- Email: [email protected]
Tb multilayer
November 2002
Materials Letters 57 (2002) 252 – 259 www.elsevier.com/locate/matlet
Irreversibility in magnetic torque curves of Co/Tb multilayer L. Louail *, D. Maouche, H. Hachemi, A. Roumili Institute of Physics, University of Setif (19000) Algeria Received 6 November 2001; received in revised form 18 February 2002; accepted 25 February 2002
Abstract The magnetic anisotropy behavior of a [Co10 A˚Tb10 A˚]10 superlattice prepared by molecular beam epitaxy has been studied by means of a torque magnetometer. A complex magnetic behavior has been noticed. The rotational hysteresis loop has been analysed and interpreted as a function of both the temperature and the external magnetic field. D 2002 Elsevier Science B.V. All rights reserved. PACS: 75.60.Nt; 75.70.Ak; 76.30.Kg Keywords: Magnetic multiplayer; Rotational hysteresis; Rare-earth elements
1. Introduction Different properties of fundamental and technological interest can be associated to each system, like magnetic anisotropy for rare-earth and high Curie temperature for transition-metal. Coupling these two types of elements leads to new results since the polarization of the rare-earth 4f by the transitionmetal 3d orbitals enhances the magnetic properties of the rare-earth. Rare-earth/transition-metal (RE –TM) thin films have been intensively studied during recent years. The main reasons for this were the interesting problems of interface, quasi-two-dimensional magnetism and also promising application perspectives as magnetic information storage media,
*
Corresponding author. E-mail address: [email protected] (L. Louail).
for example, perpendicular recording. Thin films based on rare-earth and transition-metal elements have been attractive materials for magneto-optic recording purposes and magnetostrictive devices [1 –4]. From a general point of view, two different origins for magnetism have to be considered: localized open shell, like 4f orbitals of rare-earth elements, or spin-polarized band states of the 3d transition-metals. Many studies on rare-earth/transition-metal multilayers have been performed for reasons of scientific interest and application to magneto-optical recording [5 –13]. Perpendicular magnetic anisotropy was also observed in Fe/Pr, Fe/Nd, Fe/Eu, Fe/Dy and Fe/Tb multilayers [14 –17]. In this paper, we report the results of the study by means of torque magnetometer curves of the magnetic anisotropy behavior of a [Co10 A˚Tb10 A˚]10 multilayer as a function of temperature in applied field of 12 kOe and as a function of applied field at 100 K.
0167-577X/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 7 7 X ( 0 2 ) 0 0 7 7 5 - 9
L. Louail et al. / Materials Letters 57 (2002) 252–259
2. Experimental 2.1. Film preparation It is clear that the origin of perpendicular anisotropy in Tb – (Co,Fe) films is related to structure anisotropy and therefore to their preparation. The studied sample has been prepared by MBE in a vacuum chamber under a residual pressure of about 4 10 10 Torr. It was grown upon glass substrate. Tb and Co were evaporated from electron guns and deposited onto the sub-
Fig. 1. Magnetic torque experimental curves of [Co10 temperature.
˚ A
253
strate kept at 200 jC, in order to allow surface mobility, while limiting interfacial diffusion. The deposition rate, calibrated using a quartz crystal monitor and an ˚ s 1. The stacking sequence optical sensor, was 2.5 A ˚ (buffer of the multilayer is the following: Ru 200 A layer)/Mo30A˚/(Co10 A˚/Tb10 A˚)10/Co10 A˚/Mo30 A˚. The Co grows epitaxially and almost layer by layer on the buffer. The deposit of Tb induces additional streaks on the reflection high-energy electron diffraction (RHEED) patterns, which cannot be simply indexed. This indicated a bidimensional growth and a complex
Tb10 A˚]10 multilayer in the applied magnetic field of 12 kOe, as a function of
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L. Louail et al. / Materials Letters 57 (2002) 252–259
Fig. 2. Rotational hysteresis loops as a function of temperature in applied field of 12 kOe.
