Magnetic skyrmions hold promise for spintronic devices. To explore the dynamical properties of skyrmions in devices, a nanoscale method to image spin textures in response to a stimulus is essential. Here, we apply a technique for operando electrical current pulsing of chiral magnetic devices in a Lorentz transmission electron microscope. In ferromagnetic multilayers with interfacial Dzyaloshinskii–Moriya interaction, we study the creation and annihilation of skyrmions localized by point-like pinning sites due to defects. Using a combination of experimental and micromagnetic techniques, we establish a thermal contribution for the creation and annihilation of skyrmions in our study. Our work reveals a mechanism for controlling skyrmion density, which enables an examination of skyrmion magnetic field stability as a function of density. We find that high-density skyrmion states are more stable than low-density states or isolated skyrmions resisting annihilation over a magnetic field range that increases monotonically with density.

Magnetic skyrmions are topological spin textures that could potentially store and process information with non-volatility, high speed, and low power consumption.1–6 The recent discovery of homochiral Néel skyrmions in asymmetric ferromagnetic multilayers with interfacial Dzyaloshinskii–Moriya interaction (DMI) further enhances the potential of skyrmion-based devices because they are stable at room temperature, and because the films supporting this type of skyrmion are compatible with modern nanofabrication processes.7–13 In addition, manipulation of skyrmions with electric current is possible using spin–orbit torque at ferromagnet/heavy metal interfaces,7,9,13–20 which enables skyrmion speeds exceeding 100 m/s on a racetrack.7,17,19

Pioneering skyrmion research used micro-scale skyrmions that can be tracked with magneto-optical microscopy.2,9,13,20–22 However, the push for high-density information processing has led to the use of skyrmions at or below the 100 nm length scale, which requires higher resolution imaging techniques. Lorentz transmission electron microscopy (LTEM), with spatial resolution on the order of a few nanometers and time-resolution of sub-seconds,23 stands out as an excellent option to study both the magnetic structure and evolution of skyrmions. Although some of the most urgent questions regarding skyrmion dynamics involve control using electric current, a few studies report operando current control in an LTEM setting. Furthermore, most of these operando biasing studies are on single-crystalline materials, thinned and micropatterned by focused ion beam (FIB).24–26 In the case of ferromagnetic multilayers with interfacial DMI, only millimeter-scale sample areas with a DC bias have been reported.27 Almost contemporary to this work, current pulses have been applied to achieve high density skyrmions in a synthetic antiferromagnet heterostructure in the LTEM environment.28 These works demonstrate the critical importance of integrating electrical current driven skyrmion devices with biasing holders that enable operando LTEM measurements.

In this work, we present a microfabricated device that enables the operando current pulsing to chiral magnetic samples in LTEM. We observe strongly pinned skyrmions that can be nucleated with electric current but are strongly bound to pinning sites. Using a thermally assisted nucleation and annihilation mechanism via current-induced Joule heating, we control the skyrmion density in these devices. These findings highlight the potential value of skyrmion pinning sites and provide an alternative to controlling skyrmion density from previously studied mechanisms such as changing the tilt angle of the magnetic field or varying the temperature.29,30 Moreover, micromagnetic simulations clarify that the nucleation and annihilation of skyrmions are consistent with a thermally assisted process in which the spin texture finds its energetic minimum of configuration space. Finally, we study the magnetic field stability of skyrmion textures as a function of their skyrmion density and find that as the density increases, the textures become increasingly stable against magnetic field perturbations.

In this study, we investigate Néel-type chiral textures stabilized in heavy metal ferromagnet heterostructures,7,8,11,12,15,19,29–33 with ten repeats of a Pt(1.5 nm)/Co(1.5 nm)/Ru(1.5 nm) trilayer stack [Fig. 1(a)] deposited by magnetron sputtering in an Ar environment deposition chamber with a base pressure of ∼10−7 Torr. A 3 nm layer of Ti was used for seeding and capping. We grow identical films on a patterned device template for the operando experiment and two additional substrates: a thermally oxidized silicon substrate and an unpatterned SiNx membrane. A film grown on a thermally oxidized silicon substrate is used to characterize magnetic properties. At room temperature, the saturation magnetization is Ms = 1340 kA/m, and the effective anisotropy is Keff = 56 kJ/m3 as measured using vibrating sample magnetometry (VSM). The positive sign of Keff indicates that the sample exhibits an out-of-plane easy axis. Figure 1(c) shows the out-of-plane magnetic moment normalized by Ms as a function of magnetic field.

