume that the ferromagnetic magnetization is independent of the temperature. The exchange coupling at the interface is directly proportional to both the FM magnetization and AFM sublattice magnetization close to their interface, so we assume that the exchange coupling at the interface is temperature-dependent as the result of the temperature dependence of AFM sublattice magnetization. In our model, we include two contributions to the temperature dependence. The first is associated with magnetic parameters, such as the exchange coupling at the interface and the uniaxial anisotropy of the AFM grains. The second is involved in the superparamagnetism of AFM grains. For the former, we assume that the AFM magnetization M AFM [ 1 (T/T N ) 2] 1/2 based on Stoner s magnetic theory. [17] On the other hand, according to the assumption of C. Hou, et al., [13] we take that the AFM anisotropy K AFM MAFM 3, the interface exchange coupling J E1 M AFM, where T is the temperature of the system, and T N is the Néel temperature. For the latter, the thermal fluctuation of orientations of easy axes of antiferromagnetic grains at preparing has been considered.

4 626 ZHAO Jin-Wei, HU Jing-Guo, and CHEN Guang Vol. 41 The original distribution of the easy axis of AFM grain is determined by the thermal equilibrium of preparation. Namely, the distribution of the easy axis of the AFM grain for the given applied field is described by the Boltzmann factor exp( E/k B T B ), where E is the energy of the system at equilibrium, and k B T B is the thermal energy at preparation. Here, we take T B = 0.02 T N. the FM layer with the low FM anisotropy energy is easy pinned by the AFM layer. However, with the increase of the FM anisotropy energy as in Fig. 2(b), the coercivity always increase distinctly at any temperature while the curve shape is nearly invariable. It suggests that the soft FM layer coupled by antiferromagnetic layer may be very applicable to design magnetic devices with high exchange bias and low coercivity. In fact, there are two contributions for the coercivity. One comes from the anisotropy of the FM layer, so the increase of the anisotropy of the FM layer results in the increase of the coercivity. The other comes from the interface coupling, which enhances the coercivity and determines the curve shape. Interestingly, the blocking temperature, in which the exchange bias approaches zero, is nearly invariable. It suggests that the blocking temperature is nearly independent of the FM anisotropy energy. Fig. 2 Exchange bias (a) and coercivity (b) vs. temperature for K AFMd = 4.0, J E1 = 1.0, and A mean=16 nm 2. Figure 2 shows the calculated results for the temperature dependence of the exchange bias and coercivity when the FM anisotropy energy is changed. As shown in Fig. 2(a), with the decrease of the FM anisotropy energy, the curve shape becomes heaved. When we take the available reduced parameter of Ni 80 Fe 20 /Fe 50 Mn 50 bilayer, our results are in good agreement with experimental results qualitatively as shown in square line. [16] However, when the FM anisotropy energy decreases to small enough, the temperature dependence of the exchange bias will show a flat region at low temperatures. It is due to the fact that Fig. 3 Temperature dependences of exchange bias (a) and coercivity (b) for K FMd = 1.0, J E1 = 1.0, and A mean=16 nm 2. The calculated results of the temperature dependence