reconstruction on the Co surface. To avoid all chemical contamination, especially oxidation, and to protect the ˚ thick Mo capping Tb, the sample is protected by a 30-A layer. The structure quality of the sample has been checked by in situ RHEED observation. The RHEED patterns exhibit thin and continuous streaks, which reveal a good crystalline quality of the samples. 2.2. Magnetization measurements Magnetization measurements were performed using a torque magnetometer that served for characterizing the magnetic anisotropy of the films. In this technique, the sample is suspended in a field and magnetized to saturation, so that the magnetization lies everywhere in the same easy direction, then the sample will rotate so that this easy direction is aligned with the field. A torque is exerted on the sample, causing it to rotate, and this would be equal to the torque, which would be acting on the magnetization vector, causing it to rotate into alignment with the field, if the sample was held clamped. The torque L per unit volume, is given by: L¼
@E @#
and therefore, the torque on the sample will be: L ¼ þDE=D#. In practice, the sample is set in a predetermined position and the field is applied. The torsion head is turned until the sample is brought back to its original position and, by separate calibration of the torsion head; this gives a direct reading of the torque exerted. In this paper, we confine our attention to the static rotational hysteresis, i.e., the energy required to rotate a ferromagnetic specimen through an angle of 360j in a magnetic field assuming that the rate of rotation is very low, i.e., a rotation of 360j in about 30 min. Magnetic field up to 12 kOe was applied perpendicularly to the film plane and the temperature changes from 35 K to room temperature. The rotational hysteresis energy is defined as the algebraic sum of the area enclosed between the positive and negative sections of the torque curve. Alternatively, if the field is rotated through 360j in the opposite direction, e.g., anticlockwise, the two torque curves enclose an area that is equal to twice the rotational hysteresis energy. Cc(h) and Cac(h) are the torque curves for clockwise and anticlockwise rotation of the applied field. A clockwise rotation through 360j was followed by an anticlockwise rotation through the same angle.
L. Louail et al. / Materials Letters 57 (2002) 252–259
3. Results and discussion As a function of temperature, the multilayer shows a complex magnetic behavior. The thermal behavior of the torque intensity curves in a magnetic field of 12 kOe perpendicularly applied to the film plane is shown in Fig. 1. At 35 K, the clockwise and the anticlockwise torque curves were identical, so that the rotational
Fig. 3. Magnetic torque experimental curves of [Co10
˚ A
255
hysteresis energy is nearly zero. The area enclosed between the torque curves is nil. The curves show two maxima, signs of energy equilibrium positions. When the temperature reaches 50 K, a very weak rotational hysteresis energy appears. The clockwise and the anticlockwise curves begin to be distinguishable from one another. Irreversibility begins to be observed. Above 75 K, torque curves take another shape. A rotational hysteresis loop is clearly present. The area
Tb10 A˚]10 multilayer at 100 K as a function of applied magnetic field.
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L. Louail et al. / Materials Letters 57 (2002) 252–259
between clockwise and the anticlockwise curves increases with increasing temperature. This area becomes more important at 100 K where the curves exhibit four instead of two maxima. Beyond 125 K, the clockwise and the anticlockwise torque curves restart to come closer and the area enclosed between these curves decreases. The reversibility appears again. Above 200 K, the torque curves do not enclose an area; the rotational hysteresis loop is no more observed. One can assign this phenomenon to the interface between Co and Tb layers. We have to assume that the Co layers induce a magnetic order in the Tb layers by a long-range coupling mechanism with a larger length than the thickness of the mixed interface. Indeed, Tb/ Co multilayers can contribute to a better understanding of the interface anisotropy. Both the broken symmetry at the boundaries of the layers—in the sense of Ne´el’s surface anisotropy—and the single ion anisotropy of the Tb—because of the anisotropic coordination at the interfaces between the Tb and Co layers—may be considered as the physical origin of the magnetic anisotropy and then rotational hysteresis. The change in torque curves with temperature can also be explained by an intrinsic variation of the bulk magnetocrystalline anisotropy as a function of temperature, for instance, related to thermal expansion or temperature dependence of magnetostriction coeffi-
cients, as discussed recently for tetragonaly distorted Ni/Cu(100) films [18]. It is also possible that the magnetic moment of the Co atoms at the interface decreases strongly with increasing temperature, so that the interface contribution (which favors in our films perpendicular easy axis) decreases faster than the dipolar interaction which induces a decrease of the effective second-order anisotropy. On the other hand, the thermal variations of torque curves can be related to the phenomenological aspect of the coherent rotation model as described by the equation: E ¼ MHcosðh uÞ þ Keff sin2 h þ K2 sin4 h h being the angle between the normal to sample and the magnetization and u the angle between the normal to sample and the applied magnetic field. The Keff and K2 parameters represent, respectively, the effective and second order anisotropy constants. In fact, a more rigorous treatment has also to consider the entropy related to the fluctuations of the magnetization direction as the temperature reaches a certain value [19 –24]. Since only the anisotropy constants have temperature dependence in the coherent rotation model, it is clear that they implicitly include entropy effects. More theoretical and experimental work would be necessary in order to disentangle the role of both effects.