FIG. 1.

(a) Sample material composition. (b) Magnetic hysteresis for a magnetic field applied out of the plane. (c) Image of an operando LTEM device taken in a high-angle annular dark-field (HAADF) mode of the TEM. Since the annular dark-field detector detects the electrons scattered to the high angle and shows a mass-thickness contrast, the darkest contrast is where the electron beam passes through the transparent membrane and the brightest part is where it is scattered by the patterned magnetic material. The red dashed line defines the boundary of the patterned magnetic film, which function as a 4-wire current device. The white dashed diamond indicates the field of view we used to investigate the device channel. (d)–(h) LTEM images from the device channel at different magnetic fields in the order the magnetic field was applied. The black-white stripe-like contrast in the LTEM is created along the domain wall, and the intensity is proportional to a projection of the curl of the local magnetic moment in the beam propagation direction.11,34 We use image processing described in Sec. S4 in the supplementary material to maximize the image contrast from the magnetic moment. Since no contrast in LTEM images from Néel domain walls can be seen when the electron beam is at the normal incident,34 we use a 20° tilt of the sample in the direction perpendicular to the direction in which electric current is applied. In (e), the polarity of the skyrmion is opposite from (h) as indicated by the reversed order of bright and dark contrast. The reference image used to subtract the background was taken at ±210 mT and is shown Fig. S4 in the supplementary material.

FIG. 1.

(a) Sample material composition. (b) Magnetic hysteresis for a magnetic field applied out of the plane. (c) Image of an operando LTEM device taken in a high-angle annular dark-field (HAADF) mode of the TEM. Since the annular dark-field detector detects the electrons scattered to the high angle and shows a mass-thickness contrast, the darkest contrast is where the electron beam passes through the transparent membrane and the brightest part is where it is scattered by the patterned magnetic material. The red dashed line defines the boundary of the patterned magnetic film, which function as a 4-wire current device. The white dashed diamond indicates the field of view we used to investigate the device channel. (d)–(h) LTEM images from the device channel at different magnetic fields in the order the magnetic field was applied. The black-white stripe-like contrast in the LTEM is created along the domain wall, and the intensity is proportional to a projection of the curl of the local magnetic moment in the beam propagation direction.11,34 We use image processing described in Sec. S4 in the supplementary material to maximize the image contrast from the magnetic moment. Since no contrast in LTEM images from Néel domain walls can be seen when the electron beam is at the normal incident,34 we use a 20° tilt of the sample in the direction perpendicular to the direction in which electric current is applied. In (e), the polarity of the skyrmion is opposite from (h) as indicated by the reversed order of bright and dark contrast. The reference image used to subtract the background was taken at ±210 mT and is shown Fig. S4 in the supplementary material.

Close modal

An extended film deposited on an unpatterned SiNx membrane is used to observe the magnetic behavior as a function of magnetic field. Additionally, this sample allows us to quantify the DMI constant using Lorentz microscopy. Since no contrast in the LTEM image is produced by a Néel type domain wall when the sample is normal to the beam propagation direction,11,34 we measure with a 4 mm defocus and a 20° stage tilt. In this setting, we observe the breaking up of labyrinthine domains into skyrmions as we increase the magnetic field from zero to saturation,30 whereas decreasing the field from saturation to zero does not lead to the nucleation of skyrmions (supplementary material S1). We find an average domain wall width of L0 = 119.7 ± 0.2 nm from taking the Fourier transform of the labyrinthine domain state image at zero field and fitting the radially averaged Fourier transform to the Gaussian function.35 We calculate the DMI constant (|D|) from the energy model for the parallel stripe domain provided in Ref. 36. The lack of zero-tilt domain contrast indicates that we have Néel domain walls. Thus, we conclude that the DMI constant is above the threshold value. This sets the lower bound of Aex to be approximately 28.5 pJ/m. We determine the upper bound of Aex to be 30 pJ/m.37,38 Under these assumptions, we find that the possible range of the DMI constant |D| is 1.77–1.90 mJ/m2. The detailed method for calculating the range of DMI constant is discussed in supplementary material S5. The DMI constant we obtain is slightly small but comparable to a previous report.39 We also note that the dipolar field may play a significant role in forming skyrmions in our sample, as predicted for skyrmions with diameters between 10 and 100 nm.40 

