Journal of Magnetism and Magnetic Materials 240 (2002) 30–33
Detection of domain wall propagation in a mesoscopic wire F. Cayssola,*, D. Ravelosonaa, J. Wunderlicha, C. Chapperta, V. Matheta, J.-P. Jametb, J. Ferre! b a
Institut d’Electronique Fondamentale (IEF), UMR CNRS 8622, Universite! Paris Sud, Batiment 220 91405 Orsay, France b Laboratoire de Physique des solides, UMR CNRS 8602, Universite! Paris Sud, 91405 Orsay, France
Abstract Extraordinary Hall effect was used to detect the propagation of a domain wall in magnetic devices patterned in sputter grown Pt/Co(1 nm)/Pt sandwiches with perpendicular easy magnetization axis. In such films, domain walls propagate as coherent 1D nano-object in a 2D medium with weak fluctuation energy density. In a patterned device, the competition between global wall energy and Zeeman energy strongly influences the wall propagation. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Domain wall propagation; Extraordinary Hall effect; Magnetic ultra-thin films; Perpendicular anisotropy
Recently, the dynamics of magnetic switching processes in patterned magnetic elements has become an updated topic. In particular, the effect of geometry such as the shape or the size of the patterned structure should have a strong influence on the dynamical properties of a domain wall (DW). Therefore, high sensitivity real-time detection of DW motion is of great importance. Recently, the propagation of a magnetic DW in a submicron magnetic wire magnetized in-plane was investigated by using the giant magnetoresistance (GMR) effect [1]. Here, we use extraordinary Hall effect (EHE) [2] to detect the propagation of a single domain wall in micron size perpendicularly magnetized cross and wires. For our experiments we use sputter grown epitaxial Pt(3.4 nm)/Co(tCo=1 nm)/Pt(4.5 nm)/Al2O3 ultra-thin films with high perpendicular anisotropy (Ku B1 107 erg/cm3). In such films, the magnetization reversal is dominated by easy DW propagation, following rare nucleation events located on large extrinsic defects [3]. Hence, the propagation field Hpi is much smaller than the nucleation field, which gives rise to very square hysteresis loops. Single- or double- (Fig. 4(a)) symmetric Hall cross devices with 2–0.5 mm width were then patterned using electron beam lithography and ion beam etching. In *Corresponding author. E-mail address:
[email protected] (F. Cayssol).
order to have a single DW propagating in the device, we control the nucleation of a single reversed domain outside the cross by adjoining a large nucleation area to one of the current wires of the cross [4]. Our low noise experimental setup allows us to detect the motion of a DW with a spatial resolution as low as 10 nm. A polar magneto-optical Kerr effect (PMOKE) microscope is also used to directly image the magnetic domains in our devices, with a spatial resolution around 0.4 mm. For the Hall measurement, a strong negative perpendicular field is first applied in order to saturate the magnetization of the sample. Then a positive constant field is established to initiate the nucleation of a reversed single domain in the nucleation area (Fig. 1(a)), and its expansion into the cross (Fig. 1(b)). A single DW propagating along the current wire is shown in the inset to Fig. 1(b). Due to the very low thickness of the Co layer (tCo ¼ 1 nm), such a DW (B5 nm wide) can be treated as a quasi-Bloch wall [5]. Furthermore, due to the initial high lateral uniformity of the film, the DW behaves as a 1D coherent nano-object propagating in a confined 2D geometry, with only weak spatial fluctuation of wall energy density [3,6]. Hence, the straightness of the wall, minimizing the wall energy, indicates easy DW propagation with low friction on the wire edges. When the straight DW reaches the cross, remaining straight would mean infinite increase in energy. In a previous paper [2], we have shown that the subsequent
0304-8853/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 1 ) 0 0 7 2 0 - X
F. Cayssol et al. / Journal of Magnetism and Magnetic Materials 240 (2002) 30–33
Fig. 1. MO Kerr images taken on a Pt/Co(tCo=1 nm)/Pt 2 mm wide Hall cross, showing the nucleation event in a large reservoir area (a) and the injection inside the magnetic wire of a single domain wall (b). The inset to (b) shows the presence of a straight DW inside the magnetic wire. The propagation of the DW in the Hall cross is detected by measuring Va Vb :
Fig. 3. (a) Normalized Hall voltage variation versus time for a symmetric Hall cross of width w ¼ 0:5 mm patterned in a Pt/ Co(tCo=1 nm)/Pt film, for different magnetic fields. The observed plateaus correspond to a pinning of the DW. (b) Pinning time t versus applied field. The dependence is compatible with a thermally activated behavior as described by Eq. (2).
cross center: s Hpextmax ¼ ; wMs
Fig. 2. Bubble-like DW propagating inside a symmetric Hall cross, as deduced from our simple energetic model [3].