Fig. 4. Rotational hysteresis loops as a function of applied magnetic field at 100 K.
L. Louail et al. / Materials Letters 57 (2002) 252–259
Contrary to the reversible torque curves that we found in Co/Pt multilayers [25 – 28], where we were able to determine the magnetocrystalline anisotropy constants, the irreversible torque curves are deduced from half the difference of the two clockwise and the anticlockwise contributions: CðhÞ ¼ ½Ca ðhÞ Cac ðhÞ=2 where Ca(h) and Cac(h) are the clockwise and the anticlockwise torque curves, respectively. This sepa-
257
ration between both reversible and irreversible contributions has been introduced by Meiklejohn and Bean [29]. As shown in Fig. 2, the irreversible contribution depends on the rotation angle of the applied magnetic field. The rotational hysteresis C(h) as a function of temperature exhibits very marked maxima along the different directions associated to anisotropy magnetocrystalline of the multilayer. It is therefore the sign of irreversible movements, which occur at the approach of these directions in the magnetic moments contained
Fig. 5. Rotational hysteresis magnitude as a function of both (a) the temperature and (b) the applied field.
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in the sample and that are not perfectly aligned with the applied field. The applied field being, in our experiences, always distinctly superior to the saturation field of Co layers, one can deduce that these irreversible movements take place inside the Tb layers. In order to establish the origin of the rotational hysteresis loops, we have examined the behavior of rotational hysteresis with the applied magnetic field. This study is carried out at 100 K and the used magnetic field ranges from 1 to 12 kOe, maximal value delivered by our electromagnet. We have plotted in Fig 3 the behavior of torque curves as a function of applied field. When the applied magnetic field is weak, the clockwise and the anticlockwise curves are identical. The curves are reversible. When the applied field increases, the area between clockwise and anticlockwise curves begins to appear at 6 kOe; the rotational hysteresis loop is observed and it increases with increasing applied filed up to 12 kOe. The modification of torque curves with increasing applied field results either from strain-induced effects [30] or from symmetry change of the Co atoms located at the upper interface [31] or has another electronic origin [32]. We think that it is probably due to Tb layers, because Tb/Co multilayers show a very interesting magnetic coupling behavior. Pure Tb is paramagnetic at room temperature (Tc = 219.5 K [33]). In multilayers which consist of alternating thin layers of pure Tb and Co, however, the Tb layers show a magnetic order with an antiferromagnetic coupling to the Co atoms, as it is well known from the TbCo alloys [34,35]. This magnetic coupling between the Tb and Co layers can be confirmed by the observation of compensation points, which directly indicate the antiferromagnetic coupling in these films. We show in Fig. 4 the variation of the rotational hysteresis loops as a function of the applied magnetic field. As indicated above, the Tb layers responsible for the change of rotational hysteresis with magnetic field significantly enhances the anisotropy of the film as well as its temperature coefficient because the adsorption of a small amount of a rare-earth element on Co ultra-thin films tends to favor perpendicular anisotropy, in agreement with results known for Co/ Tb multilayers [36,37]. We then focussed our interest on the magnitude of the rotational hysteresis curves as a function of both
temperature and magnetic field. As shown in Fig. 5(a), the magnitude is zero at low temperature because the area enclosed between the positive and negative sections of the torque curve is zero. The magnitude increases with increasing temperature and shows a maximum at 100 K, and then it decreases up to 200 K and becomes zero at high temperature. As a function of applied field, the magnitude of rotational hysteresis curves is zero at low field values, then it increases with increasing magnetic field in a nearly linear manner up to 12 kOe, as shown in Fig. 5(b). The full width at half the maximum (FWHM) of the rotational hysteresis curves also changes with both temperature and applied magnetic field. As shown in Fig. 6(a), FWHM is zero at 35 K; it reaches a maximum at 50 K, then decreases rapidly with increasing temperature. The same behavior is shown
Fig. 6. FWHM of rotational hysteresis maxima as a function of both (a) the temperature and (b) the applied magnetic field.