For operando experiments, we fabricate Π-shaped devices using photolithography and lift-off techniques directly on a protochip™ fusion e-cell composed of a 50 nm thick SiNx membrane window and gold electrodes that extend to the center of the membrane [Fig. 1(b)]. Each corner of the channel is in electrical contact with contact pads that connect via spring contacts to electrical equipment outside of the transmission electron microscope. This geometry allows 4-terminal sensing with the device region between the voltage leads as the active channel imaged by LTEM. To accurately determine the current density without the confounding influence of the lead and contact resistances, we first measure the channel resistance, R = 12 ∼ 14 Ω, in the 4-terminal geometry. We monitor the voltage ΔV across V+/V on an oscilloscope as we apply pulses using an arbitrary waveform generator through I+/I. We then calculate the current density using J=ΔVRA, where A is the cross-sectional area of the film. To calculate the cross-sectional area, we multiply the channel width of 7.5 μm by the thickness of the multilayer film of 51 nm. The thickness of the film is obtained by adding the thickness of all layers. Magnetic domains from the active device channel observed at different points in the hysteresis loop are shown in Figs. 1(d)1(h). Similar to films on the unpatterned SiNx membrane, we find the transition from labyrinthine domains [Fig. 1(d)] to isolated skyrmions [Fig. 1(e)] when increasing the field from zero to saturation but no nucleation in the reverse direction starting from saturation [Fig. 1(f)]. Skyrmions at a negative field have reverse polarity as shown by a reversed intensity profile [Figs. 1(g) and 1(h)].

As we increase the magnetic field from zero, we notice that a higher skyrmion density forms in the operando device as compared to the unpatterned film grown on the SiNx membrane. Although the peak skyrmion density is found close to H = 170 mT for both samples, the skyrmion density in the operando device is up to 100 times higher than that in the unpatterned SiNx membrane. We also find a spatial non-uniformity of the density within the operando device. Areas close to the electrode show a smaller skyrmion density compared to the center of the channel. Further investigation of the sample reveals that the fusion e-cell chips provided from ProtochipsTM contain a manufacturing residue of gold nanoparticles on the SiNx surface with a diameter between 5 nm and 15 nm (supplementary material S2). The films that grow on these particles show local buckling and intermixing of the repeated multilayers, creating strong local pinning sites for magnetic textures. Within the channel area, the density of gold nanoparticles is sparser near the electrode and more concentrated toward the center of the membrane. This is reflected in the non-uniform distribution of field nucleated skyrmion between region 1 and region 2, as specified in Fig. 2(a).

FIG. 2.

(a) LTEM image of field nucleated skyrmions in the device at H = 170 mT. (b) Skyrmion density measured from region 1 and region 2 of the device, and from the extended film deposited on a SiNx membrane. (c) and (d) Average line cut profile of skyrmions found in region 1 and region 2. The gray area shows the maximum and minimum intensity of the profile obtained from all skyrmions found in the respective region (inset) averaged intensity map of skyrmions.

FIG. 2.

(a) LTEM image of field nucleated skyrmions in the device at H = 170 mT. (b) Skyrmion density measured from region 1 and region 2 of the device, and from the extended film deposited on a SiNx membrane. (c) and (d) Average line cut profile of skyrmions found in region 1 and region 2. The gray area shows the maximum and minimum intensity of the profile obtained from all skyrmions found in the respective region (inset) averaged intensity map of skyrmions.

Close modal

Because the field-nucleated skyrmion density is different in region 1 and region 2 of the operando device, we compare the internal structure of the skyrmions in each of the two regions using the intensity profile of skyrmions in the LTEM image. The average diameter of skyrmions is d = 94 ± 11 nm and d = 99 ± 10 nm for skyrmions in region 1 and region 2, respectively, which is similar to the d = 101 nm found from skyrmions on the film grown on an unpatterned SiNx membrane. Moreover, an averaged line cut profile and intensity map of the skyrmions obtained from region 1 [Fig. 2(c)] and region 2 [Figs. 2(d)] are indistinguishable. This suggests that although more skyrmions are nucleated due to the anchoring of the domain walls by pinning sites in region 1, the overall structure and size are not affected.

