IEEE TRANSACTIONS ON MAGNETICS, VOL. 39, NO. 5, SEPTEMBER 2003
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Magnetic Domain Wall Dynamics in a Permalloy Nanowire Del Atkinson, Dan A. Allwood, Colm C. Faulkner, Gang Xiong, Michael D. Cooke, and Russell P. Cowburn
Abstract—Experimental results of domain wall propagation velocity as a function of applied field in a 200-nm-wide permalloy nanostructure are presented. The structure was fabricated by focused-ion beam milling and designed to separate the domain wall nucleation from propagation. The measured velocities are very high, up to 1500 m/s at 49 Oe and the field dependence of the velocity is interpreted in terms of thermally activated wall motion through a series of pinning sites and a wall geometry that changes as a function of field. Index Terms—Domain walls, permalloy, thermal activation.
magnetic
nanostructure,
I. INTRODUCTION
I
N RECENT years, the ability to measure magnetization switching in single micrometer and submicrometer scale structures has developed rapidly allowing new insights into the processes of magnetization change [1]–[4]. Such studies have relevance to recording media and magnetic random access memory (MRAM) applications. Measurements of single elongated nanostructures [5], [6] highlighted the importance of nucleation, propagation and the statistical nature of the magnetization reversal process in such structures. Domain wall propagation in confined structures is of fundamental interest [7]–[10] and has direct technological relevance to a magnetic logic scheme demonstrated recently [11]. The dynamics of domain walls are of particular interest as the width of the magnetic structure approaches the wall width (calculated to be [11], [12]). of the order of a hundred nanometers in Recently, we outlined a planar magnetic nanostructure designed to separate the processes of nucleation and propagation for single domain walls and used this structure to study the velocity of domain wall propagation [13]. Here, we describe the experimental procedure, present further data and a detailed discussion of the physical mechanisms that may explain the observed velocity behavior. II. EXPERIMENTAL DETAILS A 200-nm-wide magnetic structure was fabricated by focused ion-beam milling. The sample was prepared on a silicon substrate and consisted of a 300- -wide 25-nm-thick thermally evaporated aluminum strip line with a 5-nm film of on top. The planar nanowire was patterned with a beam of foions at 30 keV [14]. Magnetization reversal events cused Manuscript received January 2, 2003. This work was supported by Eastgate Investments Ltd., Dubai. The authors are with the Department of Physics, University of Durham, Durham DH1 3HP, U.K. (e-mail:
[email protected]). Digital Object Identifier 10.1109/TMAG.2003.815548
Fig. 1. Schematic of structure used to separate domain wall nucleation from propagation to allow the study of the propagation velocity. Dimensions are in micrometers. Positions I and II indicate the laser spot positions. Not to scale.
were measured using a continuous wave (CW) laser magnetooptical Kerr effect (MOKE) magnetometer [15]. Fig. 1 shows a schematic of the nanostructure. Domain wall velocities were obtained from the transit time (pulsed field duration) taken for a wall to travel along a known length of the wire. A domain wall was first nucleated in the “pad” and moved to the first corner by a field in the -direction from an electromagnet. This field was removed and a rapid flat-topped magnetic field pulse was applied in the -direction by a current pulse in the strip line [16]. During this pulse the domain wall propagated along the middle section. A second field from the electromagnet was then applied in the -direction. The magnitude of this field was such that if a domain wall had reached the second corner (moved during the field pulse) it would be propagated down into the final part of the structure and detected as a switching event. The magnetization state was reset after each sequence. Care was taken to ensure that directly nucleated reversal did not occur in the middle section. This was achieved by determining the field amplitude needed for reversal in the middle section without a wall being initially setup at the first corner. Propagation experiments were then carried out with pulsed fields below this amplitude. The measurement sequence was repeated many times (at a repetition frequency of 27 Hz) to effectively count the number of switching events. For each pulse length, measurements were made at a range of pulsed field amplitudes to determine the switching probabilities. Two measurement positions were interrogated using the MOKE magnetometer. Position I allowed direct counting of reversal events where a domain wall had entered the second corner. This position also allowed a study of the propagation of a wall into a corner, i.e., where the spin structure is changing. Position
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(a) Fig. 3. Domain wall velocity as a function of magnetic field determined at position I ( ) and position II ( ). Lines are guides to the eye.
(b) Fig. 2. (a) Nonswitching probabilities as a function of field amplitude for 152 ns) fixed pulse durations (2720 ns, 1034 ns, 508 ns, 300 ns, the exponential fits are guides to the eye. (b) Nonswitching probabilities as a function of pulse-length at constant field ( 27 Oe, 32 Oe). The lines are best fits using (1) giving values of 1.93 for 27 Oe and 1.55 for 32 Oe.
