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Magnetic domain wall creep in the presence of an effective interlayer coupling field
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 320 (2008) 2571–2575 www.elsevier.com/locate/jmmm
Magnetic domain wall creep in the presence of an effective interlayer coupling field P.J. Metaxasa,b,, J.P. Jameta, J. Ferre´a, B. Rodmacqc, B. Dienyc, R.L. Stampsb a
Laboratoire de Physique des Solides, University of Paris-Sud, CNRS, UMR 8502, F-91405 Orsay Cedex, France b School of Physics, M013, University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia c SPINTEC, URA CNRS/CEA 2512, CEA-Grenoble, 38054 Grenoble Cedex 9, France Received 12 December 2007; received in revised form 26 February 2008 Available online 3 April 2008
Abstract We investigate thermally activated domain wall creep in a system consisting of two ultrathin Co layers with perpendicular anisotropy coupled antiferromagnetically through a 4 nm thick Pt spacer layer. The field driven dynamics of domain walls in the softer Co layer have been measured while keeping the harder Co layer negatively saturated. The effect of the interlayer interaction on the soft layer is interpreted in terms of an effective coupling field, H J , which results in an asymmetry between the domain wall speeds measured under positive and negative driving fields. We show that creep theory remains valid to describe the observed wall motion when the effective coupling field is included in the creep velocity law as a component of the total field acting on the wall. Using the resultant modified creep expression, we determine a value for the effective coupling field which is consistent with that measured from the shift of the soft layer’s minor hysteresis loop. The net antiferromagnetic coupling is attributed to a combination of RKKY and orange-peel coupling. r 2008 Elsevier B.V. All rights reserved. PACS: 75.60.Ch; 75.70.Cn; 62.20.Hg Keywords: Magnetic ultrathin films; Domain wall motion; Creep; Interlayer coupling; Magneto-optical Kerr microscopy
1. Introduction Magnetic multilayers are currently the subject of intense research, driven in a large part by magnetic memory applications [1]. Since domain wall motion is often the dominant reversal mechanism in these mutlilayer devices [2,3], it is important to understand how it is altered in such systems due, for example, to coupling between the multiple layers. However, while the dynamics of domain walls in continuous [4–8] and patterned [9–12] single layer films are rather well understood, the extent of quantitative measurements of domain wall dynamics in bilayer and multilayer magnetic systems remains quite limited [13–16], especially in systems with perpendicular anisotropy.
Corresponding author at: School of Physics, M013, University of Western Australia, 35 Stirling Hwy, Crawley WA 6009, Australia. E-mail address: [email protected] (P.J. Metaxas).
0304-8853/$ - see front matter r 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2008.03.041
The effect of an interlayer coupling of energy, J, is generally interpreted in terms of an effective coupling field [17,18]: HJ ¼
J M St
(1)
where M S and t are, respectively, the saturation magnetization and thickness of the layer upon which the coupling field is acting. While the coupling field may be measured macroscopically from the shift of the layer’s minor hysteresis loop (e.g. Refs. [17–19]), more local measurements which examine the effect of the coupling on the reversal processes that occur during hysteresis can potentially provide a more easily interpreted measurement of H J and subsequently J [20]. Fukumoto et al. [13] have measured viscous domain wall motion (motion for which pinning is negligible) in an in-plane magnetized NiFe layer in the presence of an effective coupling field resulting from coupling to a saturated Co layer. While the situation may
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be more complex in patterned structures [16] or when the other layers in the system are non-uniformly magnetized [15], there it was shown that H J could be considered simply as an additional component of the total effective field acting on the wall. Rather than viscous dynamics, here we examine thermally activated domain wall creep in the presence of an effective coupling field. We measure this motion in a Pt/ Co/Pt/Co/Pt system in which the two antiferromagnetically coupled Co layers both exhibit perpendicular anisotropy. In single layer ultrathin Pt/Co/Pt films [5,6,8,21], it has been shown that the motion of the narrow domain walls in such films is consistent with predictions of general theories for 1D elastic interfaces moving in 2D weakly disordered media [5,22–24]. This is due to these films’ strong perpendicular anisotropy, low Co layer thickness and inherent weak disorder (due to structural inhomogeneities [7]) as well as the intrinsic elasticity of the walls (due to their per-unit-length energy) which competes with the pinning and roughening effects of the disorder. Thermally activated domain wall creep occurs at low applied fields when the field alone is insufficient to overcome the pinning [22,23]. Here we shall examine how creep in the softer of the two Co layers is affected by coupling to the uniformly magnetized harder Co layer. This is an initial step toward experiments which examine domain wall dynamics in both of the coupled Co layers. We begin the paper by demonstrating that the net interlayer coupling in our film is antiferromagnetic and by obtaining an initial macroscopic measurement of H J from the horizontal shift of the soft layer’s minor hysteresis loop. We then show that the domain wall motion in the soft layer is consistent with creep theory when the effective coupling field resulting from the coupling to the hard layer is included in the creep law as a component of the total effective field acting on the wall. From these measurements we are able to obtain a value for H J , and subsequently J, based upon the effect the coupling has on the walls during their motion.
which is magnetically harder, consistent with results for single layer Pt/Co/Pt films [8]. In the inset of Fig. 1 we show the minor loop of the soft layer, obtained with the hard layer negatively saturated. The antiferromagnetic coupling to the hard layer results in a positive effective coupling field which acts on the soft layer (the sign of H J will depend on the orientation of the magnetization of the hard layer). This results in the observed leftward shift of the minor loop along the field axis. The shift gives us an initial macroscopic determination of the effective coupling field which we will denote by H hyst ¼ 3:9 2:1 Oe. Note that the shift was measured for J 4 different field sweep rates between 0:1 kOe=s and 0:8 kOe=s for which no sweep rate dependence was observable. Averaged, the four measurements yield H hyst ¼ 4 3 Oe. The significant percentage error is largely J due to the limited field resolution of the magnetometer.