Next, we examine the response of chiral textures to electric current pulses. Due to limitations in bandwidth of the holder, the current pulses have a rise time of τ ∼ 100 ns. For the input current pulses shorter than 200 ns, the amplitude of the pulse decreases, while the pulse width remains around 200 ns due to the limited bandwidth of the biasing holder. Thus, we apply current pulses with the input width of 100 ns or greater to minimize the deformation of the pulse shape. The pulse width presented in the remainder of this work is an input value from the arbitrary waveform generator, and the current density is the peak current density obtained from the measured pulse shape in an oscilloscope in the 4-terminal configuration. Before applying the current, the sample is initialized to the labyrinth state by applying a strong negative field beyond saturation, passing through the zero-field and then setting H = + 100 mT [Fig. 3(a)]. Upon application of the current pulse with a current density of J = 7.2 × 1011 A/m2 and a pulse width of 300 ns, we observe the nucleation of skyrmions from labyrinthine domains [Fig. 3(b)]. To examine if skyrmion nucleation occurs as a search for the energy minimum, we also initialize the sample with the field polarized state at the same field by applying a strong positive field beyond saturation and reducing the field to H = + 100 mT [Fig. 3(c)]. The sample stays at a field polarized single domain state due to the flat hysteresis loop [Fig. 1(c)]. We find that skyrmions are nucleated with the similar density using the same current pulse, which supports our picture of thermally assisted energy minimization.

FIG. 3.

(a) A stripe domain state at magnetic field H = 100 mT and (b) a nucleated skyrmion lattice after the application of a current pulse. (c) A field polarized state at the same magnetic field and (d) a nucleated skyrmion lattice after the application of a current pulse. In both cases, the current pulse with current density of J = 7.2 × 1011 A/m2 and pulse width of t = 300 ns was applied.

FIG. 3.

(a) A stripe domain state at magnetic field H = 100 mT and (b) a nucleated skyrmion lattice after the application of a current pulse. (c) A field polarized state at the same magnetic field and (d) a nucleated skyrmion lattice after the application of a current pulse. In both cases, the current pulse with current density of J = 7.2 × 1011 A/m2 and pulse width of t = 300 ns was applied.

Close modal

Recently, the role of defects in ferromagnetic multilayer films supporting skyrmions has been of key interest, because the defect may contribute to the behavior of skyrmions during transportation, creation, and annihilation process.41–43 While some studies suggest that skyrmions can move efficiently around defects in a racetrack44 or reduce the deflection angle from skyrmion Hall effect,14 other studies have concluded that they could be a source of pinning for domain walls and skyrmions.15,43,45,46 Also, non-trivial collective motion and dynamics of skyrmions have been predicted, assuming Thiele's equation of motion in the presence of pinning potentials.41,42,47 Experimentally, we find no evidence of current-induced translational motion of skyrmions in our device, which we attribute to the strong pinning of skyrmions by defects. Whether there is a contribution from more complex dynamic behaviors such as jamming or collective motion42,47,48 is a subject of further studies. Nevertheless, the immobility of the skyrmions suggests that the spin orbit-torque contributes as a secondary effect in our experiment. This is also consistent with the recent findings that show a significant contribution from the spin–orbit torque only for the current pulses with 10 ns or shorter pulse width, and dominant thermal effect for pulses longer than 100 ns.15,49

To investigate how current pulses affect the density of the skyrmions, we analyze the statistics of skyrmion nucleation and annihilation under varied external magnetic fields and also using the thermal energy deposited by a current pulse as control variables. We classify three different regimes of behavior in terms of three magnetic fields that we label high field (H = 180 mT), intermediate field (H = 140 mT), and low field (H = 90 mT). We calculate thermal energy via Joule heating from, E=V2(t)/Rdt, where the square of voltage measured from the oscilloscope (supplementary material S3) is divided by the resistance and integrated over the duration of the current pulse.

