Research ArticleMAGNETISM

Blowing magnetic skyrmion bubbles

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Science  11 Jun 2015:
aaa1442
DOI: 10.1126/science.aaa1442

Abstract

The formation of soap bubbles from thin films is accompanied by topological transitions. Here we show how a magnetic topological structure, a skyrmion bubble, can be generated in a solid state system in a similar manner. Using an inhomogeneous in-plane current in a system with broken inversion asymmetry, we experimentally “blow” magnetic skyrmion bubbles from a geometrical constriction. The presence of a spatially divergent spin-orbit torque gives rise to instabilities of the magnetic domain structures that are reminiscent of Rayleigh-Plateau instabilities in fluid flows. We determine a phase diagram for skyrmion formation and reveal the efficient manipulation of these dynamically created skyrmions, including depinning and motion. The demonstrated current-driven transformation from stripe domains to magnetic skyrmion bubbles could lead to progress in skyrmion-based spintronics.

Magnetic skyrmions are topological spin textures that can be stabilized by Dzyaloshinskii-Moriya interactions (DMI) (19) in chiral bulk magnets, e.g., MnSi, FeGe, etc. Thanks to their unique vortex-like spin-texture they exhibit many fascinating features including emergent electromagnetic fields, which enable their efficient manipulation (4, 5, 810). A particularly technologically interesting property is that skyrmions can be driven by a spin transfer torque mechanism at a very low current density, which has been demonstrated at cryogenic temperatures (4, 5, 8, 10). Besides bulk chiral magnetic interactions, the interfacial symmetry-breaking in heavy metal/ultra-thin ferromagnet/insulator (HM/F/I) trilayers introduces an interfacial DMI (1114) between neighboring atomic spins, which stabilizes Néel walls (cycloidal rotation of the magnetization direction) with a fixed chirality over the Bloch walls (spiral rotation of the magnetization direction) (1520). This is expected to result in the formation of skyrmions with a hedgehog configuration (14, 18, 2125). This commonly accessible material system exhibits spin Hall effects from heavy metals with strong spin-orbit interactions (26), which in turn give rise to well-defined spin-orbit torques (SOTs) (17, 19, 2729) that can control magnetization dynamics efficiently. However, it has been experimentally challenging to utilize the electric current and/or its induced SOTs (8, 21, 23, 24, 27, 3032) for dynamically creating and/or manipulating hedgehog skyrmions. Here we address that issue.

Central to this work is how electric currents can manipulate a chiral magnetic domain wall (DW), i.e., the chirality of the magnetization rotation (as shown in Fig. 1A) is identical for every domain wall. This fixed chirality is stabilized by the interfacial DMI (1719, 21, 28). In HM/F/I heterostructures the current flowing through the heavy metal generates a transverse vertical spin current thanks to the spin Hall effect (27), which results in spin accumulation at the interface with the ferromagnetic layer. This spin accumulation gives rise to a SOT acting on the chiral DW (Fig. 1A). The resultant effective spin Hall field can be expressed as (1719, 27) Embedded Image (1)where Embedded Image is the magnetization unit vector, Embedded Image is the unit vector normal to the film plane and Embedded Image is the direction of electron particle flux. Here Embedded Image can be written as Embedded Image, where Embedded Image is the spin of an electron, e is the charge of an electron, tf is the thickness of the ferromagnetic layer, and MS is the saturation (volume) magnetization. The spin Hall angle Embedded Image is defined by the ratio between spin current density (JS) and charge current density (JC). For homogeneous current flow along the x axis (Fig. 1B), a chiral SOT enables efficient DW motion (1719). In the case of a stripe domain with a chiral DW (Fig. 1B), the symmetry of Eq. 1 leads to a vanishing torque on the side walls parallel to the current and therefore only the end of the stripe domain is moved; if the opposite end is pinned, this results in an elongation of the stripe.

Fig. 1 Schematic of the transformation of stripe domains into magnetic skyrmion bubbles.

