ARTICLE
Received 1 Nov 2016
| Accepted 24 Apr 2017 | Published 8 Jun 2017
Current-induced skyrmion generation and
dynamics in symmetric bilayers
A. Hrabec
1,2
, J. Sampaio
1
, M. Belmeguenai
3
, I. Gross
2,4
, R. Weil
1
, S.M. Che
´
rif
3
, A. Stashkevich
3,5
, V. Jacques
2
,
A. Thiaville
1
& S. Rohart
1
Magnetic skyrmions are quasiparticle-like textures which are topologically different from
other states. Their discovery in systems with broken inversion symmetry sparked the
search for materials containing such magnetic phase at room temperature. Their topological
properties combined with the chirality-related spin–orbit torques make them interesting
objects to control the magnetization at nanoscale. Here we show that a pair of coupled
skyrmions of opposite chiralities can be stabilized in a symmetric magnetic bilayer system
by combining Dzyaloshinskii–Moriya interaction (DMI) and dipolar coupling effects. This
opens a path for skyrmion stabilization with lower DMI. We demonstrate in a device with
asymmetric electrodes that such skyrmions can be independently written and shifted by
electric current at large velocities. The skyrmionic nature of the observed quasiparticles is
confirmed by the gyrotropic force. These results set the ground for emerging spintronic
technologies where issues concerning skyrmion stability, nucleation and propagation are
paramount.
DOI: 10.1038/ncomms15765
OPEN
1
Laboratoire de Physique des Solides, Univ. Paris-Sud, Universite
´
Paris-Saclay, CNRS, UMR 8502, F-91405 Orsay Cedex, France.
2
Laboratoire Charles
Coulomb, Universite
´
de Montpellier and CNRS UMR 5221, 34095 Montpellier, France.
3
LSPM (CNRS-UPR 3407), Universite
´
Paris 13, Sorbonne Paris Cite
´
,
99 avenue Jean-Baptiste Cle
´
ment, 93430 Villetaneuse, France.
4
Laboratoire Aime
´
Cotton, CNRS, Universite
´
Paris-Sud, ENS Cachan, Universite
´
Paris-Saclay,
91405 Orsay Cedex, France.
5
International Laboratory MultiferrLab, ITMO University, St. Petersburg 197101, Russia. Correspondence and requests for
materials should be addressed to S.R. (email: stanislas.rohart@u-psud.fr).
NATURE COMMUNICATIONS | 8:15765 | DOI: 10.1038/ncomms15765 | www.nature.com/naturecommunications 1
O
ver the past 2 years, a concerted effort has been made
worldwide to study how magnetic skyrmions, a chiral
phase evidenced in materials with broken inversion
symmetry
1–4
, can appear and be displaced in ultrathin
ferromagnetic films and nanotracks
5,6
. From an experimental
viewpoint, there remain three important challenges that are
determinant for whether skyrmions will be useful in future data
storage technologies. First, the ability to tailor the chirality and
energy of domain walls (DWs), such that isolated skyrmions
remain sufficiently stable at room temperature against the
ferromagnetic ground state. Second, it is important to drive the
skyrmions efficiently with spin-transport torques, such as the spin
Hall effect (SHE), as the reproducible displacement of skyrmions
is crucial to information transfer. Third, it is essential to be
able to nucleate skyrmions readily, since the ability to write (new)
information is primordial to any storage application.
Experimental demonstrations of certain aspects of these three
points have been reported
4,7–11
, however, independent writing
and shifting in a single device remains a challenge.
Recently, significant developments in spintronics have being
directly connected with broken inversion symmetry. On one
hand, this allows spin–orbit torques to improve the efficiency of
current-induced magnetization manipulation
12–15
. On the other
hand, such a situation allows to tailor DW chirality and lower
the DW energy through the Dzyaloshinskii–Moriya interaction
(DMI)
16–19
, a requirement that ultimately permits the
stabilization of skyrmions and their use in spintronics
2,3,5
.
In general, the search for skyrmion host media requires a large
DMI, which restricts the choice of materials.
