eScholarship provides open access, scholarly publishing
services to the University of California and delivers a dynamic
research platform to scholars worldwide.
Lawrence Berkeley National Laboratory
Direct observation of stochastic domain-wall depinning in magnetic nanowires
Lawrence Berkeley National Laboratory
Direct Observation of Stochastic Domain-Wall Depinning in Magnetic
Mi-Young Im,1* Lars Bocklage,2 Peter Fischer,1 and Guido Meier2
1Center for X-ray Optics, Lawrence Berkeley National Laboratory, Berkeley CA94720,
2Institut für Angewandte Physik und Zentrum für Mikrostrukturforschung, Universität
Hamburg, Jungiusstrasse 11, 20355 Hamburg, Germany
The stochastic field-driven depinning of a domain wall pinned at a notch in a magnetic
nanowire is directly observed using magnetic X-ray microscopy with high lateral
resolution down to 15 nm. The depinning-field distribution in Ni80Fe20 nanowires
considerably depends on the wire width and the notch depth. The difference in the
multiplicity of domain-wall types generated in the vicinity of a notch is responsible for
the observed dependence of the stochastic nature of the domain wall depinning field on
the wire width and the notch depth. Thus the random nature of the domain wall
depinning process is controllable by an appropriate design of the nanowire.
For concepts of logic and storage devices utilizing magnetic domain-wall (DW)
displacement along a nanowire [1-5] one of the fundamental issues is the precise control
of DW motion. The latter is directly linked to the reproducibility of DW propagation,
pinning, and depinning. Tunable and repeatable DW motion is important for achieving
high performance in DW logic and memory devices [6-9], and the stochastic nature of
DW motion is a major challenge to be overcome to apply the scheme of DW motion to
next generation memory technologies [10-11]. One attempt to control the DW motion is
to manufacture artificial trapping sites within magnetic nanowires [12-17].
Experimental studies on DW dynamics about artificial trapping sites reported so far
have been performed by indirect probes like macroscopic hysteresis loops and
magnetoresistance measurements [13,14,18,19]. Moreover, the few direct observations
have not focussed on the in-depth investigation of the stochastic behavior of DW
motion around trapping sites in magnetic nanowires [17, 20]. Thus, statistical
observation of DW propagation in the vicinity of artificial trapping sites in nanowires
together with the experimental clarification of the stochastic nature of DW motion have
yet remained a scientific challenge.
In this Letter, we report the direct observation of the stochastic behavior of the DW
depinning field in notch-patterned Ni80Fe20 (permalloy) nanowires with different wire
widths (w), notch depths (Nd), and film thicknesses (t) using magnetic transmission soft
X-ray microscopy (MTXM) with a lateral resolution of 15 nm obtained by recent
achievements in Fresnel zone plate technology . The MTXM beamline (6.1.2) used
to observe the evolution of magnetic DWs is installed at the Advanced Light Source in
Berkeley, CA. The experimental setup of this X-ray microscope is described elsewhere
in detail . A condensor zone plate (CZP) with a pinhole close to the sample acts as a
linear monochromator, which provides selective X-rays, e.g., with an energy
corresponding to the Ni L3 (854 eV) or Fe L3 (706 eV) absorption edge. Magnetic
contrast in MTXM is provided by the X-ray magnetic circular dichroism . Magnetic
imaging of the permalloy nanowires was performed in an in-plane geometry where the
wires are mounted under an angle of 60° with respect to the photon beam direction and
parallel to the magnetic field. To study DW motion magnetic images in nanowires are
recorded with varying external magnetic field generated by a solenoid with field
strengths of up to ±100 mT. The fine magnetic contrast without structural contrast is
accomplished by normalization of an image taken at a particular field using an image
obtained at a saturation field. The nanowires are prepared on 100 nm thick silicon-
nitride membranes by electron-beam lithography and thermal evaporation. For
protection of the permalloy 2 nm aluminum is sputtered, which is oxidized in a pure
Typical structural images of the wires with triangular notches measured by scanning-
electron microscopy (SEM) are shown in Figs. 1(a) to 1(c). Magnetic images are taken
at the Fe L3 absorption edge. The wires are initially saturated to positive x direction and
then a reversed field is applied to trigger the nucleation and propagation of a magnetic
DW along the wire. DW evolution images for 50 nm thick wires with widths of w = 150,
250, and 450 nm are demonstrated in Figs. 1(d) to 1(f), where the notch depth is about
50 % of the width of each wire. As demonstrated by the experiments shown in
Figs. 1(d) to 1(f) the magnetic DW is created within the elliptical pad due to its lower