5 No. 4 Temperature Dependence of Exchange Bias and Coercivity in Ferromagnetic Layer Coupled 627 of the exchange bias and coercivity for various values of the AFM anisotropy energy are shown in Fig. 3. From Fig. 3(a), we find that with the increase of the AFM anisotropy energy, the blocking temperature increases and approaches the Néel temperature at large AFM anisotropy energy but the exchange bias increases at any temperature. It predicts that the pinning effect of the AFM layer is important for the occurring of exchange bias. As for coercivities shown in Fig. 3(b), with increasing temperature, the coercivity firstly decreases distinctly then increases and approaches the peaks around the blocking temperature, finally decreases, which is in good agreement with previous results qualitatively. [5,7,8] However, the value is nearly independent of the AFM anisotropy energy. It accounts for that the interface coupling effect has been displayed in this case. We can conclude that it is effective to improve the magnetic devices of exchange bias by means of hard AFM layer coupled. Fig. 4 Temperature dependences of exchange bias (a) and coercivity (b) for K FMd = 1.0, K AFMD = 4.0, and A mean=16 nm 2. In order to investigate the effect of the exchange coupling energy, we calculate the temperature dependence of the exchange bias and coercivity for different exchange coupling energy as shown in Fig. 4. With increase of the bilinear coupling energy, the exchange bias and coercivity generally increase, but the exchange bias dependence on temperature becomes slower while that of the coercivity increases for large exchange coupling. Moreover, with increasing bilinear coupling energy, the block temperature increases and the exchange bias becomes saturation and invariability at the low temperature range, but the temperature dependence of coercivity is similar while the value of peak decreases with exchange coupling increasing. Finally, we must point out that, in our case, the coercivity does not approach zero when the temperature gets at the Néel temperature because the magnetization of the FM layer is still stable. 4 Conclusion We presented a model of the temperature dependence of the exchange bias and the coercivity for bilayer of ferromagnetic layer and antiferromagnetic grain layer. In this model, the temperature dependence results from thermal fluctuation of states of the antiferromagnetic grains due to thermally activated transition between the equilibrated states of the AFM grains, and temperature-modulated relative magnetic parameters. Meanwhile, the thermal fluctuation of orientations of easy axes of antiferromagnetic grains at preparing has been considered. The numerical results show that in general, at low temperatures, the AFM state in each grain is stable as the FM magnetization is rotated, in which there is the higher exchange bias and low coercivity. But they decrease with increasing temperature due to the fact that the AFM state becomes unstable with increasing temperature. At higher temperatures the thermal excitations are over energy barriers, the exchange bias becomes zero while the coercivity reaches a peak. Moreover, their behavior will be effectively modified by selecting relative magnetic parameters properly. The saturation of the exchange bias at low temperatures is mainly determined by the exchange coupling at interface. When reduced value of magnetic parameter is available, our results agree with the experimental results qualitatively. [5,7,8,16,18] These agreements indicate that our model and general analytic results are reasonable. Based on this fact we suggest that the FM/AFM

6 628 ZHAO Jin-Wei, HU Jing-Guo, and CHEN Guang Vol. 41 bilayer with high exchange bias and low coercivity, which is nearly independent of temperature, can be obtained by means of soft FM layer coupled by hard AFM layer with special exchange coupling. References [1] W.H. Meiklejohn and C.P. Bean, Phys. Rev. 102 (1956) 1413; 105 (1957) 904. [2] B. Dieny, V.S. Speriosu, S.S.P. Parkin, B.A. Gurney, P. Baumgart, and D.R. Wilhoit, J. Appl. Phys. 69 (1991) [3] J. Nogués and I.K. Schuller, J. Magn. Magn. Mat. 192 (1999) 203. [4] J.C. Scott, J. Appl. Phys. 57 (1985) [5] E. Fulcomer and S.H. Charap, J. Appl. Phys. 43 (1972) [6] X.W. Wu and C.L. Chien, Phys. Rev. Lett. 81 (1998) [7] H. Fujiwara, K. Nishioka, C. Hou, M.R. Parker, S. Gangopadhyay, and R. Metzger, J. Appl. Phys. 79 (1996) [8] T. Lin, D. Mauri, N. Staud, C. Hwang, J.K. Howard, and G.L. Gorman, Appl. Phys. Lett. 65 (1994) [9] H.W. Xi and R.M. White, Phys. Rev. B61 (2000) 80; Phys. Rev. B61 (2000) [10] J.G. Hu, G.J. Jin, and Y.Q. Ma, J. Appl. Phys. 91 (2002) 2180; J. Appl. Phys. 92 (2002) 1009; Mod. Phys. Lett. B15 (2001) 1087; J. Appl. Phys. 94 (2003) [11] M.D. Stiles and R.D. McMichael, Phys. Rev. B59 (1999) 3722; N.C. Koon, Phys. Rev. Lett. 78 (1997) [12] M.D. Stiles and R.D. McMichael, Phys. Rev. B60 (1999) [13] C. Hou, H. Fujiwara, K. Zhang, A. Tanaka, and Y. Shimizu, Phys. Rev. B63 (2001) [14] S.S.P. Parkin, V.R. Deline, R.O. Hilleke, and G.P. Felcher, Phys. Rev. B42 (1990) [15] V.I. Nikitenko, V.S. Gornakov, L.M. Dedukh, Yu.P. Kabanov, A.F. Khapikov, A.J. Shapiro, R.D. Shull, A. Chaihen, and R.P. Michel, Phys. Rev. B57 (1998) R8111. [16] K. Nishioka. C. Hou, H. Fujiwara, and R.D. Metzger, J. Appl. Phys. 80 (1996) [17] E.C. Stoner, Proc. Roy. Soc. A165 (1938) 372. [18] C. Tsang and K. Lee, J. Appl. Phys. 53 (1982) 2605; L. Wee, R.L. Stamps, and R.E. Camley, J. Appl. Phys. 89 (2001) 6913.