II was chosen as switching due to wall propagation by the pulsed field was observed directly. However, in position II the detection of reversal events was complicated by the fact that partial switching events (where the wall stopped within the laser spot) m) spread could also be detected because of the finite ( of the laser spot. In this case, the reversal statistics represent a convolution of the true stochastic reversal behavior and the laser spot profile. For reversal events measured at position I the propagation distance (between the two corners) was 21.6 m and between the first corner and the center of the laser spot at position II the distance was 18 m. III. RESULTS AND DISCUSSION Fig. 2(a) shows the probability of nonswitching as a function of field for different pulse durations measured at position I. From the field-dependent measurements a limited data set showing the time dependence of the switching process was extracted [Fig. 2(b)]. The probability of switching increased with both pulsed field amplitude and pulse duration as expected for thermally activated switching. Following the Arrhenius–Néel theory, the probability of nonswitching as a function of time can be fitted with an exponential of the form [6] (1) where represents a characteristic waiting time. The value of depends on the energy barriers that are overcome by thermal . activation. In the case of activation over a single barrier, and have been attributed to distributions Values of of energy barriers [6] and reversal “by a series of independent
thermally activated processes” [17], respectively. The data in Fig. 2(b) were fitted using (1) (with a small adjustment to the time to take into account the wall transit time). The values of obtained from the fits indicate that the reversal process in this nanostructure is characterized by thermal activation over multiple energy barriers. Since the domain wall is present before the field pulse is applied the energy barriers may be attributed to domain wall pinning sites distributed along the length of the nanostructure. Whether these sites are located at the edges or within the structure is unknown, although it is known that ion implantation can increase domain wall pinning in permalloy [18]. The field magnitude for each pulse duration (used to obtain the wall velocity) was taken from the probability of nonswitching as a function of field at the level of 50%. Fig. 3 shows the field dependence of the domain wall velocity obtained at positions I and II. The velocity data are in reasonable agreement up to 35 Oe and then diverge at higher fields. In both datasets, the slope of the velocity curve increases with field up to about 35 Oe and then both slopes fall over the next few oersteds. For the direct measurements (position II) the slope of the velocity curve then increases rapidly up to the maximum field studied. Over the same field range, the slope obtained at position I remains roughly constant. The domain wall propagation time can be considered to comprise a stochastic time element due to thermally activated depinning and a transit-time element for the gyromagnetic process governing wall motion between pinning sites. Hence, the observed velocity can be viewed as an average along the wire. Fig. 4 shows a simple model of this process for a single pin. For ning site and single wall mobility value of 31 the results obtained here the form of the velocity-field data up to 35 Oe is consistent with thermally activated motion, although in this case the wall moves through a series of pinning sites as discussed earlier. The break of slope around 35 Oe is inconsistent with a simple thermal activation model. A similar slope anomaly was observed for an ultrathin cobalt film [19] and interpreted as Walker breakdown (which corresponds to the maximum velocity that can be sustained for a simple planar wall [20]). If the anomaly observed here is Walker breakdown, the rapid increase in the slope at higher fields (position II data) suggests a change to a wall structure that can propagate faster. Such changes in wall structure as a function of velocity have also been suggested in thin-films [19].
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enough into the corner to then be moved down to position I. A higher pulsed field amplitude would then be needed to move the wall further into the corner allowing it to be propagated down to position I. Furthermore, since the whole structure is exposed to the pulsed field the spins at the corner will rotate (also shown by OOMMF modeling), and change the spin structure at the corner. IV. CONCLUSION Fig. 4. Modeled results for wall velocity as a function of field assuming thermally activated depinning from a single energy barrier and gyromagnetically limited mobility of 31 . The arrow indicates the effect of reducing the energy barrier.
ms Oe
The velocity of domain walls in a 200-nm-wide permalloy nanostructure was measured as a function of magnetic field. The velocity varies in a complex way with field and is very high at the higher fields (1500 m/s at 49 Oe). The field dependence of the velocity is consistent with thermally activated wall motion through a series of pinning sites coupled with a wall geometry that changes as a function of field. REFERENCES
Fig. 5. OOMMF modeled results for domain wall velocity, and wall width as a function of field. Walker breakdown occur at about 18 Oe in this model.