We start at a high field where skyrmions with a density of 1.2 ± 0.4 μm−2 are field nucleated using the procedure described above. After application of a 700 ns current pulse at a J = 3.2 × 1011 A/m2 current density, we observe that the number of skyrmions decreases to around a quarter of the initial number [Fig. 4(a)]. Next, we varied the pulse width from 200 ns to 700 ns at a fixed current density of J = 3.2 × 1011 A/m2 to study how the number of skyrmions decreases as the pulse width increases. To see a more general trend of skyrmion annihilation as a function of pulse energy, we expanded the range of applied current density from J = 1.6 × 1011 A/m2 to J = 5 × 1011 A/m2 and pulse widths from 100 ns to 700 ns. We plot the ratio of the number of skyrmions before and after the current pulse (Na/Nb) as a function of input energy [Fig. 4(b)]. Under the assumption that the temperature increase ΔT varies linearly with the current pulse energy, the data follow an Arrhenius trend as indicated by the fit line. While this result does not elucidate a detailed mechanism of annihilation, it supports a thermally assisted process in which the spin texture is excited by current pulses, likely including Joule heating, to leave a local energy minimum and find a more stable energy minimum in the configuration space.

FIG. 4.

(a) Annihilation of skyrmions after a current pulse at H = 180 mT and (b) the trend of annihilation as a function of current pulse energy. The blue dashed line is a fit to an Arrhenius function. (c) and (g) show the trend of skyrmion density as a function of current pulse energy at H = 140 mT and H = 90 mT, respectively. (d)–(f) and (h)–(j) show the image of the channel after applying the current pulse at different points in the curve from (c) and (g), respectively. To count the number of skyrmions in the sample, we use an image processing method that matches the averaged image of visually selected skyrmions with the features in the image (Sec. S4 in the supplementary material).

FIG. 4.

(a) Annihilation of skyrmions after a current pulse at H = 180 mT and (b) the trend of annihilation as a function of current pulse energy. The blue dashed line is a fit to an Arrhenius function. (c) and (g) show the trend of skyrmion density as a function of current pulse energy at H = 140 mT and H = 90 mT, respectively. (d)–(f) and (h)–(j) show the image of the channel after applying the current pulse at different points in the curve from (c) and (g), respectively. To count the number of skyrmions in the sample, we use an image processing method that matches the averaged image of visually selected skyrmions with the features in the image (Sec. S4 in the supplementary material).

Close modal

At intermediate and low magnetic fields in which the magnetic initialization leads to a labyrinth state, skyrmions nucleate by breaking apart the labyrinthine domains during the current pulse as we observed earlier (Fig. 3). Because the initial states contain zero or few skyrmions, we only consider the density of skyrmions after current pulses for the analysis in Figs. 4(c)4(g). When current pulses are applied at an intermediate field (H = 140 mT), we observe an initial increase in the skyrmion density to 4.5 ± 0.3 μm−2 using E = 90 nJ pulses. The density then drops and stabilizes to ∼1.5 μm−2 for the higher energy pulses. We note that a mixed state of isolated skyrmions and labyrinthine domains appears before the skyrmion density reaches a maximum, whereas only isolated skyrmions are present when the density saturates to a lower value. This suggests that the skyrmions are first nucleated by the breaking apart of labyrinthine domains via a thermally assisted process but are still metastable. When the injected thermal energy exceeds a threshold value, it contributes to skyrmion annihilation that drives the system toward a more stable energy minimum in the skyrmion configuration state with a lower skyrmion density.

Finally, we repeat the experiment at the lowest magnetic field, H = 90 mT. Here, the initial state is a dense labyrinthine domain state. Unlike at the intermediate field in which we observe a peak and then saturation at a lower density, at this field, we find a monotonically increasing trend of skyrmion density over a wide range of injected energy that appears to approach saturation for the largest energy pulses [Fig. 4(g)]. We obtain the highest skyrmion density observed in the study, 11.5 ± 0.3 μm−2, which is more than five times higher than what we obtained from field nucleation. Moreover, the monotonic trend of the skyrmion density with respect to injected energy indicates that we can achieve arbitrary skyrmion density between 0 and 11.5 μm−2 by applying an appropriate current pulse to the device.