2. Sample details and hysteresis
3. Domain wall dynamics
The sample was sputter deposited at room temperature onto an etched substrate and has the following structure: Si/SiO2/Pt(4.5 nm)/Co(0.5 nm)/Pt(4 nm)/Co(0.8 nm)/ Pt(3.5 nm). Out of plane hysteresis loops obtained using polar magneto-optical Kerr effect (PMOKE) magnetometry at room temperature are shown in Fig. 1. It can be seen from the major loop that the two Co layers, both exhibiting perpendicular anisotropy, switch separately at the rather low field sweep rate used for this measurement ð0:1 kOe=sÞ. The switch at 50 Oe can be identified with that of the 0.5 nm Co layer which intrinsically yields a smaller magneto-optic signal (attenuated further by the upper 0.8 nm Co layer and the Pt spacer and capping layers). The larger jump corresponds to the 0.8 nm layer
Having an initial macroscopic determination of the effective coupling field, we now examine the direct effect of the coupling on domain wall dynamics in the soft layer. The pinning potential experienced by the wall as it moves through the film is characterized by two parameters: U C , related to the height of the pinning barriers and H dep , the depinning field. The velocity of domain walls in isolated films in the low field creep regime ðH5H dep Þ is then predicted to depend on the applied field, H, as [22,23] U C H dep m v ¼ v0 exp (2) kB T H
Fig. 1. Major and minor polar Kerr rotation (PKR) hysteresis loops measured at l ¼ 543 nm with a field sweep rate of 0:1 kOe=s. The arrows represent the field cycling direction. The soft layer’s minor hysteresis loop is shown in the inset with the leftward horizontal loop shift (resulting from antiferromagnetic coupling to the negatively saturated hard layer) labeled as H hyst J .
where T is the temperature, v0 is a numerical prefactor and m is a universal exponent equal to 14 for a 1D interface
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moving in a 2D weakly disordered medium [25,26]. We will denote the field independent part of the energy barrier as E B ¼ U C H mdep . While the pinning potential, and hence U C and/or H dep , can be modified by the addition of structural defects [6], patterning [10] or exchange biasing [27], here only the field term of the creep law should be affected by the coupling field since H J will not, a priori, alter the disorder itself. Furthermore, although this is a bilayer system, walls exist only in one of the two Co layers and hence the system dimensionality is unchanged from the single layer case [5,8]. The magnetic domains in the soft layer were imaged at room temperature using a PMOKE microscope with a resolution of 0:4 mm and a field of view of 55 mm 83 mm. The differing strengths of the magneto-optic signals from the two Co layers allowed domains in each layer to be easily differentiated. In this way, we could ensure that the hard layer remained negatively saturated to match the conditions during the measurement of H hyst and avoid J additional magnetostatic coupling due to the existence of domains in the hard layer [15,28]. For each measurement of the velocity, v, of walls in the soft layer, we began with both layers negatively saturated. A short positive nucleating field pulse was then applied with an amplitude and duration such that reverse domains were nucleated solely in the soft layer. An image of the nucleated domains was then taken. A positive or negative field pulse was subsequently applied to displace the wall, after which a second image of the domain structure was taken. The displacement, and subsequently the wall velocity, could then be determined from the difference between the first and second image (Fig. 2). This was done for various values of the applied field to finally obtain the field dependence of the wall velocity. See Ref. [8] for further details. It was necessary to apply a negative offset field before and after the application of the field pulse used to displace the walls. If left in zero field, reverse domains in the soft layer would expand, their motion driven by the positive effective coupling field. Application of the offset field canceled the effect of the positive H J , thereby stabilizing the walls for imaging. The application of this offset field before and after the field pulse ensured that the observed wall displacement corresponded only to that occurring during the pulse. An offset field on the order of 5 Oe was sufficient for imaging purposes, consistent with H hyst J . Note
Fig. 2. Difference between PMOKE microscope domain images taken before and after the application of an applied field pulse, H. The dark region corresponds to the area swept out by a domain wall in the 0.5 nm Co layer during a field pulse.
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Fig. 3. Natural logarithm of the wall speed in the soft layer plotted against jHj1=4 for positive and negative applied fields. The inset shows the same 1=4 ln jvj data plotted against jH þ H wall with H wall ¼ 4:9 Oe. The linear J j J fit for jH þ H wall jo 300 Oe is shown as a solid line with gradient J E B =kB T 40.