shape anisotropy compared to the narrow wire. By increasing the field strength the DW
propagates towards the notch. The DW evolution process observed between the pad and
the notch is overall identical in all wires with different widths and pad sizes, even
though the wire of width w = 450 nm with a relatively wide neck shows the distinction
that the DW starts leaving toward the notch before the magnetization reversal of the
elliptical pad is fully completed. The DW is pinned at a notch due to the pinning force
exerted by this notch and the pinned DW is a tail-to-tail wall considering saturation (+x)
and reversing (–x) field direction . When the external force acting on the pinned
DW overcomes the pinning force by the notch, the DW is depinned and propagates to
the sharp tip at the right end of the wire where it is annihilated. One can see in Figs. 1(d)
to 1(f) that the DW depinning field decreases with increasing wire width, which is the
consequence of different sizes of DWs governed by different wire widths. The size of
the DW trapped at a notch grows as the wire is widened. A bigger DW is energetically
unfavorable rather than a smaller DW, thus the DW depinning field reduces with
increasing wire width [13,14,16,19].
To investigate the statistical behavior of the DW depinning field at a notch, we
recorded magnetic images in successive hysteretic reversal cycles starting at a fully
saturated state of the wire. In repeated measurements we found that the pinning
probability of a DW is a function of the wire width. The probability is decreased from
about 92 to 75 % of the total number of repeated measurements as the wire narrows
from 450 to 250 nm. Three representative DW evolution image sequences for wires of
w = 150, 250, and 450 nm are shown in Fig. 2(a). Here, the colors from red to blue
indicate the DW pinning and depinning-field strenghts. Within repeated experiments
carried out at the same wire under identical measurement conditions the DW depinning
field shows stochastic behavior, as visualized by various colors. Considering that the
depinning field of a DW in a magnetic nanowire is strongly correlated with the DW
structure [12-14, 24], the stochastic nature of the DW depinning field can be interpreted
to be induced by the generation of various DW types in the vicinity of a notch. We
observed that DWs with different micromagnetic structures are depinned at different
fields. Figure 2(b) presents detailed pictures of DWs at a notch in the wire of w = 250
nm and Nd ~ 50 %, which reveals that depinning fields are related to the various DW
structure. Another notable feature observed in repeated experiments is that the
depinning field appears different even though the DW pinning field is identical, which
implies that the DW depinning process is not subordinate to the DW pinning mechanism.
This result suggests that complicated phenomena around a notch like the creation of
different DW structures and the interaction between the DW and the notch plays the
dominant role in the DW depinning process [12,13].
The stochastic nature of the DW depinning field for different notch depths and wire
widths has been systematically investigated by determination of the DW depinning-field
distribution from depinning events taken in repeated experiments at least 40 times for
each wire. The depinning field is measured by sweeping the external field in steps of
about 0.5 mT. In Fig. 3(a) the depinning-field distribution for 50 nm thick wires of
Nd ~ 50 % with widths of w = 150, 250, and 450 nm and for wires of Nd ~ 30 % with
w = 250 nm are plotted. It can be seen in Fig. 3(a) that the width of the DW depinning-
field distribution is found to depend on the wire width and the notch depth. The DW
depinning field is widely distributed in wires of width w = 250 nm compared to wires of
widths w = 150 and 450 nm. The depinning-field distribution for wire with widths of
w = 250 nm becomes narrow as the notch depth decreases from 50 to 30 %. We also
investigated the statistical distribution of DW depinning fields for wires with a thickness
of 30 nm. Depinning-field distributions for wires of Nd ~ 50 % with w = 250 nm and
wires of Nd ~ 30 % with w = 150, 250, and 450 nm are displayed in Fig. 3(b). In the
30 nm thick wires, we focussed on the wires with Nd ~ 30 % instead of Nd ~ 50 % based
on the experimental result for the 50 nm thick wire where the wire with Nd ~ 30 %
exhibits a narrow distribution, which is more preferred for application in DW devices. A
similar trend of the influence of the width on the DW depinning-field distribution is also
witnessed in the 30 nm thick wire as shown in Fig. 3(b). It is worth pointing out that in
Fig. 3 isolated dominant peaks exist in the distributions. This result suggests that the
thermal effect on the DW depinning process is not the major cause of the observed
fluctuation of DW depinning field, since a Gaussian statistical distribution is expected
for thermally activated DW depinning [15, 25].