(A) Infinitesimal section of a chiral DW in a ferromagnet (F)/heavy metal (HM) bilayer illustrating the relationship between local magnetization vectors and the SOT-induced chiral DW motion of velocity Vdw in a device with a homogeneous electron current flow je along the +x axis. Blue color corresponds to upward orientation of magnetization, while the orange color is the downward orientation of magnetization. Bottom panel illustrates the magnetization directions inside of the Néel wall. (B) Top view of a trilayer device. The blue region is a stripe-shaped domain. Light blue arrows show the in-plane magnetization direction of the DW [as shown in the bottom panel of (A)] and indicate that the domain has left-handed chirality. The red arrows correspond to the current distribution. (C) Introducing a geometrical constriction into the device gives rise to an inhomogeneous current distribution, which generates a flow along the y-axis, jy around the narrow neck. This current distribution is spatially divergent to the right and convergent to the left of the constriction. The y-component of the current distribution is highlighted in (D). This introduces an effective spin Hall force Embedded Image along the y-axis that (E) locally expands the stripe domain on the right side. (F) Once the expansion approaches a critical point, the resultant restoring forces Fres associated with the surface tension of the DWs, are no longer able to maintain the shape and the stripe domains break into circular bubble domains, resulting in the formation of synthetic Néel skyrmions.

The situation becomes more complex when the stripe domain is subjected to an inhomogeneous current flow. This can be achieved by introducing a geometrical constriction into a current-carrying trilayer wire (Fig. 1C). Such a constriction results in an additional current component along the y axis - jy around the narrow neck (Fig. 1D). The total current j is spatially convergent/divergent to the left/right of the constriction (33). Consequently, inhomogeneous effective forces on the DWs (caused by the spin Hall field) are created along the y axis - Embedded Image, these forces act to expand the end of the domain (Fig. 1E). As the domain end continually expands its radius the surface tension in the DW (resulting from the increasing DW energy determined by the combination of exchange and anisotropy fields) increases (34), which results in breaking the stripes into circular domains (Fig. 1F).

This process resembles how soap bubbles develop out of soap films upon blowing air through a straw, or how liquid droplets form in fluid flow jets (35). Because of the interfacial DMI in the present system, the spin structures of the newly formed circular domains maintain a well-defined (left-handed) chirality (13, 14, 23, 24). These created synthetic hedgehog (Néel) skyrmions (14, 23), once formed, are stable thanks to topological protection and move very efficiently following the current direction, a process that can be described based on a modified Thiele equation (36). The dynamic skyrmion conversion could, in principle, happen at the other side of device where the spatially convergent current compresses stripe domains. However, sizeable currents/SOTs are required to compensate the enhanced (repulsive) dipolar interaction. The proposed mechanism differs from a recent theoretical proposal with similar geometry, where skyrmions are formed from the coalescence of two independent DWs extending over the full width of a narrow constriction at a current density ≈ 108 A/cm2 (32). For repeated skyrmion generation, this latter mechanism requires a continuous generation of paired DWs in the constriction, which is inconsistent with the experimental observations described below.

Transforming chiral stripe domains into skyrmions

We demonstrated this idea experimentally with a Ta(5 nm)/Co20Fe60B20(CoFeB)(1.1 nm)/TaOx(3 nm) trilayer grown by magnetron sputtering (37, 38) and patterned into constricted wires via photolithography and ion-milling (33). The wires have a width of 60 μm with a 3-μm wide and 20-μm long geometrical constriction in the center. Our devices are symmetrically designed across the narrow neck to maintain balanced demagnetization energy. A polar magneto-optical Kerr effect (MOKE) microscope in a differential mode (39) was utilized for dynamic imaging experiments at room temperature. Before applying a current, the sample was first saturated at positive magnetic fields and subsequently at a perpendicular magnetic field of Embedded Image mT, sparse magnetic stripe and bubble domains prevail at both sides of the wire (Fig. 2A). The lighter area corresponds to negative perpendicular magnetization orientation and darker area corresponds to positive orientation, respectively.