that the applied field, H, was measured with respect to zero field, not with respect to the offset field. The wall velocity in the soft layer is shown in Fig. 3 where we plot ln jvj / jHj1=4 (since v is measured under both positive and negative applied fields). Eq. (2), which predicts a linear ln jvj H 1=4 data and which only takes into account the applied field and no additional effective fields, cannot be used to describe the observed velocity-field characteristics. The hard layer is kept negatively saturated meaning that H J is always positive. This results in the clear asymmetry between the H40 and Ho0 velocity data due to the relative directions of the applied field and the effective coupling field being different for the two data sets. For H40, H J reinforces the applied field, resulting in a larger wall speed than that which would be seen for a negative applied field of equal magnitude. For Ho0, H J works against the applied field resulting in a lower wall speed. We now modify the creep law (Eq. (2)) to include the effective coupling field, H J , as a component of the total effective field acting on the wall (as done for viscous domain wall motion [13]): m UC H dep jvj ¼ v0 exp (3) kB T jH þ H J j The modified expression is formally valid in the limit jH þ H J j5H dep . We test if we can reconcile the H40 and Ho0 data sets using this modified expression and in turn find a value for the effective coupling field acting on the walls during motion. This is done by treating H J in Eq. (3) as a fit parameter, plotting ln jvj against jH þ H J j1=4 for various values of H J . As shown in the inset of Fig. 3 the
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two data sets overlap when we set H J equal to 4:9 Oe with an uncertainty in the fitting process of about 0:2 Oe. However, the real error in the value of the coupling field is somewhat larger due to parasitic fields in the vicinity of the sample which are on the order of 1 Oe. Therefore, a more reasonable value for the coupling field as determined from the velocity experiments is H wall ¼ 4:9 1:2 Oe which is J consistent, within experimental error, with H hyst J . This consistency is not unexpected since H hyst has been J measured at a rather low field sweep rate for which wall propagation is expected to be the dominant reversal process [20,29]. The data in the inset of Fig. 3 (corrected by including H J ) is linear up to about 300 Oe, confirming the validity of the universal exponent m ¼ 14 for describing low field domain wall creep in the presence of an effective coupling field. Additionally as expected, E B does not show any appreciable dependence on the relative directions of H and H J since we are able to reconcile the two data sets with only the addition of H wall to the creep law (consistent with J the independently measured H hyst J ). We can determine a value for E B in the 0.5 nm layer from a linear fit to the corrected low field data. This yields a value of 40kB T which is quite consistent with that measured in a similar single Pt/Co(0.5 nm)/Pt film for which E B was found to be 35kB T [8].
4. Interlayer coupling energy The interlayer coupling energy, J, can be calculated using Eq. (1) with H J ¼ H wall and t ¼ 0:5 nm. The J saturation magnetization of the soft layer was determined from an out of plane hysteresis loop obtained using a quantum design MPMS SQUID magnetometer, yielding a value of approximately 1100 emu=cm3 . This gives an antiferromagnetic coupling energy of J 0:28 103 erg=cm2 , the magnitude of which is quite consistent with that found via the H hyst method for coupled Pt/Co J stacks with perpendicular anisotropy at a similar Pt spacer thickness [30]. We note, however, that such weak interlayer coupling will not always have a large effect on dynamics: the significant soft layer domain wall velocity of 107 m=s observed here in zero applied field (driven purely by H J ) is due to the layer’s low E B . The net antiferromagnetic interlayer coupling which is observed here is not a common result in Pt/Co systems [28,30–34] where it is thought that both orange peel (OP) [30] and RKKY [35,36] couplings contribute to the total net coupling [30]. We have observed a change to ferromagnetic interlayer coupling on reducing the temperature in preliminary temperature dependent measurements. This is indeed consistent with the co-existence of two types of coupling with different temperature dependencies (such as OP and RKKY), the antiferromagnetic coupling being dominant at room temperature and the ferromagnetic coupling dominant at low temperature.
5. Conclusion In conclusion, we have measured domain wall dynamics in the magnetically softer Co layer of a Pt/Co/Pt/Co/Pt system with perpendicular anisotropy under the influence of an antiferromagnetic interlayer coupling to the saturated, magnetically harder Co layer. We demonstrate that creep theory can be used to describe the observed wall motion for fields jH þ H J j5H dep by including the resultant effective coupling field, H J , as a component of the total effective field which acts on the wall, as previously done for viscous domain wall motion [13]. In doing so, we determine a value for the effective coupling field (and subsequently the interlayer coupling energy), consistent with that measured from the shift of the soft layer’s minor hysteresis loop obtained using optical magnetometry. There was no appreciable change in the universal dynamic creep exponent, m ¼ 14, nor any observable dependence of U C or H dep (which characterize the disorder-induced pinning potential) on the relative directions of H and H J . The results presented here are a first step toward measurements on coupled bilayers in which there are domain walls in both Co layers which interact with one another during motion. Such experiments, in which the interlayer coupling and the driving field can be rather easily controlled (see, for example, Ref. [30]), have much potential in terms of contributing to the understanding of the dynamics of coupled elastic interfaces in disordered media [37,38].
Acknowledgments P.J.M. acknowledges the support of an Australian Postgraduate Award and a Marie Curie Early Stage Training Fellowship (MEST-CT-2004-514307). P.J.M., J.F. and R.L.S. acknowledge the support of the FAST program (French-Australian Science and Technology). P.J.M. and R.L.S. acknowledge support from the Australian Research Council. The authors would also like to thank V. Baltz and A. Mougin for useful discussions.
References [1] C. Chappert, A. Fert, F. Nguyen van Dau, Nat. Mater. 6 (2007) 813. [2] L. Thomas, M.G. Samant, S.S.P. Parkin, Phys. Rev. Lett. 84 (2000) 1816. [3] R.D. McMichael, J. Eicke, M.J. Donahue, D.G. Porter, J. Appl. Phys. 87 (2000) 7058. [4] A.P. Malozemoff, J.C. Slonczewski, Magnetic Domain Walls in Bubble Materials, Academic Press, New York, 1979. [5] S. Lemerle, J. Ferre´, C. Chappert, V. Mathet, T. Giamarchi, P. Le Doussal, Phys. Rev. Lett. 80 (1998) 849. [6] L. Krusin-Elbaum, T. Shibauchi, B. Argyle, L. Gignac, D. Weller, Nature 410 (2001) 444. [7] J. Ferre´, in: B. Hillebrands, K. Ounadjela (Eds.), Spin Dynamics in Confined Magnetic Structures I, vol. 83, Springer, Berlin, Heidelberg, 2002, p. 127.