Here we show that a globally symmetrical situation in magnetic
bilayers meets all the requirements to host skyrmions, without the
need for a very large DMI, since the control of DW chirality and
energy is assisted by dipolar coupling. It results in two
superimposed skyrmions, strongly coupled through their dipolar
stray field, which behave as a single particle called skyrmion
hereafter for simplicity. This method, compatible with spin–orbit
torque-induced dynamics, offers a larger flexibility for the
choice of materials. We show for the first time a simple and
elegant technological way to independently write and shift such
skyrmions at large velocities in a single functional device by
means of electric current.
Results
Multilayer stack design. Stabilization of isolated skyrmions
requires a fine control of the DW energy
20
between two limiting
cases: a large positive energy causes skyrmions to collapse, while a
large negative wall energy destabilizes the collinear order and
requires high magnetic fields to access the isolated skyrmions
7
.
While this is generally achieved using DMI, we show that dipolar
coupling in bilayers with perpendicular magnetization can be
successfully used too. As illustrated in Fig. 1a on a magnetic
bilayer, the stray field arising from the domains couples to the
DW magnetization, in a flux-closure configuration, and promotes
Ne
´
el walls with opposite chirality in both layers and thus lowers
the DW energy
21
. The strength of this effect can be easily tuned
by adjusting the spacer thickness, offering an additional means of
control. The symmetric superimposition of two magnetic layers,
each of them in a non-symmetric stacking, allows to satisfy both
dipolar coupling and DMI. As the sense of the magnetization
rotation induced by the stray field cannot be changed (left and
right handed in the bottom and top layer, respectively), the large
spin–orbit layers generating the interfacial DMI should be placed
as spacer if the induced DMI parameter D is positive, or as outer
layers if it is negative. Another advantage of bilayers is an increase
of the dipolar interaction between the skyrmion core and the
ferromagnetic surrounding as compared to a single layer,
which further stabilizes skyrmions. As demonstrated below,
this structure is also compatible with SHE-induced motion of
skyrmions.
We use a stack of Pt(5 nm)\FM\Au(d)\FM\Pt(5 nm) where
FM ¼ Ni\Co\Ni. The chosen FM gives the opportunity to change
the surrounding metals without significantly changing the
anisotropy which arises predominantly from the Ni\Co inter-
faces
22
. Moreover, the use of two different ferromagnets gives
more freedom to tune the stray field and the anisotropy by
adjusting the Co and Ni thicknesses. Magnetometry and Brillouin
light-scattering spectroscopy on single magnetic layers with both
stacking orders has shown that both layers are similar, which
guaranties film symmetry, only the sign of the DMI constant
being opposite (D ¼0.21
±
0.01 mJ m
2
for Pt/FM/Au and
D ¼þ0.24
±
0.01 mJ m
2
for Au/FM/Pt stacks, respectively), as
expected (Supplementary Note 1). The DMI induced at the Pt/Ni
interface thus yields a left-handed (counter-clockwise) chirality
23
as sketched in Fig. 1a, which justifies the use of Pt layers as
bottom and top layers, in order to satisfy the dipolar interaction.
The thickness of Pt has been chosen with respect to the reported
spin-diffusion length to maximize the SHE
24
and Au remains a
neutral layer due to negligible SHE
25
and small DMI
26
. While
exchange coupling has been already explored theoretically
27
and
experimentally
28
for stabilizing skyrmions, here we focus on
dipolar coupling. The thickness of Au is therefore chosen to avoid
interlayer exchange coupling
29
but also to minimize the electric
current shunting (Supplementary Note 1).
Skyrmion stabilization using dipolar couplings. To understand
the mechanism of the isolated skyrmion stabilization, one has to
disentangle and quantify several energies involved in this process.