L. Louail et al. / Materials Letters 57 (2002) 252–259
in Fig. 6(b), as a function of applied magnetic field. The FWHM is zero at low field; it shows a maximum at 6 kOe, and then decreases with increasing the magnetic field.
4. Conclusion In this work, we have studied by means of torque magnetometer curves the magnetic anisotropy behavior of the [Co10 A˚Tb10 A˚]10 multilayer as a function of both the temperature and the applied magnetic field. These curves present a complex magnetic behavior. A rotational hysteresis appears that depends on temperature. We have assigned this phenomenon to the interface between Co and Tb layers and assumed that the Co layers induce a magnetic order in the Tb layers by a long-range coupling mechanism. We have also observed that the rotational hysteresis increases with increasing external field. We think that it is probably due to the role played by Tb layers in this multilayer.
Acknowledgements This work has been carried out at the ‘‘Institut de Physique et de Chimie des Mate´riaux de Strasbourg (France) in Groupe d’Etude des Mate´riaux Me´talliques’’. We would like to thank Dr. K. Ounadjela and Pr. H. Danan for stimulating discussions.
References [1] W.B. Zeper, F. Greidanus, P.F. Garcia, IEEE Trans. Magn. MAG-25 (1989) 3764. [2] S. Hasshimoto, Y. Ochiai, K. Aso, J. Appl. Phys. 28 (1989) L1824. [3] C.J. Lin, H.V. Do, IEEE Trans. Magn. MAG-26 (1990) 1700. [4] P.F. Garcia, W.B. Zeper, F.J.A.M. Greidanus, MRS Proc. 150 (1989) 115. [5] T. Morishita, Y. Togami, K. Tsushima, J. Magn. Magn. Mater. 54 – 57 (1986) 789. [6] N. Sato, J. Appl. Phys. 59 (1986) 2514.
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[7] K. Yoden, N. Hosoito, K. Kawaguchi, K. Mibu, T. Shinjo, Jpn. J. Appl. Phys. 27 (1988) 1680. [8] Z.S. Shan, D.J. Sellmyer, J. Appl. Phys. 67 (1990) 5713. [9] T. Kimura, M. Ohtsu, M. Nawate, S. Honda, T. Kusuda, J. Magn. Soc. Jpn. 15 (1991) 437. [10] A. Fnidiki, F. Richomme, J. Teillet, F. Pierre, P. Boher, Ph. Houdy, J. Magn. Magn. Mater. 121 (1993) 520. [11] S. Honda, M. Nawate, J. Magn. Magn. Mater. 136 (1994) 163. [12] K. Mibu, N. Hosoito, T. Shinjo, J. Magn. Magn. Mater. 126 (1993) 343. [13] S. Honda, M. Nawate, I. Sakamoto, J. Appl. Phys. 79 (1996) 365. [14] J. Tejada, F. Badia, B. Martinez, J.M. Ruiz, J. Magn. Magn. Mater. 101 (1991) 181. [15] K. Yoden, N. Hosoito, K. Kawaguchi, K. Mibu, T. Shinjo, Jpn. J. Appl. Phys. 27 (1988) 1680. [16] B. Scholz, R.A. Brand, W. Keune, J. Magn. Magn. Mater. 104 (1992) 1889. [17] Z.S. Zhang, Y.T. Wang, F. Yang, F. Pan, Phys. Status Solidi 179 (2000) 237. [18] M. Farle, W. Platow, A.N. Anisimov, B. Schulz, K. Baberschke, J. Magn. Magn. Mater. 165 (1997) 74. [19] G. Garreau, E. Beaurepaire, M. Farle, J.P. Kappler, Europhys. Lett. 39 (1997) 557. [20] P.J. Jensen, K.H. Bennemann, Phys. Rev. B 42 (1990) 849. [21] A. Moschel, K.D. Usadel, Phys. Rev. B 49 (1994) 12868. [22] D. Pescia, V.L. Pokrovsky, Phys. Rev. Lett. 65 (1990) 2599. [23] P. Politi, A. Rettori, M.G. Pini, Phys. Rev. Lett. 70 (1992) 1183. [24] A.P. Levanyuk, N. Garcia, Phys. Rev. Lett. 70 (1992) 1184. [25] L. Louail, K. Ounadjela, R.L. Stamps, J. Magn. Magn. Mater. 167 (1997) L189 – L199. [26] L. Louail, K. Ounadjela, M. Hehn, K. Khodjaoui, M. Gester, H. Danan, R.L. Stamps, J. Magn. Magn. Mater. 