ARTICLE IN PRESS P.J. Metaxas et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 2571–2575 [8] P.J. Metaxas, J.P. Jamet, A. Mougin, M. Cormier, J. Ferre´, V. Baltz, B. Rodmacq, B. Dieny, R.L. Stamps, Phys. Rev. Lett. 99 (2007) 217208. [9] J.P. Jamet, J. Ferre´, P. Meyer, J. Gierak, C. Vieu, F. Rousseaux, C. Chappert, V. Mathet, IEEE Trans. Magn. 37 (2001) 2120. [10] F. Cayssol, D. Ravelosona, C. Chappert, J. Ferre´, J.P. Jamet, Phys. Rev. Lett. 92 (2004) 107202. [11] G.S.D. Beach, C. Nistor, C. Knutson, M. Tsoi, J.L. Erskine, Nat. Mater. 4 (2005) 741. [12] M. Hayashi, L. Thomas, C. Rettner, R. Moriya, S.S.P. Parkin, Nat. Phys. 3 (2007) 21. [13] K. Fukumoto, W. Kuch, J. Vogel, J. Camarero, S. Pizzini, F. Offi, Y. Pennec, M. Bonfim, A. Fontaine, J. Kirschner, J. Magn. Magn. Mater. 293 (2005) 863. [14] K. Fukumoto, W. Kuch, J. Vogel, F. Romanens, S. Pizzini, J. Camarero, M. Bonfim, J. Kirschner, Phys. Rev. Lett. 96 (2006) 097204. [15] S. Wiebel, J.P. Jamet, N. Vernier, A. Mougin, J. Ferre´, V. Baltz, B. Rodmacq, B. Dieny, J. Appl. Phys. 100 (2006) 043912. [16] J. Briones, F. Montaigne, D. Lacour, M. Hehn, M.J. Carey, J.R. Childress, Appl. Phys. Lett. 92 (2008) 032508. [17] V. Grolier, D. Renard, B. Bartenlian, P. Beauvillain, C. Chappert, C. Dupas, J. Ferre´, M. Galtier, E. Kolb, M. Mulloy, J.P. Renard, P. Veillet, Phys. Rev. Lett. 71 (1993) 3023. [18] P.A.A. van der Heijden, P.J.H. Bloemen, J.M. Matselaar, R.M. Wolf, J.M. Gaines, J.T.W.M. van Eemeren, P.J. van der Zaag, W.J.M. de Jonge, Phys. Rev. B 55 (1997) 11569. [19] Z.Y. Liu, G.H. Yu, Z.C. Wang, Phys. Rev. B 72 (2005) 064451. [20] Y. Pennec, J. Camarero, J.C. Toussaint, S. Pizzini, M. Bonfim, F. Petroff, W. Kuch, F. Offi, K. Fukumoto, F. Nguyen Van Dau, J. Vogel, Phys. Rev. B 69 (2004) 180402 (R). [21] W. Kleemann, J. Rhensius, O. Petracic, J. Ferre´, J.P. Jamet, H. Bernas, Phys. Rev. Lett. 99 (2007) 097203.
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[22] G. Blatter, M.V. Feigel’man, V.B. Geshkenbien, A.I. Larkin, V.M. Vinokur, Rev. Mod. Phys. 66 (1994) 1125. [23] P. Chauve, T. Giamarchi, P. Le Doussal, Phys. Rev. B 62 (2000) 6241. [24] T. Nattermann, V. Pokrovsky, V.M. Vinokur, Phys. Rev. Lett. 87 (2001) 197005. [25] D.A. Huse, C.L. Henley, Phys. Rev. Lett. 54 (1985) 2708. [26] D.A. Huse, C.L. Henley, D.S. Fisher, Phys. Rev. Lett. 55 (1985) 2924. [27] J.L. Menendez, D. Ravelosona, C. Chappert, R. Stamps, in: Digests of the IEEE International Magnetics Conference, INTERMAG Asia, 2005, p. 1637. [28] S. Wiebel, J.P. Jamet, N. Vernier, A. Mougin, J. Ferre´, V. Baltz, B. Rodmacq, B. Dieny, Appl. Phys. Lett. 86 (2005) 142502. [29] B. Raquet, M.D. Ortega, M. Goiran, A.R. Fert, J.P. Redoules, R. Mamy, J.C. Ousset, A. Sdaq, A. Khmou, J. Magn. Magn. Mater. 150 (1995) L5. [30] J. Moritz, F. Garcia, J.C. Toussaint, B. Dieny, J.P. Nozie`res, Europhys. Lett. 65 (2004) 123. [31] V. Baltz, A. Marty, B. Rodmacq, B. Dieny, Phys. Rev. B 75 (2007) 014406. [32] K. Le Dang, P. Veillet, C. Chappert, R.F.C. Farrow, R.F. Marks, D. Weller, A. Cebollada, Phys. Rev. B 50 (1994) 200. [33] F. Garcia, J. Moritz, F. Ernult, S. Auffret, B. Rodmacq, B. Dieny, J. Camarero, Y. Pennec, S. Pizzini, J. Vogel, IEEE Trans. Magn. 38 (2002) 2730. [34] S.S.P. Parkin, Phys. Rev. Lett. 67 (1991) 3598. [35] P. Bruno, C. Chappert, Phys. Rev. Lett. 67 (1991) 1602. [36] P. Bruno, Phys. Rev. B 52 (1) (1995) 411. [37] A.L. Baraba´si, Phys. Rev. A 46 (1992) R2977. [38] A.S. Balankin, R.G. Paredes, O. Susarrey, D. Morales, F.C. Vacio, Phys. Rev. Lett. 96 (2006) 056101.