The specific DW energy (hereafter called simply energy) s
0
,
including the exchange and anisotropy energies
30
, is lowered by
pD upon introduction of DMI
18,31
. The DMI favours a Ne
´
el wall
structure, which also gives rise to magnetostatic charges on either
side of the wall and creates a field opposed to the wall
magnetization (red arrows in Fig. 1a)
31
. This is expressed by
the energy increase d
N
. Alongside these usual energy terms, in the
case of the bilayer system one has to take into account additional
energies. The DW–DW magnetostatic interaction between two
DWs with opposite chiralities leads to another energy term
d
DW DW
which is illustrated by blue arrows in Fig. 1a. For spacer
thicknesses d smaller than the DW width D, the magnetostatic
charges created by each wall are so close that |d
N
|E|d
DW DW
|so
that these two contributions almost compensate. On the contrary,
the stray field arising from the domains, depicted by the
green arrows in Fig. 1a gives another significant energy
decrease, d
D DW
, which scales
32
approximately as 1/d and
reinforces the chiral nature of each wall
21
. The DW energy
within such system then reads
s ffi s
0
pD d
D DW
: ð1Þ
The quantitative analysis of the energies has been performed by
micromagnetic calculations. Figure 1b shows the DW energy
dependence on the spacer thickness. The DW energy increases
with increasing d as expected from the argument of 1/d
dependence. However, when the spacer thickness d is
comparable with the DW width shown in the inset of Fig. 1b,
the DW energy decreases with d. The DW width strongly
responds to the spacer thickness to accommodate the important
energy changes. One can define the optimum spacer thickness
d
opt
where the effect of dipolar energy contribution is maximized.
With our parameters, this analysis yields d
opt
close to 3 nm,
and the ratio between the DMI and magnetostatic energies is
d
D DW
/pD ¼ 1.1, that is, half of the energy minimization is due
ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms15765
2 NATURE COMMUNICATIONS | 8:15765 | DOI: 10.1038/ncomms15765 | www.nature.com/naturecommunications
to the magnetostatic energy. This approach based on isolated
DWs can be also extended to 360° DWs and skyrmions where the
stray field is slightly lower, showing that the dipolar mechanism is
efficient to stabilize skyrmions down to at least 20 nm
(Supplementary Note 2).
While the DW energy remains positive here, the dipolar
coupling between the skyrmion core and the ferromagnetic
surrounding can efficiently lower the skyrmion energy cost.
However, in ultrathin films, dipolar coupling vanishes with
the thickness
33
so that the film thickness must be larger than
a characteristic length l
c
¼ s/m
0
M
2
s
to spontaneously promote
magnetic textures
9,33
(with M
s
the spontaneous magnetization).
In our case, l
c
¼ 3.9 nm so that a single-layer film (1.5 nm thick)
can hardly be demagnetized and shows a full remanence square
hysteresis loop. On the contrary, bilayer films have a total
thickness larger than l
c
and therefore spontaneously demagnetize
in a multiple domain state, as shown by a zero remanence
hysteresis loop (Supplementary Note 1).
The magnetic texture imaged by magnetic force microscopy
(MFM, see Methods) confirms that the bilayers are at remanence
in a worm-like demagnetized state. Figure 1c–f show a sequence
of MFM images at different fields and illustrate how the
worm-like structure can be unwound into the isolated skyrmion
phase with moderate fields. As soon as an out-of-plane magnetic
field is applied the domains start to contract into skyrmions
whose size and density decrease with the magnetic field. Close to
the saturation field only a few isolated skyrmions remain. They
are the ones needed for free skyrmion dynamics studies and
applications. We note that the MFM does not provide any insight
into the topology of the created textures, a point addressed later.
In the following, we focus on skyrmions in nanostructures.
In those, size effects lower the magnetic field needed to saturate
the sample, so that applying only 6 mT is sufficient to study
isolated skyrmions of 160
±
40 nm diameter, measured within the
accuracy of the MFM (see Fig. 2).
Skyrmion nucleation. Several methods have been proposed
to nucleate skyrmions
6–8,34–35
. Here we demonstrate another
method which is characterized by its simplicity and integrability.