165 (1997) 387. [27] R.L. Stamps, L. Louail, M. Hehn, M. Gester, K. Ounadjela, J. Appl. Phys. 81 (8) (1997) 4751. [28] L. Louail, A. Azizi, B. Moula, Mater. Lett. 47 (2001) 199 – 204. [29] W.H. Meiklejohn, C.P. Bean, Phys. Rev. 105 (1957) 904. [30] C. Chappert, P. Bruno, J. Appl. Phys. 64 (1988) 5736. [31] L. Ne´el, J. Phys. Radium 15 (1954) 225. [32] B. Ujfalussy, L. Szunyogh, P. Bruno, P. Weinberger, Phys. Rev. Lett. 77 (1996) 1805. [33] Handbook of Chemistry and Physics, 70th edn., CRC Press, Boca Raton, 1989. [34] P. Hansen, C. Clausen, G. Much, M. Rosenkranz, K. Witter, J. Appl. Phys. 66 (1989) 759. [35] L. Ertl, G. Endl, H. Hoffmann, J. Magn. Magn. Mater. 113 (1992) 227. [36] R. Allenspach, J. Magn. Magn. Mater. 129 (1994) 160. [37] G. Garreau, M. Farle, E. Beaurepaire, J.P. Kappler, J. Magn. Magn. Mater. 184 (1998) 289.
Materials Letters 57 (2002) 252 – 259 www.elsevier.com/locate/matlet
Irreversibility in magnetic torque curves of Co/Tb multilayer L. Louail *, D. Maouche, H. Hachemi, A. Roumili Institute of Physics, University of Setif (19000) Algeria Received 6 November 2001; received in revised form 18 February 2002; accepted 25 February 2002
Abstract The magnetic anisotropy behavior of a [Co10 A˚Tb10 A˚]10 superlattice prepared by molecular beam epitaxy has been studied by means of a torque magnetometer. A complex magnetic behavior has been noticed. The rotational hysteresis loop has been analysed and interpreted as a function of both the temperature and the external magnetic field. D 2002 Elsevier Science B.V. All rights reserved. PACS: 75.60.Nt; 75.70.Ak; 76.30.Kg Keywords: Magnetic multiplayer; Rotational hysteresis; Rare-earth elements
1. Introduction Different properties of fundamental and technological interest can be associated to each system, like magnetic anisotropy for rare-earth and high Curie temperature for transition-metal. Coupling these two types of elements leads to new results since the polarization of the rare-earth 4f by the transitionmetal 3d orbitals enhances the magnetic properties of the rare-earth. Rare-earth/transition-metal (RE –TM) thin films have been intensively studied during recent years. The main reasons for this were the interesting problems of interface, quasi-two-dimensional magnetism and also promising application perspectives as magnetic information storage media,
*
Corresponding author. E-mail address: [email protected] (L. Louail).
for example, perpendicular recording. Thin films based on rare-earth and transition-metal elements have been attractive materials for magneto-optic recording purposes and magnetostrictive devices [1 –4]. From a general point of view, two different origins for magnetism have to be considered: localized open shell, like 4f orbitals of rare-earth elements, or spin-polarized band states of the 3d transition-metals. Many studies on rare-earth/transition-metal multilayers have been performed for reasons of scientific interest and application to magneto-optical recording [5 –13]. Perpendicular magnetic anisotropy was also observed in Fe/Pr, Fe/Nd, Fe/Eu, Fe/Dy and Fe/Tb multilayers [14 –17]. In this paper, we report the results of the study by means of torque magnetometer curves of the magnetic anisotropy behavior of a [Co10 A˚Tb10 A˚]10 multilayer as a function of temperature in applied field of 12 kOe and as a function of applied field at 100 K.