Journal of Magnetism and Magnetic Materials 320 (2008) 2571–2575 www.elsevier.com/locate/jmmm
Magnetic domain wall creep in the presence of an effective interlayer coupling field P.J. Metaxasa,b,, J.P. Jameta, J. Ferre´a, B. Rodmacqc, B. Dienyc, R.L. Stampsb a
Laboratoire de Physique des Solides, University of Paris-Sud, CNRS, UMR 8502, F-91405 Orsay Cedex, France b School of Physics, M013, University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia c SPINTEC, URA CNRS/CEA 2512, CEA-Grenoble, 38054 Grenoble Cedex 9, France Received 12 December 2007; received in revised form 26 February 2008 Available online 3 April 2008
Abstract We investigate thermally activated domain wall creep in a system consisting of two ultrathin Co layers with perpendicular anisotropy coupled antiferromagnetically through a 4 nm thick Pt spacer layer. The field driven dynamics of domain walls in the softer Co layer have been measured while keeping the harder Co layer negatively saturated. The effect of the interlayer interaction on the soft layer is interpreted in terms of an effective coupling field, H J , which results in an asymmetry between the domain wall speeds measured under positive and negative driving fields. We show that creep theory remains valid to describe the observed wall motion when the effective coupling field is included in the creep velocity law as a component of the total field acting on the wall. Using the resultant modified creep expression, we determine a value for the effective coupling field which is consistent with that measured from the shift of the soft layer’s minor hysteresis loop. The net antiferromagnetic coupling is attributed to a combination of RKKY and orange-peel coupling. r 2008 Elsevier B.V. All rights reserved. PACS: 75.60.Ch; 75.70.Cn; 62.20.Hg Keywords: Magnetic ultrathin films; Domain wall motion; Creep; Interlayer coupling; Magneto-optical Kerr microscopy
1. Introduction Magnetic multilayers are currently the subject of intense research, driven in a large part by magnetic memory applications [1]. Since domain wall motion is often the dominant reversal mechanism in these mutlilayer devices [2,3], it is important to understand how it is altered in such systems due, for example, to coupling between the multiple layers. However, while the dynamics of domain walls in continuous [4–8] and patterned [9–12] single layer films are rather well understood, the extent of quantitative measurements of domain wall dynamics in bilayer and multilayer magnetic systems remains quite limited [13–16], especially in systems with perpendicular anisotropy.
Corresponding author at: School of Physics, M013, University of Western Australia, 35 Stirling Hwy, Crawley WA 6009, Australia. E-mail address: [email protected] (P.J. Metaxas).
0304-8853/$ - see front matter r 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2008.03.041
The effect of an interlayer coupling of energy, J, is generally interpreted in terms of an effective coupling field [17,18]: HJ ¼
J M St
(1)
where M S and t are, respectively, the saturation magnetization and thickness of the layer upon which the coupling field is acting. While the coupling field may be measured macroscopically from the shift of the layer’s minor hysteresis loop (e.g. Refs. [17–19]), more local measurements which examine the effect of the coupling on the reversal processes that occur during hysteresis can potentially provide a more easily interpreted measurement of H J and subsequently J [20]. Fukumoto et al. [13] have measured viscous domain wall motion (motion for which pinning is negligible) in an in-plane magnetized NiFe layer in the presence of an effective coupling field resulting from coupling to a saturated Co layer. While the situation may
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be more complex in patterned structures [16] or when the other layers in the system are non-uniformly magnetized [15], there it was shown that H J could be considered simply as an additional component of the total effective field acting on the wall. Rather than viscous dynamics, here we examine thermally activated domain wall creep in the presence of an effective coupling field. We measure this motion in a Pt/ Co/Pt/Co/Pt system in which the two antiferromagnetically coupled Co layers both exhibit perpendicular anisotropy. In single layer ultrathin Pt/Co/Pt films [5,6,8,21], it has been shown that the motion of the narrow domain walls in such films is consistent with predictions of general theories for 1D elastic interfaces moving in 2D weakly disordered media [5,22–24]. This is due to these films’ strong perpendicular anisotropy, low Co layer thickness and inherent weak disorder (due to structural inhomogeneities [7]) as well as the intrinsic elasticity of the walls (due to their per-unit-length energy) which competes with the pinning and roughening effects of the disorder. Thermally activated domain wall creep occurs at low applied fields when the field alone is insufficient to overcome the pinning [22,23]. Here we shall examine how creep in the softer of the two Co layers is affected by coupling to the uniformly magnetized harder Co layer. This is an initial step toward experiments which examine domain wall dynamics in both of the coupled Co layers. We begin the paper by demonstrating that the net interlayer coupling in our film is antiferromagnetic and by obtaining an initial macroscopic measurement of H J from the horizontal shift of the soft layer’s minor hysteresis loop. We then show that the domain wall motion in the soft layer is consistent with creep theory when the effective coupling field resulting from the coupling to the hard layer is included in the creep law as a component of the total effective field acting on the wall. From these measurements we are able to obtain a value for H J , and subsequently J, based upon the effect the coupling has on the walls during their motion.
which is magnetically harder, consistent with results for single layer Pt/Co/Pt films [8]. In the inset of Fig. 1 we show the minor loop of the soft layer, obtained with the hard layer negatively saturated. The antiferromagnetic coupling to the hard layer results in a positive effective coupling field which acts on the soft layer (the sign of H J will depend on the orientation of the magnetization of the hard layer). This results in the observed leftward shift of the minor loop along the field axis. The shift gives us an initial macroscopic determination of the effective coupling field which we will denote by H hyst ¼ 3:9 2:1 Oe. Note that the shift was measured for J 4 different field sweep rates between 0:1 kOe=s and 0:8 kOe=s for which no sweep rate dependence was observable. Averaged, the four measurements yield H hyst ¼ 4 3 Oe. The significant percentage error is largely J due to the limited field resolution of the magnetometer.