Fig. 2 Experimental generation of magnetic skyrmions.

(A) Sparse irregular domain structures are observed at both sides of the device at a perpendicular magnetic field of Embedded Image mT. (B) Upon passing a current of je = +5 × 105 A/cm2 through the device, the left side of the device develops predominantly elongated stripe domains, while the right side converts into dense skyrmion bubbles. (C and D) By reversing the current direction to je = –5 × 105 A/cm2, the dynamically created skyrmions are forming at the left side of device. (E and F) Changing the polarity of external magnetic field reverses the internal and external magnetization of these skyrmions. (G) Phase diagram for skyrmion formation. The shaded area indicates field/current combinations that result in the persistent generation of skyrmions after each current pulse.

In contrast to the initial magnetic domain configuration, after passing a 1 s single pulse of amplitude je = +5 × 105 A/cm2 (normalized by the width of device – 60 μm), it is observed that the stripe domains started to migrate, subsequently forming extended stripe domains on the left side. These domains were mostly aligned with the charge current flow and converged at the left side of constriction. The stripes were transformed into skyrmion bubbles immediately after passing through the constriction (Fig. 2B). These dynamically created skyrmions, varying in size between 700 nm and 2 μm (depending on the strength of the external magnetic field), are stable and do not decay on the scale of a typical laboratory testing period (at least 8 hours). The size of the skyrmions is determined by the interplay between Zeeman, magnetostatic interaction and interfacial DMI. In the presence of a constant electron current density of je = +5 × 105 A/cm2, these skyrmions are created with a high speed close to the central constriction and annihilated/destroyed at the end of the wire. Capturing the transformation dynamics of skyrmions from stripe domains is beyond the temporal resolution of the present setup. Reproducible generation of skyrmions is demonstrated by repeating pulsed experiments several times (33). Interestingly, the left side of the device remains mainly in the labyrinthine stripe domain state after removing the pulse current, which indicates that both skyrmion bubbles and stripe domains are metastable.

When the polarity of the charge current is reversed to je = –5 × 105 A/cm2, the skyrmions are formed at the left side of device (Fig. 2, C and D). This directional dependence indicates that the spatially divergent current/SOT, determined by the geometry of the device, is most likely responsible for slicing stripe DWs into magnetic skyrmion bubbles, qualitatively consistent with the schematic presented in Fig. 1.

At a negative magnetic field Embedded Image mT and current at je = +5 × 105 A/cm2 (Fig. 2, E and F), a reversed contrast, resulting from opposite inner/outer magnetization orientations, is observed as compared to positive fields. We varied the external magnetic field and charge current density systematically and determined the phase diagram for skyrmion formation shown in Fig. 2G. A large population of synthetic skyrmions is found only in the shadowed region, whereas in the rest of phase diagram, the initial domain configurations remain either stationary or flowing smoothly, depending on the strength of current density, as discussed below. This phase diagram is independent of pulse duration for pulses longer than 1 μs. It should be mentioned that no creation of skyrmions in regular shaped device with a homogeneous current flow (as illustrated in Fig. 1B) is observed up to a current density of je = +5 × 106 A/cm2.

Capturing the transformational dynamics

The conversion from chiral stripe domains into magnetic skyrmions can be captured by decreasing the driving current, which slows down the transformational dynamics. Figure 3, A to D, shows the dynamics for a constant dc current density of je = +6.4 × 104 A/cm2 at Embedded Image mT. The original (disordered) labyrinthine domains on the left side squeeze to pass through the constriction (Fig. 3B). The stripe domains become unstable after passing through the constriction and are eventually converted into skyrmions on the right side of the device, as shown in Fig. 3, C and D. This can be seen in more detail in the MOKE movies (movies S1 and S2). Because the x-component of the current results in an efficient motion of DWs, the skyrmion formation can happen away from the constriction. The synthetic skyrmions do not merge into stripe domains and in fact repel each other, indicating their topological protection as well as magnetostatic interactions.