0167-577X/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 7 7 X ( 0 2 ) 0 0 7 7 5 - 9
L. Louail et al. / Materials Letters 57 (2002) 252–259
2. Experimental 2.1. Film preparation It is clear that the origin of perpendicular anisotropy in Tb – (Co,Fe) films is related to structure anisotropy and therefore to their preparation. The studied sample has been prepared by MBE in a vacuum chamber under a residual pressure of about 4 10 10 Torr. It was grown upon glass substrate. Tb and Co were evaporated from electron guns and deposited onto the sub-
Fig. 1. Magnetic torque experimental curves of [Co10 temperature.
˚ A
253
strate kept at 200 jC, in order to allow surface mobility, while limiting interfacial diffusion. The deposition rate, calibrated using a quartz crystal monitor and an ˚ s 1. The stacking sequence optical sensor, was 2.5 A ˚ (buffer of the multilayer is the following: Ru 200 A layer)/Mo30A˚/(Co10 A˚/Tb10 A˚)10/Co10 A˚/Mo30 A˚. The Co grows epitaxially and almost layer by layer on the buffer. The deposit of Tb induces additional streaks on the reflection high-energy electron diffraction (RHEED) patterns, which cannot be simply indexed. This indicated a bidimensional growth and a complex
Tb10 A˚]10 multilayer in the applied magnetic field of 12 kOe, as a function of
254
L. Louail et al. / Materials Letters 57 (2002) 252–259
Fig. 2. Rotational hysteresis loops as a function of temperature in applied field of 12 kOe.
reconstruction on the Co surface. To avoid all chemical contamination, especially oxidation, and to protect the ˚ thick Mo capping Tb, the sample is protected by a 30-A layer. The structure quality of the sample has been checked by in situ RHEED observation. The RHEED patterns exhibit thin and continuous streaks, which reveal a good crystalline quality of the samples. 2.2. Magnetization measurements Magnetization measurements were performed using a torque magnetometer that served for characterizing the magnetic anisotropy of the films. In this technique, the sample is suspended in a field and magnetized to saturation, so that the magnetization lies everywhere in the same easy direction, then the sample will rotate so that this easy direction is aligned with the field. A torque is exerted on the sample, causing it to rotate, and this would be equal to the torque, which would be acting on the magnetization vector, causing it to rotate into alignment with the field, if the sample was held clamped. The torque L per unit volume, is given by: L¼
@E @#
and therefore, the torque on the sample will be: L ¼ þDE=D#. In practice, the sample is set in a predetermined position and the field is applied. The torsion head is turned until the sample is brought back to its original position and, by separate calibration of the torsion head; this gives a direct reading of the torque exerted. In this paper, we confine our attention to the static rotational hysteresis, i.e., the energy required to rotate a ferromagnetic specimen through an angle of 360j in a magnetic field assuming that the rate of rotation is very low, i.e., a rotation of 360j in about 30 min. Magnetic field up to 12 kOe was applied perpendicularly to the film plane and the temperature changes from 35 K to room temperature. The rotational hysteresis energy is defined as the algebraic sum of the area enclosed between the positive and negative sections of the torque curve. Alternatively, if the field is rotated through 360j in the opposite direction, e.g., anticlockwise, the two torque curves enclose an area that is equal to twice the rotational hysteresis energy. Cc(h) and Cac(h) are the torque curves for clockwise and anticlockwise rotation of the applied field. A clockwise rotation through 360j was followed by an anticlockwise rotation through the same angle.