2. Sample details and hysteresis
3. Domain wall dynamics
The sample was sputter deposited at room temperature onto an etched substrate and has the following structure: Si/SiO2/Pt(4.5 nm)/Co(0.5 nm)/Pt(4 nm)/Co(0.8 nm)/ Pt(3.5 nm). Out of plane hysteresis loops obtained using polar magneto-optical Kerr effect (PMOKE) magnetometry at room temperature are shown in Fig. 1. It can be seen from the major loop that the two Co layers, both exhibiting perpendicular anisotropy, switch separately at the rather low field sweep rate used for this measurement ð0:1 kOe=sÞ. The switch at 50 Oe can be identified with that of the 0.5 nm Co layer which intrinsically yields a smaller magneto-optic signal (attenuated further by the upper 0.8 nm Co layer and the Pt spacer and capping layers). The larger jump corresponds to the 0.8 nm layer
Having an initial macroscopic determination of the effective coupling field, we now examine the direct effect of the coupling on domain wall dynamics in the soft layer. The pinning potential experienced by the wall as it moves through the film is characterized by two parameters: U C , related to the height of the pinning barriers and H dep , the depinning field. The velocity of domain walls in isolated films in the low field creep regime ðH5H dep Þ is then predicted to depend on the applied field, H, as [22,23] U C H dep m v ¼ v0 exp (2) kB T H
Fig. 1. Major and minor polar Kerr rotation (PKR) hysteresis loops measured at l ¼ 543 nm with a field sweep rate of 0:1 kOe=s. The arrows represent the field cycling direction. The soft layer’s minor hysteresis loop is shown in the inset with the leftward horizontal loop shift (resulting from antiferromagnetic coupling to the negatively saturated hard layer) labeled as H hyst J .
where T is the temperature, v0 is a numerical prefactor and m is a universal exponent equal to 14 for a 1D interface
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moving in a 2D weakly disordered medium [25,26]. We will denote the field independent part of the energy barrier as E B ¼ U C H mdep . While the pinning potential, and hence U C and/or H dep , can be modified by the addition of structural defects [6], patterning [10] or exchange biasing [27], here only the field term of the creep law should be affected by the coupling field since H J will not, a priori, alter the disorder itself. Furthermore, although this is a bilayer system, walls exist only in one of the two Co layers and hence the system dimensionality is unchanged from the single layer case [5,8]. The magnetic domains in the soft layer were imaged at room temperature using a PMOKE microscope with a resolution of 0:4 mm and a field of view of 55 mm 83 mm. The differing strengths of the magneto-optic signals from the two Co layers allowed domains in each layer to be easily differentiated. In this way, we could ensure that the hard layer remained negatively saturated to match the conditions during the measurement of H hyst and avoid J additional magnetostatic coupling due to the existence of domains in the hard layer [15,28]. For each measurement of the velocity, v, of walls in the soft layer, we began with both layers negatively saturated. A short positive nucleating field pulse was then applied with an amplitude and duration such that reverse domains were nucleated solely in the soft layer. An image of the nucleated domains was then taken. A positive or negative field pulse was subsequently applied to displace the wall, after which a second image of the domain structure was taken. The displacement, and subsequently the wall velocity, could then be determined from the difference between the first and second image (Fig. 2). This was done for various values of the applied field to finally obtain the field dependence of the wall velocity. See Ref. [8] for further details. It was necessary to apply a negative offset field before and after the application of the field pulse used to displace the walls. If left in zero field, reverse domains in the soft layer would expand, their motion driven by the positive effective coupling field. Application of the offset field canceled the effect of the positive H J , thereby stabilizing the walls for imaging. The application of this offset field before and after the field pulse ensured that the observed wall displacement corresponded only to that occurring during the pulse. An offset field on the order of 5 Oe was sufficient for imaging purposes, consistent with H hyst J . Note
Fig. 2. Difference between PMOKE microscope domain images taken before and after the application of an applied field pulse, H. The dark region corresponds to the area swept out by a domain wall in the 0.5 nm Co layer during a field pulse.
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Fig. 3. Natural logarithm of the wall speed in the soft layer plotted against jHj1=4 for positive and negative applied fields. The inset shows the same 1=4 ln jvj data plotted against jH þ H wall with H wall ¼ 4:9 Oe. The linear J j J fit for jH þ H wall jo 300 Oe is shown as a solid line with gradient J E B =kB T 40.