behavior can be predicted within a simple model of balance between wall energy (which tends to reduce the wall length) and Zeeman energy (which tends to increase the reversed area). The DW starts to bend as a circle arc with its ends pinned at the cross corners (Fig. 2(c)), until it reaches the cross center (half-circle, Fig. 2(c)). After that point the ends get free and the DW expands by increasing its diameter (Figs. 2(d) and (e)). This behavior is analogous to that of a 1D soap bubble in a 2D space. One can define a position-dependant geometrical propagation field (to move the ‘‘bubble like’’ wall at zero temperature), which takes its maximum value at the
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ð1Þ
where w is the stripe width, s the wall energy and MS the saturation magnetization. Fig. 3(a) displays Hall voltage time dependencies at different applied fields, measured on a 0.5 mm wide cross. Using the evolution of wall configurations predicted by our model, and the calculated Hall sensitivity distribution of the cross [7], one can relate the Hall voltage to the circle arc wall position. The plateau at about 30% relative signal in Fig. 3(a) can thus be identified with pinning at the maximum of propagation field, when the wall reaches the cross center. Furthermore, as shown in Fig. 3(b), the applied field dependence of the pinning time t is compatible with a thermally activated behavior of the form [9] 2MS V ext tðHapp Þ ¼ t0 exp ð2Þ Hp max Happ : kB T Using a typical value t0 B2 ns for our systems [9],1,2 we measure Hpextmax ¼ 480 Oe, much higher than the 1 The value of Hpextmax is not very sensitive to the value of t0 chosen. 2 The calculated value of Hpw does not depend very much on the value chosen for v0 :
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F. Cayssol et al. / Journal of Magnetism and Magnetic Materials 240 (2002) 30–33
Table 1 Maximun propagation field Hpextmax predicted by our simple model (Eq. (1)) and measured propagation field Hpmeas at the cross centera Sample
Tco (nm)
w (mm)
s (erg/cm2)
Hpmeas (Oe) experimental
A B
1.0 1.0
2 0.5
7.4 7.4
46 480
Hpextmax (Oe) model
26 104 pffiffiffiffiffiffiffiffiffiffiffiffi a The Bloch wall energy is given by s ¼ 4 Keff A [5]. Keff ¼ 2 KV þ 2KS =tCo 2pMS with A being the exchange constant, MS the saturation magnetization, KS the interface anisotropy constant and KV the bulk anisotropy constant. The following values have been used: MS ¼ 1422 emu=cm3 ; KV ¼ 5:8106 erg=cm3 ; KS ¼ 0:63 erg=cm2 and AE5107 erg=cm: Only KV and KS are measured values.
value Hpextmax ¼ 104 Oe calculated by taking reasonable magnetic parameters in Eq. (1). Similar experiments [2] were made on a 2 mm wide cross (patterned on a different film but with same nominal parameters). The comparison between measured and predicted values of maximum propagation fields are given in Table 1. One observes that, if experiments verify qualitatively the predicted increase of Hpextmax when w decreases, measured values are always much higher than predicted ones. The main origin of this discrepancy is that our model assumes a perfectly uniform film. In real device, the intrinsic propagation field Hpi ; due to the film structural defects, has to be taken into account. It can be shown [8] that the propagation field Hp to be considered is then the sum Hp ¼ Hpi þ Hpextmax : In order to check this prediction we need to determine Hpi for each device. To do that we used Hall effect to measure the DW velocity inside a parallel wire, by measuring the time dependence of the Hall voltage difference VH1 VH2 between two connected Hall crosses (Fig. 4(a)). Ensuring that the signal change comes from a single domain wall propagating from one cross to the other, then we can precisely deduce the average wall velocity. As shown in Fig. 4(b), its variation as a function of the applied field is also compatible with a thermally activated behavior given by 2MS V vðHapp Þ ¼ v0 exp ð3Þ Hpw Happ ; kB T where Hpw is the propagation field inside the wire. Assuming v0 ¼ 2 m/s (see footnote 2) we evaluate Hpw B400 Oe. If we take Hpi BHpw ; then the total maximum propagation field HP in the cross comes out to about 500 Oe, in excellent agreement with the experimental value of 480 Oe. However, this assumes that pinning at the wire edges is negligible. Applying the same simple energy model to
Fig. 4. (a) Normalized signal variation VH1 VH2 versus time for a double Hall crosses (width=2 mm, l ¼ 9 mm) patterned in a Pt/Co(tCo=1 nm)/Pt film. The signal variation corresponds to a DW located between the two Hall crosses. (b) Average DW velocity inside the wire as a function of the applied field.
DW propagation in a parallel wire with sinusoidal edge roughness of amplitude w1 and roughness wave number k ¼ p=2w1 ; one can predict an induced propagation field H pedge given by s k qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Hpedge ¼ ð4Þ 2 ffi: 2Ms w0 =w1 1 Using the same parameters as for Eq. (1), with w1 ¼ 10 nm (measured on electron microscopy images), one gets Hpedge B80 Oe. This value is small but nonnegligible compared to the experimental value. More elaborate samples are being made, that will allow precise determination of all three propagation fields described above. This work was supported by the European Union TMR network SUBMAGDEV, and the Japanese . WunNEDO contract ‘‘Nanopatterned magnets’’. Jorg derlich benefited from a Marie-Curie thesis grant.
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F. Cayssol et al. / Journal of Magnetism and Magnetic Materials 240 (2002) 30–33 [5] Y. Yafet, E.M. Gyorgg, Phys. Rev B 38 (1988) 9145. [6] S. Lemerle, et al., Phys. Rev. Lett. 80 (1999) 849. [7] A. Thiaville, et al., J. Appl. Phys. 82 (1997) 3182.
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[8] J. Wunderlich, Thesis of Universit!e Paris, Sud, May 2001. [9] A. Kirilyuk, et al., J. Magn. Magn. Mater. 171 (1997) 45.