L. Louail et al. / Materials Letters 57 (2002) 252–259
3. Results and discussion As a function of temperature, the multilayer shows a complex magnetic behavior. The thermal behavior of the torque intensity curves in a magnetic field of 12 kOe perpendicularly applied to the film plane is shown in Fig. 1. At 35 K, the clockwise and the anticlockwise torque curves were identical, so that the rotational
Fig. 3. Magnetic torque experimental curves of [Co10
˚ A
255
hysteresis energy is nearly zero. The area enclosed between the torque curves is nil. The curves show two maxima, signs of energy equilibrium positions. When the temperature reaches 50 K, a very weak rotational hysteresis energy appears. The clockwise and the anticlockwise curves begin to be distinguishable from one another. Irreversibility begins to be observed. Above 75 K, torque curves take another shape. A rotational hysteresis loop is clearly present. The area
Tb10 A˚]10 multilayer at 100 K as a function of applied magnetic field.
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L. Louail et al. / Materials Letters 57 (2002) 252–259
between clockwise and the anticlockwise curves increases with increasing temperature. This area becomes more important at 100 K where the curves exhibit four instead of two maxima. Beyond 125 K, the clockwise and the anticlockwise torque curves restart to come closer and the area enclosed between these curves decreases. The reversibility appears again. Above 200 K, the torque curves do not enclose an area; the rotational hysteresis loop is no more observed. One can assign this phenomenon to the interface between Co and Tb layers. We have to assume that the Co layers induce a magnetic order in the Tb layers by a long-range coupling mechanism with a larger length than the thickness of the mixed interface. Indeed, Tb/ Co multilayers can contribute to a better understanding of the interface anisotropy. Both the broken symmetry at the boundaries of the layers—in the sense of Ne´el’s surface anisotropy—and the single ion anisotropy of the Tb—because of the anisotropic coordination at the interfaces between the Tb and Co layers—may be considered as the physical origin of the magnetic anisotropy and then rotational hysteresis. The change in torque curves with temperature can also be explained by an intrinsic variation of the bulk magnetocrystalline anisotropy as a function of temperature, for instance, related to thermal expansion or temperature dependence of magnetostriction coeffi-
cients, as discussed recently for tetragonaly distorted Ni/Cu(100) films [18]. It is also possible that the magnetic moment of the Co atoms at the interface decreases strongly with increasing temperature, so that the interface contribution (which favors in our films perpendicular easy axis) decreases faster than the dipolar interaction which induces a decrease of the effective second-order anisotropy. On the other hand, the thermal variations of torque curves can be related to the phenomenological aspect of the coherent rotation model as described by the equation: E ¼ MHcosðh uÞ þ Keff sin2 h þ K2 sin4 h h being the angle between the normal to sample and the magnetization and u the angle between the normal to sample and the applied magnetic field. The Keff and K2 parameters represent, respectively, the effective and second order anisotropy constants. In fact, a more rigorous treatment has also to consider the entropy related to the fluctuations of the magnetization direction as the temperature reaches a certain value [19 –24]. Since only the anisotropy constants have temperature dependence in the coherent rotation model, it is clear that they implicitly include entropy effects. More theoretical and experimental work would be necessary in order to disentangle the role of both effects.
Fig. 4. Rotational hysteresis loops as a function of applied magnetic field at 100 K.
L. Louail et al. / Materials Letters 57 (2002) 252–259
Contrary to the reversible torque curves that we found in Co/Pt multilayers [25 – 28], where we were able to determine the magnetocrystalline anisotropy constants, the irreversible torque curves are deduced from half the difference of the two clockwise and the anticlockwise contributions: CðhÞ ¼ ½Ca ðhÞ Cac ðhÞ=2 where Ca(h) and Cac(h) are the clockwise and the anticlockwise torque curves, respectively. This sepa-
257
ration between both reversible and irreversible contributions has been introduced by Meiklejohn and Bean [29]. As shown in Fig. 2, the irreversible contribution depends on the rotation angle of the applied magnetic field. The rotational hysteresis C(h) as a function of temperature exhibits very marked maxima along the different directions associated to anisotropy magnetocrystalline of the multilayer. It is therefore the sign of irreversible movements, which occur at the approach of these directions in the magnetic moments contained
Fig. 5. Rotational hysteresis magnitude as a function of both (a) the temperature and (b) the applied field.