To quantitatively examine the degree of stochastic nature of the DW depinning field
with varying wire width and notch depth, we have determined the standard deviation σ
of the DW depinning field from statistical analysis of repeated measurements. The
standard deviation of the DW depinning field indicates the degree of depinning-field
fluctuation. Figure 4 shows the standard deviations as a function of the wire width (a)
and the notch depth (b) for wires of t = 30 and 50 nm. In the case of a 150 nm wide wire
with Nd ~ 50 % and a thickness of 50 nm, the standard deviation of the depinning field
is minimized to below 0.7 mT. In the case of a 250 nm wide wire with Nd ~ 50 % and a
thickness of 30 nm, the standard deviation of the depinning field is as high as ~5.5 mT.
Figure 4 demonstrates that the standard deviation depends sensitively on the wire width
and the notch depth, which implies that the stochastic nature of the DW depinning field
is decisively influenced by the geometry of the wire. The alteration of the stochastic
nature of the DW depinning field with respect to wire width and notch depth is found to
be a general tendency irrespective of the wire thickness in permalloy wires, although
there are slight differences in the absolute value and the variation rate of the standard
deviation with the wire width and the notch depth. Considering that the depinning field
of the DW is strongly related to the DW structure and thus the stochastic nature of the
DW depinning field is governed by the number of different DW structures that can be
generated in a wire, the stochastic nature of the DW depinning field witnessed in the
present experiments is presumably caused by the diversity of generable DW structures
in the vicinity of a notch. In wires exhibiting narrower fluctuations of the DW depinning
field less types of DWs are accessible compared to wires with strongly fluctuating
depinning fields. Thus, we conclude that the key to obtain a reproducible DW depinning
process is a single DW type at a notch, which can be achieved by a proper selection of
the wire and notch geometry.
Our experiments report the direct observation of the stochastic nature of the DW
depinning field at a notch in permalloy wires. We find that the stochastic nature of the
DW depinning field depends on the wire width and the notch depth. The number of DW
types generated in the vicinity of a notch wire has a strong impact on the random nature
of the DW depinning field. Our results clearly demonstrate that the stochastic nature of
the DW depinning process can be minimized by proper geometrical design of the wires.
This work was supported by the Director, Office of Science, Office of Basic Energy
Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.
Financial support of the Deutsche Forschungsgemeinschaft via SFB 668 “Magnetism
from the Single Atom to the Nanostructure“ and via Graduiertenkolleg 1286
“Functional Metal-Semiconductor Hybrid Systems“ is gratefully acknowledged.
 D. A. Allwood, G. Xing, M. D. Cooke, C. C. Faulkner, D. Atkinson, N. Vernier,
and R. P. Cowburn, Science 296, 2003 (2002).
 S. S. P. Parkin, U. S. Patent 6834005 (2004).
 R. P. Cowburn, Nature 448, 544 (2007).
 T. Ono, H. Miyajima, K. Shigeto, K. Mibu, N. Hosoito, and T. Shinjo, Science 84,
 D. Atkinson, D. A. Allwood, G. Xiong, M. D. Cooke, C. C. Faulkner, and R. P.
Cowburn, Nature 2, 85 (2003).
 M. Kläui, C. A. F. Vaz, J. Rothman, J. A. C. Bland, W.Wernsdorfer, G. Faini, and
E. Cambril, Phys. Rev. Lett. 90, 097202 (2003).
 M. Kläui, C. A. F. Vaz, J. A. C. Bland, W.Wernsdorfer, G. Faini, E. Cambril, L. J.
Heyderman, F. Nolting, and U. Rüdiger, Phys. Rev. Lett. 94, 106601 (2005).