Fig. 3 Capturing the transformational dynamics from stripe domains to skyrmions and motion of skyrmions.

(A to D) At a constant dc current je = +6.4 × 104 A/cm2 and Embedded Image mT, the disordered stripe domains are forced to pass through the constriction, and are eventually converted into skyrmions at the right side of the device. Red circles highlight the resultant newly-formed skyrmions. (E) Illustration of the spin-Hall effective field acting on these dynamically created skyrmions; the direction of motion follows the electron current. (F to I) The efficient motion of these skyrmions for a current density je = +3 × 104 A/cm2. (F) First, a 1 s long single pulse je = +5 × 105 A/cm2 initializes the skyrmion state. (G to I) Subsequently, smaller currents (below the threshold current to avoid generating additional skyrmions through the constriction) are used to probe the current-velocity relation. It is observed that these skyrmions are migrating stochastically, and moving out of the field of view. See MOKE movies S1, S2, and S4 for the corresponding temporal dynamics. (J) The current-velocity dependence of skyrmions is acquired by studying approximately 20 skyrmions via averaging their velocities by dividing the total displacement with the total time period.

Some important features should be noticed. There exists a threshold current je–sk = ±6 × 104 A/cm2 for persistently generating skyrmion bubbles from stripe domains for pulses longer than 1 μs. Above this current, the enhanced spin-orbit torques produce the instability of the DWs, which results in the continuous formation of skyrmions. The present geometry for skyrmion generation is very efficient, resulting in the observed threshold current 3 orders of magnitude smaller than suggested by previous simulation studies (107-8 A/cm2) in MnSi thin films with a bulk DMI where the driving mechanism is the conventional spin transfer torque (30). Below this threshold for continuous skyrmion generation, there is a threshold depinning current je–st = ±4.1 × 104 A/cm2 that produces a steady motion of stripe domains. The force (pressure) on the stripe from SOT at this current exceeds the one required to maintain its shape. When je–st < je < je–sk, the stripe domains are moving smoothly through the constriction and prevail at both sides of devices, with just the occasional formation of skyrmions.

Depinning and Motion of synthesized S = 1 skyrmions

The magnetic skyrmion bubbles discussed so far have a topological charge given by the skyrmion number S = 1, as is determined by wrapping the unit magnetization vector over the sphere Embedded Image (1, 8). These S = 1 synthetic skyrmions move thanks to the opposite direction of effective SOTs on the opposite sides of the skyrmion (Fig. 3E). Following the initialization by a current pulse je = +5 × 105 A/cm2 (which is larger than the threshold current je–sk for generating skyrmions), we studied the efficient depinning and motion of synthetic skyrmions (Fig. 3, F to I) at Embedded Image mT. At the current density je = +3 × 104 A/cm2, there is no migration of stripe domains through the constriction (hence an absence of newly-formed skyrmions). It is however, clear to see that the previously generated skyrmions at the right side of the device are gradually moving away following the electron flow direction. During the motion, no measurable distortion of these synthetic skyrmions is observed within the experimental resolution, consistent with the well-defined chirality of the skyrmion bubble. The average velocity Embedded Image is determined by dividing the displacement Embedded Image with the total time period Embedded Image. For the present current density, the motion of synthetic skyrmion is stochastic and influenced by random pinning with an average velocity of about 10 μm/s, the current dependence of which is summarized in Fig. 3J. The ratio of the velocity to the applied current is comparable to what is observed for the chiral DW motion in the related systems (17, 19).

Current characteristics of S = 0 magnetic bubbles

Because of the competition between long-range dipolar and short-range exchange interaction, a system with a weak perpendicular magnetic anisotropy undergoes a spin reorientation transition with in-plane magnetic fields that is typified by a stripe-to-bubble domain phase transition (39, 40). Such an in-plane field induced bubble state is established by sweeping magnetic field from Embedded Image mT to Embedded Image mT. Current-driven characteristics of the in-plane field induced magnetic bubbles are in stark contrast to the mobile magnetic skyrmions generated from SOTs. These bubbles shrink and vanish in the presence of a positive electron current density (Fig. 4, A to E), or elongate and transform into stripe domains in the presence of negative electron current density (Fig. 4, F to J). Such a distinct difference directly indicates the different spin structures surrounding these field induced bubbles, and thereby different skyrmion numbers.