To obtain micromagnetic insights into the experimental results, we carry out a simulation using MuMax3.50 The simulation was performed on a 2 × 2 μm2 area with a cell size of 4 × 4 × 45 nm3. All material parameters are the same as those determined for the experimentally studied films and scaled with respect to effective medium model. In our micromagnetic simulation, the Zeeman energy term is included for the calculation of the total energy. The total magnetic field is applied, as in the experiment, at a sample tilt angle of 20°. We also note that while the small simulation area and periodic boundary conditions are used to simplify the micromagnetic problem, this also limits the textures to have only integer periods.

We first investigate the energetics of spin textures, searching for the texture that yields the lowest energy at different magnetic fields. To obtain the total energy of a magnetic texture, we initialize the simulation with each texture at zero field and evolve it over an increasing field, minimizing the total energy at a regular field interval. Skyrmion arrays for the field-dependent simulation are initialized with Nsk = 42 [Fig. 5(e)], which was preserved over the entire range of the field we apply in Fig. 5(a). Although this approach does not reveal the full energy landscape including the magnitude of the potential barrier for skyrmion annihilation, it gives us a qualitative picture of the system ground state. Thermal excitation of the sample will enable the magnetic textures to leave local energy minima and, in some cases, enter the ground state.

FIG. 5.

(a) Energy density of uniform, stripe domain, and skyrmion array states as a function of magnetic field. Arrows at 90 mT and 125 mT indicate the transition fields. (b) Minimized total energy from the simulation of skyrmion array as a function of skyrmion density normalized to the energy when skyrmion density is zero. Simulated magnetic textures on the bottom show the simulated magnetic texture for stripe domain at H = 120 mT (c) and at points designated along the curve H = 120 mT (d)–(f). The magnetic field is applied with a tilt angle of 20° from the z axis.

FIG. 5.

(a) Energy density of uniform, stripe domain, and skyrmion array states as a function of magnetic field. Arrows at 90 mT and 125 mT indicate the transition fields. (b) Minimized total energy from the simulation of skyrmion array as a function of skyrmion density normalized to the energy when skyrmion density is zero. Simulated magnetic textures on the bottom show the simulated magnetic texture for stripe domain at H = 120 mT (c) and at points designated along the curve H = 120 mT (d)–(f). The magnetic field is applied with a tilt angle of 20° from the z axis.

Close modal

We observe two transitions of the ground states within the range of the field we apply. At magnetic fields below 90 mT [left arrow in Fig. 5(a)], stripe domains have the lowest energy, which explains their prominence at low magnetic fields in the experiment. Above 90 mT, a skyrmion array becomes the most energetically favorable state until the second transition at 125 mT [right arrow in Fig. 5(a)] above which the field polarized uniform state has the lowest energy. This observation is in agreement with Ref. 49 that used a similar computational approach.

To further illuminate the relationship between skyrmion density and the magnetic field, we calculate the system energy as we vary the skyrmion density around the magnetic fields in which a skyrmion array is the ground state. Parts (d)–(f) of Fig. 5 show the simulated spin textures with different skyrmion densities after the system is relaxed. We record the total energy of each of these states and plot it as a function of skyrmion density in Fig. 5(b). At field H = 130 mT, the global energy minimum is difficult to distinguish and close to a ferromagnetic state where skyrmion density is zero. As we lower the applied magnetic field to H = 120 mT, an energy minimum emerges at non-zero skyrmion density. The energy minimum becomes more pronounced as the field further decreases to H = 110 mT. This simulation result is consistent with our experimental results in which we observe skyrmion annihilation at high fields and an increasing trend of skyrmion density after nucleation at lower fields.