To gain further insight into the domain wall geometry, the zero temperature micromagnetic modeling code OOMMF [21] was used to study the wall velocity and domain wall geometry. The modeled system was a 5-nm-thick, 200-nm-wide, and 6- -long isotropic defect-free NiFe structure. The cell size was 5 nm. The domain wall velocity was determined as a function of field. Fig. 5 summarizes the model behavior. Modeling showed that as the velocity increased the wall width fell by about 20% before Walker breakdown occurred and the wall rotated from perpendicular to wire axis by several degrees. Considering these results along with [20] (2) relating the domain wall mobility to domain wall width and gyromagnetic damping factor , where is the gyromagnetic ratio, suggests that the intrinsic gyromagnetically governed mobility may vary continuously as a function of field because the domain wall becomes narrower. A changing wall angle will further complicate the situation. Returning to the experimental data, the velocity as a function of field may also reflect a changing domain wall geometry as this could affect the energetics of the wall interaction with pinning sites and, hence, thermal activation. A change of wall geometry as a function of velocity (or field) may aid in explaining the divergence between the two velocity datasets. For a wall to be propagated down from the corner and be detected at position I the wall must end up at a position within the corner after the pulsed field such that the subsequent magnetic field from the electromagnet in the -direction can propagate the wall. If the wall geometry changes (narrows and/or tilts) the wall interaction with the spin environment of the corner may prevent the wall (having reached the corner) moving far
[1] J. Wu et al., “Picosecond large angle reorientation of the magnetization in Ni Fe circular thin-film elements,” J. Appl. Phys, vol. 91, pp. 278–286, 2002. [2] T. Gerrits et al., “Ultrafast precessional magnetization reversal by picosecond magnetic field pulse shaping,” Nature, vol. 418, pp. 509–512, 2002. [3] N. D. Rizzo et al., “Ultrafast precessional magnetization reversal by picosecond magnetic field pulse shaping,” Appl. Phys. Lett., vol. 80, pp. 2335–2337, 2002. [4] D. Schuh et al., “Hall-magnetometry on ferromagnetic dots and dot arrays,” IEEE Trans. Magn., vol. 37, pp. 2091–2093, July 2001. [5] W. Wernsdorfer et al., “Nucleation of magnetization reversal in individual nanosized nickel wires,” Phys. Rev. Lett, vol. 77, pp. 1873–1876, 1996. [6] , “Measurements of magnetization switching in individual nickel nanowires,” Phys. Rev. B, vol. 55, pp. 11 552–11 559, 1997. [7] G. Tatara, G. Fukuyama, and H. Fukuyama, “Macroscopic quantum tunneling of a domain-wall in a ferromagnetic metal,” Phys. Rev. B, vol. 72, pp. 772–775, 1994. [8] J. P. Jamet et al., “Giant enhancement of the domain wall velocity in irradiated ultrathin magnetic nanowires,” IEEE Trans. Magn., vol. 37, pp. 2120–2122, July 2001. [9] T. Ono et al., “Propagation of a magnetic domain wall in a submicrometer magnetic wire,” Science, vol. 284, pp. 468–470, 1999. [10] U. Ebels et al., “Spin accumulation and domain wall magnetoresistance in 35-nm Co wires,” Phys. Rev. Lett., vol. 84, pp. 983–986, 2000. [11] D. A. Allwood et al., “Submicrometer ferromagnetic NOT gate and shift register,” Science, vol. 296, pp. 2003–2006, 2002. [12] T. Trunk et al., “Domain wall structure in Permalloy films with decreasing thickness at the Bloch to Neel transition,” J. Appl. Phys., vol. 89, pp. 7606–7608, 2001. [13] D. Atkinson et al., “Magnetic domain-wall dynamics in a submicrometre ferromagnetic structure,” Nature Mater., vol. 85–87, 2003. [14] G. Xiong, D. A. Allwood, M. D. Cooke, and R. P. Cowburn, “Magnetic nanoelements for magnetoelectronics made by focused-ion-beam milling,” Appl. Phys. Lett., vol. 79, pp. 3461–3463, 2001. [15] R. P. Cowburn, D. K. Koltsov, A. O. Adeyeye, and M. E. Welland, “Probing submicron nanomagnets by magneto-optics,” Appl. Phys. Lett., vol. 73, pp. 3947–3949, 1998. [16] D. Atkinson, D. A. Allwood, M. D. Cooke, and R. P. Cowburn, “Nanosecond pulsed field magnetization reversal in thin-film NiFe studied by Kerr effect magnetometry,” J. Phys. D: Appl. Phys., vol. 34, pp. 3019–3023, 2001. [17] M. Lederman, S. Schultz, and M. Ozaki, “Measurement of the dynamics of the magnetization reversal in individual single-domain ferromagnetic particles,” Phys. Rev. lett., vol. 73, pp. 1986–1989, 1994. [18] D. Ozkaya, R. M. Langford, W. L. Chan, and A. K. Petford-Long, “Effect of Ga implantation on the magnetic properties of permalloy thin films,” J. Appl. Phys., vol. 91, pp. 9937–9942, 2002. [19] A. Kirilyuk et al., “Magnetization reversal in ultrathin ferromagnetic films with perpendicular anisotropy,” J. Magn. Magn. Mater., vol. 171, pp. 45–63, 1997. [20] A. P. Malozemoff and J. C. Slonczewski, Magnetic Domain Walls in Bubble Materials. NewYork: Academic, 1979. [21] [Online]. Available: http://math.nist.gov/oommf/