 M. Hayashi, L. Thomas, R. Moriya, C. Rettner, and S. S. P. Parkin, Science 320,
 A. J. Zambano and W. P. Pratt, Jr., Appl. Phys. Lett. 85, 1562 (2004).
 G. Meier, M. Bolte, R. Eiselt, B. Krüger, D.-H. Kim, and P. Fischer, Phys. Rev.
Lett. 98, 187202 (2007).
 M.-Y. Im, S.-H. Lee, D.-H. Kim, P. Fischer, and S.-C. Shin, Phys. Rev. Lett. 100,
 M. Hayashi, L. Thomas, C. Rettner, R. Moriya, X. Jiang, and S. S. P. Parkin, Phys.
Rev. Lett. 97, 207205 (2006).
 C. C. Faulkner, M. D. Cooke, D. A. Allwood, D. Petit, D. Atkinson, and R. P.
Cowburn, J. Appl. Phys. 95, 6717 (2004).
 M. Kläui, H. Ehrke, U. Rüdiger, T. Kasama, R. E. Dunin-Borkowski, D. Backes,
L. J. Heyderman, C. A. F. Vaz, J. A. C. Bland, G. Faini, E. Cambril, and
W.Wernsdorfer, Appl. Phys. Lett. 87, 102509 (2005).
 P. Lendecke, R. Eiselt, G. Meier, and U. Merkt, J. Appl. Phys. 103, 073909 (2008).
 A. Himeno, T. Okuno, T. Ono, K. Mibu, S. Nasu, and T. Shinjo, J. Magn. Magn.
Mater. 286, 167 (2005).
 M. Herrmann, S. McVitie, and J. N. Chapman, J. Appl. Phys. 87, 2994 (2000).
 W. Kleemann, J. Rhensius, O. Petracic, J Ferré, and J. P. Jamet, Phys. Rev. Lett.
99, 097203 (2007).
 Y. Yokoyama, Y. Suzuki, S. Yuasa, K. Ando, K. Shigeto, T. Shinjo, P. Gogol, J.
Miltat, A. Thiaville, T. Ono, and T. Kawagoe, J. Appl. Phys. 87, 5618 (2000).
 L. Thomas, C. Rettner, M. Hayashi, M. G. Samant, and S. S. P. Parkin, Appl. Phys.
Lett. 87, 262501 (2005).
 W. Chao, B. H. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood,
Nature 435, 1210 (2005).
 P. Fischer, D.-H. Kim, W. Chao, J. A. Liddle, E. H. Anderson, and D. T. Attwood,
Materials Today 9, 26 (2006).
 G. Schütz, W. Wagner, W. Wilhelm, P. Kienle, R. Zeller, R. Frahm, and G.
Materlik, Phys. Rev. Lett. 58, 737 (1987).
 R. Skomski and J. M. D. Coey, Permanent Magnetism (Institute of Physics,
 E. Martinez, L. Lopez-Diaz, O. Alejos, L. Torres, and C. Tristan, Phys. Rev. Lett.
98, 267202 (2007).
Fig. 1. (a) Typical SEM image of a 50 nm thick nanowire with a width of 150 nm
together with enlarged notch patterns with notch depths of about 30 % (b) and about
50 % (c) of the wire width. Three representative image sequences of magnetic domain
wall evolution along the hysteresis cycle for wire widths of w = 150 nm (d), 250 nm (e),
and 450 nm (f). The magnetic field of the DW evolution pattern is indicated on the
Fig. 2. (a) Domain wall evolution patterns taken from three consecutive experiments
under identical measurement conditions for wires of width w = 150, 250, and 450 nm.
The color scale represents the field when a domain wall is pinned and depinned at a
notch. (b) Domain-wall structures for the wire of w=250 nm and Nd~50 % observed in
the vicinity of a notch right before the depinning.
Fig. 3. Distributions of domain wall depinning fields for (a) 50 nm thick and (b) 30 nm
thick nanowires determined from depinning fields taken by repeated experiments with
at least 40 repetitions for each wire under identical measurement conditions.
Fig. 4. Standard deviations of the domain wall depinning field with respect to (a) wire
width and (b) notch depth. The standard deviation of the depinning field was taken from
the statistical analysis of more than 30 DW depinning fields for each wire.
13 Download full-text