that the applied field, H, was measured with respect to zero field, not with respect to the offset field. The wall velocity in the soft layer is shown in Fig. 3 where we plot ln jvj / jHj1=4 (since v is measured under both positive and negative applied fields). Eq. (2), which predicts a linear ln jvj H 1=4 data and which only takes into account the applied field and no additional effective fields, cannot be used to describe the observed velocity-field characteristics. The hard layer is kept negatively saturated meaning that H J is always positive. This results in the clear asymmetry between the H40 and Ho0 velocity data due to the relative directions of the applied field and the effective coupling field being different for the two data sets. For H40, H J reinforces the applied field, resulting in a larger wall speed than that which would be seen for a negative applied field of equal magnitude. For Ho0, H J works against the applied field resulting in a lower wall speed. We now modify the creep law (Eq. (2)) to include the effective coupling field, H J , as a component of the total effective field acting on the wall (as done for viscous domain wall motion [13]): m UC H dep jvj ¼ v0 exp (3) kB T jH þ H J j The modified expression is formally valid in the limit jH þ H J j5H dep . We test if we can reconcile the H40 and Ho0 data sets using this modified expression and in turn find a value for the effective coupling field acting on the walls during motion. This is done by treating H J in Eq. (3) as a fit parameter, plotting ln jvj against jH þ H J j1=4 for various values of H J . As shown in the inset of Fig. 3 the
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two data sets overlap when we set H J equal to 4:9 Oe with an uncertainty in the fitting process of about 0:2 Oe. However, the real error in the value of the coupling field is somewhat larger due to parasitic fields in the vicinity of the sample which are on the order of 1 Oe. Therefore, a more reasonable value for the coupling field as determined from the velocity experiments is H wall ¼ 4:9 1:2 Oe which is J consistent, within experimental error, with H hyst J . This consistency is not unexpected since H hyst has been J measured at a rather low field sweep rate for which wall propagation is expected to be the dominant reversal process [20,29]. The data in the inset of Fig. 3 (corrected by including H J ) is linear up to about 300 Oe, confirming the validity of the universal exponent m ¼ 14 for describing low field domain wall creep in the presence of an effective coupling field. Additionally as expected, E B does not show any appreciable dependence on the relative directions of H and H J since we are able to reconcile the two data sets with only the addition of H wall to the creep law (consistent with J the independently measured H hyst J ). We can determine a value for E B in the 0.5 nm layer from a linear fit to the corrected low field data. This yields a value of 40kB T which is quite consistent with that measured in a similar single Pt/Co(0.5 nm)/Pt film for which E B was found to be 35kB T [8].
4. Interlayer coupling energy The interlayer coupling energy, J, can be calculated using Eq. (1) with H J ¼ H wall and t ¼ 0:5 nm. The J saturation magnetization of the soft layer was determined from an out of plane hysteresis loop obtained using a quantum design MPMS SQUID magnetometer, yielding a value of approximately 1100 emu=cm3 . This gives an antiferromagnetic coupling energy of J 0:28 103 erg=cm2 , the magnitude of which is quite consistent with that found via the H hyst method for coupled Pt/Co J stacks with perpendicular anisotropy at a similar Pt spacer thickness [30]. We note, however, that such weak interlayer coupling will not always have a large effect on dynamics: the significant soft layer domain wall velocity of 107 m=s observed here in zero applied field (driven purely by H J ) is due to the layer’s low E B . The net antiferromagnetic interlayer coupling which is observed here is not a common result in Pt/Co systems [28,30–34] where it is thought that both orange peel (OP) [30] and RKKY [35,36] couplings contribute to the total net coupling [30]. We have observed a change to ferromagnetic interlayer coupling on reducing the temperature in preliminary temperature dependent measurements. This is indeed consistent with the co-existence of two types of coupling with different temperature dependencies (such as OP and RKKY), the antiferromagnetic coupling being dominant at room temperature and the ferromagnetic coupling dominant at low temperature.
5. Conclusion In conclusion, we have measured domain wall dynamics in the magnetically softer Co layer of a Pt/Co/Pt/Co/Pt system with perpendicular anisotropy under the influence of an antiferromagnetic interlayer coupling to the saturated, magnetically harder Co layer. We demonstrate that creep theory can be used to describe the observed wall motion for fields jH þ H J j5H dep by including the resultant effective coupling field, H J , as a component of the total effective field which acts on the wall, as previously done for viscous domain wall motion [13]. In doing so, we determine a value for the effective coupling field (and subsequently the interlayer coupling energy), consistent with that measured from the shift of the soft layer’s minor hysteresis loop obtained using optical magnetometry. There was no appreciable change in the universal dynamic creep exponent, m ¼ 14, nor any observable dependence of U C or H dep (which characterize the disorder-induced pinning potential) on the relative directions of H and H J . The results presented here are a first step toward measurements on coupled bilayers in which there are domain walls in both Co layers which interact with one another during motion. Such experiments, in which the interlayer coupling and the driving field can be rather easily controlled (see, for example, Ref. [30]), have much potential in terms of contributing to the understanding of the dynamics of coupled elastic interfaces in disordered media [37,38].
Acknowledgments P.J.M. acknowledges the support of an Australian Postgraduate Award and a Marie Curie Early Stage Training Fellowship (MEST-CT-2004-514307). P.J.M., J.F. and R.L.S. acknowledge the support of the FAST program (French-Australian Science and Technology). P.J.M. and R.L.S. acknowledge support from the Australian Research Council. The authors would also like to thank V. Baltz and A. Mougin for useful discussions.
References [1] C. Chappert, A. Fert, F. Nguyen van Dau, Nat. Mater. 6 (2007) 813. [2] L. Thomas, M.G. Samant, S.S.P. Parkin, Phys. Rev. Lett. 84 (2000) 1816. [3] R.D. McMichael, J. Eicke, M.J. Donahue, D.G. Porter, J. Appl. Phys. 87 (2000) 7058. [4] A.P. Malozemoff, J.C. Slonczewski, Magnetic Domain Walls in Bubble Materials, Academic Press, New York, 1979. [5] S. Lemerle, J. Ferre´, C. Chappert, V. Mathet, T. Giamarchi, P. Le Doussal, Phys. Rev. Lett. 80 (1998) 849. [6] L. Krusin-Elbaum, T. Shibauchi, B. Argyle, L. Gignac, D. Weller, Nature 410 (2001) 444. [7] J. Ferre´, in: B. Hillebrands, K. Ounadjela (Eds.), Spin Dynamics in Confined Magnetic Structures I, vol. 83, Springer, Berlin, Heidelberg, 2002, p. 127.