To study the skyrmion dynamics in confined structures we have
fabricated the device shown in Fig. 2a containing four parallel,
1 mm wide wires. The electrical contacts are fabricated in a
non-symmetric fashion where one side of the wires is connected
by sharp tips and the other by a wide electrode. At the tip current
lines divergence
36
, heating, and spin accumulation
37
are largest,
disturbing the magnetic configuration. As a result, skyrmions
spontaneously appear there and are injected into the track.
Figure 2b shows a systematic skyrmion nucleation in two adjacent
wires in the vicinity of the contact. Skyrmions are injected
into fully saturated wires ( 6 mT applied field) by a series of
7-ns-long pulses. Above a threshold of j
c
’ 2:610
11
Am
2
the
skyrmions are injected at the tip, as shown after application of the
first pulse, and carried away into the tracks. When the polarity of
the electric current is reversed this injection mechanism does not
work, as the nucleated skyrmions are pushed by the current
toward the tip. Nucleation at the wide electrode has never been
observed. Therefore due to this geometrical asymmetry one
polarity of the electric current serves as a skyrmion generator
while the other simply shifts the existing skyrmions.
Skyrmion dynamics. After filling the tracks with skyrmions
we reverse the polarity of the current to avoid interaction
with newly injected skyrmions, and so switch to the skyrmion
shifting mode. To measure the velocities as a function of current
density, we measure the skyrmion displacement after application
of each current pulse, of duration ranging from 3 to 10 ns.
Figure 2c shows a sequence of images demonstrating skyrmion
displacement by 3-ns-long pulses with a current density
j ¼ 3.9 10
11
Am
2
. The resulting measured skyrmion velocity
as a function of current densities at B
z
¼6 mT presented
in Fig. 2d reveals skyrmion velocities up to 60 m s
1
. From one
1 10 100 1,000
3.6
3.8
4.0
4.2
FM
FM
Au
Pt
Pt
25 mT
14 mT10 mT
2 mT
b
DW energy (mJ m
–2
)
Spacer thickness d (nm)
Single layer
d
1 10 100 1,000
13
14
e
c
a
(nm)
d (nm)
Single layer
d
f
Figure 1 | Skyrmion stabilization. (a) Sketch of the Pt/FM/Au/FM/Pt stack. The black arrows indicate magnetization orientation inside the two layers
containing a DW. The coloured arrows correspond to DW internal (red), DW–DW (blue) and domain–DW (green) magnetostatic interactions respectively.
(b) Calculated DW energy and width parameter D as a function of the Au spacer thickness d. The circles correspond to the experimental case d ¼ 3nm.
(c–f) Field-dependent MFM images revealing the process of skyrmion formation. The bright and dark contrast corresponds to repulsive and attractive force
respectively. The sample is in a demagnetized state at low field. The remagnetization with increasing field leads to condensation of skyrmions and a
decrease of their density. Scale bar, 1 mm.
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms15765 ARTICLE
NATURE COMMUNICATIONS | 8:15765 | DOI: 10.1038/ncomms15765 | www.nature.com/naturecommunications 3
pulse to another, even at the largest current densities, successive
displacement lengths are not equal, which underlines the role of
defects and that skyrmions move by hopping within the potential
landscape
38
. They advance in the track until they get pinned,
or reach a strongly pinned skyrmion which prevents further
propagation by skyrmion-skyrmion repulsion.
The skyrmions move in the direction opposite to the electrons
which suggests that the spin Hall effect governs their
dynamics
6,15
. When an electric current passes through the Pt
layers, a spin accumulation with opposite polarities is generated
at each interface, as sketched in Fig. 2d. The force acting on a
skyrmion can be expressed as
6
F
SH
¼
‘
2e
pjy
SH
be
z
e
p
ð2Þ
where j is the current density, y
SH
is the SHE angle and b is a
skyrmion characteristic length (half its perimeter when the
skyrmion radius R is much larger than the DW width parameter
D). The SHE-induced spin accumulation is along the vector
e
p
¼ n j, with n being the outer normal to the SHE layer at the
interface considered, and its sign is given by that of the SHE angle
y
SH
(positive for Pt
24
). With e
z
the vertical direction in the
laboratory frame (for example, from substrate towards film), used
to define the chirality of the skyrmions, the sign of the force is set
by the chirality, as specified by the
±
symbol in equation (2)
where þ stands for right-hand chirality. Since the spin
accumulation and the chirality are both opposite at each
interface, the forces acting on the skyrmions depicted in Fig. 2d
point in the same direction in both magnetic layers. The
skyrmions in both layers are therefore pushed in the same
direction, along the electrical current here. The obtained velocities
quantitatively agree with the model for free skyrmion dynamics
in a disorder-free medium (Supplementary Note 4).