Fig. 4 Absence of motion for the in-plane magnetic fields stabilized S = 0 magnetic bubbles.

(A) In-plane magnetic field induced bubbles are created by first saturating at in-plane field Embedded Image mT and subsequently decreasing to Embedded Image mT. Depending on the direction of the current, these magnetic bubbles either shrink or expand. (A to E) The shrinking bubbles are observed upon increasing the current density from je = +5 × 104 A/cm2 to +2.5 × 105 A/cm2 in 5 × 104 A/cm2 steps. (F to J) The expansion of bubbles is revealed for currents from je = –0.5 × 105 A/cm2 to –2.5 × 105 A/cm2 in 5 × 104 A/cm2 steps. (K) These results are linked to the different spin textures that were stabilized along the DW by the in-plane magnetic fields, namely, S = 0 skyrmion bubbles, which lead to different orientations of the spin Hall effective fields and different directions of DW motion as illustrated.

For the in-plane field induced magnetic bubbles, because the spin structures of DWs follow the external magnetic fields (18, 41, 42) (Fig. 4K), the corresponding skyrmion number is S = 0. Because of the same direction of the spin Hall effective fields given by the reversed DW orientations, topologically trivial S = 0 magnetic bubbles experience opposite forces on the DWs at opposite ends. This leads to either a shrinking or elongation of the bubbles depending on the direction of currents, which is consistent with our experimental observation. This also explains the in-plane current induced perpendicular magnetization switching in the presence of in-plane fields (27, 42).

Perspectives

Recent experimental efforts toward creating individual magnetic skyrmions use either tunneling current from a low-temperature spin-polarized scanning tunneling microscope (43) or geometrical confinement via sophisticated nanopatterning (4446). Our results demonstrate that spatially divergent current-induced SOTs can be an effective way for dynamically generating mobile magnetic skyrmions at room temperature in commonly accessible material systems. The size of these synthetic skyrmions could be scaled down by properly engineering the material specific parameters that control the various competing interactions in magnetic nanostructures (23, 24, 47). We expect that similar instabilities will be generated from divergent charge current flows. Whereas the mechanism for synthetic skyrmion generation can be qualitatively linked to the spatially divergent spin Hall spin torque, a comprehensive understanding of this dynamical conversion, particularly at the picosecond/nanosecond time scale where the intriguing magnetization dynamics occurs, requires further experimental and theoretical investigations. Spatially divergent SOT-driven structures also offer a readily accessible model system for studying topological transitions and complex “flow” instabilities (35), where the parameters governing the flow, such as surface tension, can be systematically tuned by the magnetic interactions. At the same time, this dynamic approach for skyrmion generation in the near future could enable the demonstration of advanced skyrmionic device concepts, for example, functional skyrmion racetrack memory (14, 23, 36, 48).

Supplementary Materials

www.sciencemag.org/cgi/content/full/science.aaa1442/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S7

References

Movies S1 to S5

References and Notes

  1. Supplementary materials are available on Science Online.
  2. Acknowledgments: Work carried out at Argonne National Laboratory was supported by the U.S. Department of Energy, Office of Science, Materials Science and Engineering Division. Lithography was carried out at the Center for Nanoscale Materials, which is supported by the DOE, Office of Science, Basic Energy Science under Contract No. DE-AC02-06CH11357. Work performed at UCLA was partially supported by the NSF Nanosystems Engineering Research Center for Translational Applications of Nanoscale Multiferroic Systems (TANMS). The authors also acknowledge insightful discussion with I. Martin and I. Aronson.
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