258
L. Louail et al. / Materials Letters 57 (2002) 252–259
in the sample and that are not perfectly aligned with the applied field. The applied field being, in our experiences, always distinctly superior to the saturation field of Co layers, one can deduce that these irreversible movements take place inside the Tb layers. In order to establish the origin of the rotational hysteresis loops, we have examined the behavior of rotational hysteresis with the applied magnetic field. This study is carried out at 100 K and the used magnetic field ranges from 1 to 12 kOe, maximal value delivered by our electromagnet. We have plotted in Fig 3 the behavior of torque curves as a function of applied field. When the applied magnetic field is weak, the clockwise and the anticlockwise curves are identical. The curves are reversible. When the applied field increases, the area between clockwise and anticlockwise curves begins to appear at 6 kOe; the rotational hysteresis loop is observed and it increases with increasing applied filed up to 12 kOe. The modification of torque curves with increasing applied field results either from strain-induced effects [30] or from symmetry change of the Co atoms located at the upper interface [31] or has another electronic origin [32]. We think that it is probably due to Tb layers, because Tb/Co multilayers show a very interesting magnetic coupling behavior. Pure Tb is paramagnetic at room temperature (Tc = 219.5 K [33]). In multilayers which consist of alternating thin layers of pure Tb and Co, however, the Tb layers show a magnetic order with an antiferromagnetic coupling to the Co atoms, as it is well known from the TbCo alloys [34,35]. This magnetic coupling between the Tb and Co layers can be confirmed by the observation of compensation points, which directly indicate the antiferromagnetic coupling in these films. We show in Fig. 4 the variation of the rotational hysteresis loops as a function of the applied magnetic field. As indicated above, the Tb layers responsible for the change of rotational hysteresis with magnetic field significantly enhances the anisotropy of the film as well as its temperature coefficient because the adsorption of a small amount of a rare-earth element on Co ultra-thin films tends to favor perpendicular anisotropy, in agreement with results known for Co/ Tb multilayers [36,37]. We then focussed our interest on the magnitude of the rotational hysteresis curves as a function of both
temperature and magnetic field. As shown in Fig. 5(a), the magnitude is zero at low temperature because the area enclosed between the positive and negative sections of the torque curve is zero. The magnitude increases with increasing temperature and shows a maximum at 100 K, and then it decreases up to 200 K and becomes zero at high temperature. As a function of applied field, the magnitude of rotational hysteresis curves is zero at low field values, then it increases with increasing magnetic field in a nearly linear manner up to 12 kOe, as shown in Fig. 5(b). The full width at half the maximum (FWHM) of the rotational hysteresis curves also changes with both temperature and applied magnetic field. As shown in Fig. 6(a), FWHM is zero at 35 K; it reaches a maximum at 50 K, then decreases rapidly with increasing temperature. The same behavior is shown
Fig. 6. FWHM of rotational hysteresis maxima as a function of both (a) the temperature and (b) the applied magnetic field.
L. Louail et al. / Materials Letters 57 (2002) 252–259
in Fig. 6(b), as a function of applied magnetic field. The FWHM is zero at low field; it shows a maximum at 6 kOe, and then decreases with increasing the magnetic field.
4. Conclusion In this work, we have studied by means of torque magnetometer curves the magnetic anisotropy behavior of the [Co10 A˚Tb10 A˚]10 multilayer as a function of both the temperature and the applied magnetic field. These curves present a complex magnetic behavior. A rotational hysteresis appears that depends on temperature. We have assigned this phenomenon to the interface between Co and Tb layers and assumed that the Co layers induce a magnetic order in the Tb layers by a long-range coupling mechanism. We have also observed that the rotational hysteresis increases with increasing external field. We think that it is probably due to the role played by Tb layers in this multilayer.
Acknowledgements This work has been carried out at the ‘‘Institut de Physique et de Chimie des Mate´riaux de Strasbourg (France) in Groupe d’Etude des Mate´riaux Me´talliques’’. We would like to thank Dr. K. Ounadjela and Pr. H. Danan for stimulating discussions.
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