Insight into topology via skew deflection. One way to confirm
that we deal with topological textures is to prove that they
experience a gyrotropic force
39
, expressed as
F
G
¼Gv¼ 0; 0;
m
0
M
s
t
g
0
O
v
x
; v
y
; 0
ð3Þ
01234
0
20
40
60
80
100
j
x
j
t
d
Velocity (m s
–1
)
Current density (10
11
A m
–2
)
j
a
c
j
j
z
j
F
b
Figure 2 | Skyrmion generation and dynamics. (a) AFM image of the asymmetric device with the skyrmion injection tips. (b) Skyrmion writing by at
B
z
¼6 mT by 7 ns long, j ¼ 2.8 10
11
Am
2
pulses starting from a fully saturated state, with one injected skyrmion after application of first pulse,
and several skyrmion after a train of pulses. The dashed lines and triangles correspond to the wire edges and electric contacts respectively. Scale bar, 1 mm.
(c) Series of images showing skyrmion shift along the track between 3 ns, j ¼ 3.9 10
11
Am
2
electric pulses. Scale bar, 500 nm. (d) Measured velocity of
skyrmions as a function of current densities at B
z
’6 mT. Error bars correspond to the s.d. The inset shows a sketch of the skyrmion cross section with
the spin accumulation due to the electrical current j. The resulting force F (green arrows) defined by equation (2) causes both skyrmions to move in the
same direction (against the electron flow). AFM, atomic force microscopy.
j
v
a
bc
v
B
z
F
g
F
g
Figure 3 | The gyrotropic force. (a) SEM micrograph of the sample geometry used for skyrmion generation demonstration. The 3 mm ferromagnetic stripe
is connected to Ti\Au pads with an injection finger 300 nm wide. Scale bar, 3 mm. (b) Resulting state after application of a series of 8 ns long pulses in an
external field of B
z
’6 mT where j ¼ 3 10
11
Am
2
. Scale bar, 1 mm. (c) The same experiment with B
z
’þ6 mT shows skyrmion accumulation on the
left side of the device. The dashed line indicates position of the Ti/Au finger. SEM, scanning electron microscopy.
ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms15765
4 NATURE COMMUNICATIONS | 8:15765 | DOI: 10.1038/ncomms15765 | www.nature.com/naturecommunications
where G is the gyrotropic vector, O ¼ 4pSp with S being the
winding number and p the core polarity. O thus intimately binds
the topology of the quasiparticle to its motion, providing a way to
reveal its topological state. The skyrmion dynamics can be
described by the massless Thiele equation
39,40
Gv aDv þ F
SH
¼0 ð4Þ
where F
SH
is the force expressed by equation (2), a the Gilbert
damping and D the dissipative tensor (Supplementary Note 4
for its calculation). The gyrotropic force therefore deviates the
skyrmions from the direction of F
SH
in a similar manner as
electrons moving in a magnetic field
41–43
.