When skyrmions are closely packed, the interaction between skyrmions can dominate the stability of skyrmions making the annihilation process different from that of isolated skyrmions.22,51 To verify this idea, we experimentally prepare our device using current pulse nucleation, choosing magnetic fields such that we systematically vary the skyrmion density. We then increase (or decrease) the magnetic field to find the magnetic field at which the skyrmions are annihilated, thus establishing the magnetic field range over which skyrmions persist. The evolution of spin textures follow different paths depending on the direction of the field variation. When the field increases, the skyrmions collapse and the density decreases until we are left with a field polarized magnetic state [orange arrow, Figs. 6(a) and 6(b)]. For increasing fields, the behavior is independent of the skyrmion density. On the other hand, when the field decreases, the skyrmions expand and in some cases begin to form short labyrinthine domains [blue arrow, Figs 6(a) and 6(b)]. As the chiral textures expand, however, adjacent domain walls repel each other,41,52 which preserves the roughly circular skyrmion morphology. Therefore, as the initial density of skyrmion increases, individual skyrmions face a barrier to expanding into a labyrinthine domain. As a result, while the upper bound of the field that supports skyrmions remain consistent, the lower bound of the field that preserves the morphology of skyrmions decreases with the initial skyrmion density [Fig. 6(c)]. While a similar effect has been observed in micrometer-scale skyrmions thermally nucleated by lasers,22 we demonstrate that this type of topological protection is more general, independent of skyrmion size and the material system supporting it. It is also to be noted that similar expansion of skyrmions into short labyrinthine domains has also observed for sub-10-nm size skyrmions.53 

FIG. 6.

Stability of nucleated skyrmions to the changes in the magnetic field. Skyrmions are nucleated at (a) 90 mT and (b) 140 mT and subject to changes in the field. After nucleation, images were taken sequentially as the field increases or decreases. Reinitialization is done only when the direction of the field variation changes. (c) Upper bound (red squares) and lower bound (blue circles) of the magnetic field at which skyrmionic bubbles are found as a function of initial skyrmion density.

FIG. 6.

Stability of nucleated skyrmions to the changes in the magnetic field. Skyrmions are nucleated at (a) 90 mT and (b) 140 mT and subject to changes in the field. After nucleation, images were taken sequentially as the field increases or decreases. Reinitialization is done only when the direction of the field variation changes. (c) Upper bound (red squares) and lower bound (blue circles) of the magnetic field at which skyrmionic bubbles are found as a function of initial skyrmion density.

Close modal

In conclusion, we demonstrate a device for high-resolution, operando LTEM current pulsing experiments. We find that skyrmions can be robustly generated in samples with strong pinning sites. While the details of skyrmion nucleation and annihilation are determined by the interplay of several parameters, the density of skyrmions can be controlled with current-induced thermal pulses. Using this effect, we initialize our device with controlled skyrmion densities and verify an enhanced stability of high-density skyrmions that is persistent over a wide range of magnetic fields.

Our work on thermally assisted control of skyrmion density in films with strong pinning suggests a new possibility to engineer skyrmion density and dynamics using defects that are inherent to the device.54–56 Additionally, the development of biasing TEM sample holders with higher bandwidths will enable expanded operando experimental capabilities for understanding skyrmion behaviors such as transportation by short pulses and magnetic resonance. Although LTEM imaging for the operando studies of magnetic devices prefers magnetic materials with non-vanishing net magnetic moments for a better image contrast, there are new developing magnetic imaging techniques, such as four-dimensional Lorentz scanning TEM imaging57,58 which possesses a much higher field sensitivity and is compatible with the biasing devices. Therefore, it is possible to expand the application of these techniques to emerging skyrmion materials with small net magnetization such as ferrimagnets and synthetic antiferromagnets. We expect that the experimental framework for operando LTEM imaging presented here could offer a useful tool for the further investigation of ultra-small skyrmions that require truly nanoscale resolution to visualize magnetic texture and dynamics.59,60

See the supplementary material for the assessment of the film grown on an unpatterned SiNx membrane, plane view TEM image of the gold nanoparticles, cross-sectional TEM image of the film grown on a gold nanoparticle, and the typical current pulse shape used in the experiment. The supplementary material also includes the image processing procedure and calculation methods for magnetic parameters used in the manuscript.

A.M.P. and Z.C. contributed equally to this work.

This work is primarily supported by the DARPA TEE Program (No. D18AC00009). Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of DARPA. L.Z. acknowledges support by the Office of Naval Research (ONR) (No. N00014-15-1-2449). We acknowledge the use of shared facilities including the Cornell Center for Materials research, and NSF MRSEC (No. DMR-1719875) and the Cornell NanoScale Facility, an NNCI member supported by the NSF (No. NNCI-1542081). We thank Professor Robert A. Buhrman for helpful discussion.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Supplementary Material