ARTICLE IN PRESS P.J. Metaxas et al. / Journal of Magnetism and Magnetic Materials 320 (2008) 2571–2575 [8] P.J. Metaxas, J.P. Jamet, A. Mougin, M. Cormier, J. Ferre´, V. Baltz, B. Rodmacq, B. Dieny, R.L. Stamps, Phys. Rev. Lett. 99 (2007) 217208. [9] J.P. Jamet, J. Ferre´, P. Meyer, J. Gierak, C. Vieu, F. Rousseaux, C. Chappert, V. Mathet, IEEE Trans. Magn. 37 (2001) 2120. [10] F. Cayssol, D. Ravelosona, C. Chappert, J. Ferre´, J.P. Jamet, Phys. Rev. Lett. 92 (2004) 107202. [11] G.S.D. Beach, C. Nistor, C. Knutson, M. Tsoi, J.L. Erskine, Nat. Mater. 4 (2005) 741. [12] M. Hayashi, L. Thomas, C. Rettner, R. Moriya, S.S.P. Parkin, Nat. Phys. 3 (2007) 21. [13] K. Fukumoto, W. Kuch, J. Vogel, J. Camarero, S. Pizzini, F. Offi, Y. Pennec, M. Bonfim, A. Fontaine, J. Kirschner, J. Magn. Magn. Mater. 293 (2005) 863. [14] K. Fukumoto, W. Kuch, J. Vogel, F. Romanens, S. Pizzini, J. Camarero, M. Bonfim, J. Kirschner, Phys. Rev. Lett. 96 (2006) 097204. [15] S. Wiebel, J.P. Jamet, N. Vernier, A. Mougin, J. Ferre´, V. Baltz, B. Rodmacq, B. Dieny, J. Appl. Phys. 100 (2006) 043912. [16] J. Briones, F. Montaigne, D. Lacour, M. Hehn, M.J. Carey, J.R. Childress, Appl. Phys. Lett. 92 (2008) 032508. [17] V. Grolier, D. Renard, B. Bartenlian, P. Beauvillain, C. Chappert, C. Dupas, J. Ferre´, M. Galtier, E. Kolb, M. Mulloy, J.P. Renard, P. Veillet, Phys. Rev. Lett. 71 (1993) 3023. [18] P.A.A. van der Heijden, P.J.H. Bloemen, J.M. Matselaar, R.M. Wolf, J.M. Gaines, J.T.W.M. van Eemeren, P.J. van der Zaag, W.J.M. de Jonge, Phys. Rev. B 55 (1997) 11569. [19] Z.Y. Liu, G.H. Yu, Z.C. Wang, Phys. Rev. B 72 (2005) 064451. [20] Y. Pennec, J. Camarero, J.C. Toussaint, S. Pizzini, M. Bonfim, F. Petroff, W. Kuch, F. Offi, K. Fukumoto, F. Nguyen Van Dau, J. Vogel, Phys. Rev. B 69 (2004) 180402 (R). [21] W. Kleemann, J. Rhensius, O. Petracic, J. Ferre´, J.P. Jamet, H. Bernas, Phys. Rev. Lett. 99 (2007) 097203.
2575
[22] G. Blatter, M.V. Feigel’man, V.B. Geshkenbien, A.I. Larkin, V.M. Vinokur, Rev. Mod. Phys. 66 (1994) 1125. [23] P. Chauve, T. Giamarchi, P. Le Doussal, Phys. Rev. B 62 (2000) 6241. [24] T. Nattermann, V. Pokrovsky, V.M. Vinokur, Phys. Rev. Lett. 87 (2001) 197005. [25] D.A. Huse, C.L. Henley, Phys. Rev. Lett. 54 (1985) 2708. [26] D.A. Huse, C.L. Henley, D.S. Fisher, Phys. Rev. Lett. 55 (1985) 2924. [27] J.L. Menendez, D. Ravelosona, C. Chappert, R. Stamps, in: Digests of the IEEE International Magnetics Conference, INTERMAG Asia, 2005, p. 1637. [28] S. Wiebel, J.P. Jamet, N. Vernier, A. Mougin, J. Ferre´, V. Baltz, B. Rodmacq, B. Dieny, Appl. Phys. Lett. 86 (2005) 142502. [29] B. Raquet, M.D. Ortega, M. Goiran, A.R. Fert, J.P. Redoules, R. Mamy, J.C. Ousset, A. Sdaq, A. Khmou, J. Magn. Magn. Mater. 150 (1995) L5. [30] J. Moritz, F. Garcia, J.C. Toussaint, B. Dieny, J.P. Nozie`res, Europhys. Lett. 65 (2004) 123. [31] V. Baltz, A. Marty, B. Rodmacq, B. Dieny, Phys. Rev. B 75 (2007) 014406. [32] K. Le Dang, P. Veillet, C. Chappert, R.F.C. Farrow, R.F. Marks, D. Weller, A. Cebollada, Phys. Rev. B 50 (1994) 200. [33] F. Garcia, J. Moritz, F. Ernult, S. Auffret, B. Rodmacq, B. Dieny, J. Camarero, Y. Pennec, S. Pizzini, J. Vogel, IEEE Trans. Magn. 38 (2002) 2730. [34] S.S.P. Parkin, Phys. Rev. Lett. 67 (1991) 3598. [35] P. Bruno, C. Chappert, Phys. Rev. Lett. 67 (1991) 1602. [36] P. Bruno, Phys. Rev. B 52 (1) (1995) 411. [37] A.L. Baraba´si, Phys. Rev. A 46 (1992) R2977. [38] A.S. Balankin, R.G. Paredes, O. Susarrey, D. Morales, F.C. Vacio, Phys. Rev. Lett. 96 (2006) 056101.