To study this behaviour we have lifted the geometrical
constrain and patterned the ferromagnetic stack into a 3 mm
wide strip where the skyrmions can move freely in the lateral
direction. The electrical contact is designed asymmetrically by a
300 nm wide non-magnetic finger and a straight electrode as
shown in Fig. 3a. We have verified that in this geometry the
skyrmions can be only generated by one polarity of the current
similarly to the case shown in Fig. 2b. The ferromagnet was first
saturated and then a series of 8 ns long, j ¼ 3 10
11
Am
2
current pulses at B
z
¼6 mT has been applied in order to inject
the skyrmions. Figure 3b demonstrates a resulting magnetic
configuration after application of a series of pulses showing
several skyrmions. The skyrmions are ejected at the tip and are
carried away by the current with a certain deflection towards
right. Note that this deflection is also visible in Fig. 2c (to the left
as the current is opposite). In order to prove the behaviour
predicted by equation (3) we have generated skyrmions with
opposite core magnetization by applying B
z
¼þ6 mT, that is,
changing the sign of O. Figure 3c shows a resulting skyrmion
configuration after application of a train of pulses of the same
polarity as in Fig. 3b. In this case, the skyrmions accumulate on
the left side of the sample. We emphasize that the direction of the
magnetic field shown in Fig. 3b,c is absolute and the skyrmion
accumulation indeed appears on the side predicted by
equation (3). The effect of Oersted field can be excluded as it
would give the opposite deflection direction (Supplementary
Note 3). This undoubtedly confirms that our textures have S40
topology compatible with skyrmions. A quantitative determina-
tion of the winding number is impossible as the track width and
the skyrmion trajectory between the imperfections limit the
deflection
42,44,45
. Note that S ¼ 1 state would imply a deflection
angle of E73° (Supplementary Note 4).
Discussion
The guideline used here widens the possibilities of skyrmion
stabilization and manipulation and, hence, their applications.
Indeed, we have engineered a magnetic bilayer system which
efficiently employs all the available energies (DMI and dipolar
couplings) to stabilize a pair of skyrmions. The two skyrmions
have the same topological charge while having opposite chiralities
and are strongly coupled through their dipolar stray field. The
opposite chirality in combination with a reversed spin accumula-
tion results in a system suitable for the current-induced dynamics.
We have developed functional devices with asymmetric electrodes
designed for systematic current-induced skyrmion generation and
motion. The skyrmion nature of the quasiparticles was demon-
strated by topological filtering employing the gyrotropic force.
Methods
Sample preparation. Samples were grown in an ultra-high vacuum evaporator
with base pressure of 10
10
mBar. The multilayers of Pt\FM\Au\FM\Pt with
FM ¼ Ni(4Å)\Co(7 Å)\Ni(4 Å) were deposited on a high-resistive silicon with
native oxide layer in order to minimize the Joule heating effect during electric
current pulse application
46
. The symmetry of the stack has been verified by
magnetometry measurements on Pt/FM/Au and Au/FM/Pt stacks using SQUID
(M
s
¼ 0.85 MA m
1
, anisotropy field of about 150 mT), and Brillouin
light-scattering spectroscopy (BLS) to determine DMI
47
(see Supplementary
Note 1). The films were patterned by e-beam etching using an aluminium hard
mask, which was consequently removed by chemical etching. The Ti\Au contacts
were made in the second step via lift-off technique.
Magnetization imaging and dynamics
. MFM was performed on a commercial
Bruker Dimension 3000 microscope with a stage customized for high frequency
transport measurements with a typical pulse rise/fall time o1 ns (ref. 48). The
MFM tips are home made with a non-magnetic capping layer in order to increase
the distance between the magnetic tip coating and the surface to minimize the
magnetic perturbations during the atomic force microscopy scan. Due to the fact
that the tips are magnetically extremely soft and so follow the applied field, the
skyrmions always appear as a bright (that is, repulsive) contrast due to the
antiparallel magnetic configuration between the tip and the skyrmion. To avoid any
heating and related thermal drifts, we have used a permanent magnet which
implies an error of 20% on the given values of magnetic field. Current densities are
defined as the average across the entire sample thickness (magnetic and non-
magnetic layers).
Micromagnetic calculations
. Micromagnetic modelling was carried out using the
OOMMF code
49
where the cell size used was 0.5 nm 1.5 nm 1.5nm. We used
the measured material parameters K
u
¼ 0.5 MJm
3
, M
s
¼ 0.85 MA m
1
and used
A ¼ 12 pJ m
1
as an average of the bulk exchange constants for Co and Ni.
Data availability. All the data are available from the authors upon reasonable
requests.
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