Introduction

The propagation of ___domain walls in magnetic materials, which forms the basis of race track memory1,2,3 and ___domain wall logic circuits4,5, can be stochastic6,7. Controlling the propagation of ___domain walls with both spin currents and/or external magnetic fields8 is important for the seamless operation of these devices. In order to achieve controlled propagation of magnetic domains, devices based on localized anisotropy, strain modulation9,10,11, geometric confinement6,12, localized heating13, external magnetic fields, and spin currents1 have been proposed. These strategies offer unique challenges. For example, in the strain-mediated scheme, a local piezoelectric sublayer introduces strain (through lattice distortion) in the magnetic layer by the application of a local electric field. This method can be cumbersome to fabricate due to complicated growth requirements for epitaxial piezoelectric layers. The switching speed is also a concern (>10 ns switching time of ferroelectric domains14,15). Similarly, geometric confinement-based ___domain wall pinning introduces significant challenges in the fabrication of the ferromagnet as the dimensions need to be restricted to sub-100 nm16.

Interaction between 2D Van der Waals (VdW) crystals like graphene or hexagonal boron nitride (h-BN) and ferromagnets (FM) can unlock a new array of fascinating phenomena due to the specific nature of these interfaces. Interfacing graphene with Co induces a giant perpendicular magnetic anisotropy (PMA)17,18. Capping an FM with graphene exhibits large interfacial Dzyaloshinskii–Moriya interaction (iDMI) emerged from Rashba-type spin–orbit coupling at the graphene/FM interface19,20. The iDMI is pivotal for generating, stabilizing, and controlling chiral magnetic structures, with potential applications in memory and logic devices. Localized nanoscale iDMI has been demonstrated to effectively achieve ___domain wall pinning. Notably, the iDMI can be actively tuned through gate voltage modulation, offering electrical control over the chiral magnetic structures and ___domain wall motion. Therefore, studying the iDMI in the graphene/ferromagnet interface is crucial. Direct visualization using transmission electron microscopy (TEM) can provide a comprehensive understanding of this phenomenon.

The present study experimentally demonstrates a method for controlling the ___domain wall motion in a ferromagnetic system by introducing local interfaces between a ferromagnet and 2D material that exhibit significant iDMI19. A 5 nm Ni80Fe20 with Gilbert’s damping factor of 0.0091 has been chosen as the ferromagnet (see Supplementary Note S1 for estimation of the damping factor).

To study the effect of the interface-induced pinning, graphene was transferred to the NiFe thin film. The expansion of the magnetic domains with an external magnetic field near a Gr/NiFe interface is studied to observe the effect of the local iDMI. The magnetic ___domain mapping requires high spatial resolution near the Gr/NiFe interface, and thus, Lorentz-transmission electron microscopy (L-TEM) is a much-desired tool for such observations21. We have performed in-situ ___domain wall expansion studies using the fringing field of the objective lens of the microscope. The scheme for introducing in-situ magnetic fields for the L-TEM experiments is shown in Fig. 1a. An out-of-plane magnetic field has been applied to the sample using the magnetic field of the objective lens. The in-plane fields required for the in-situ magnetic field effect studies are introduced by small tilts (along x or y direction based on alpha or beta tilt) of the sample holder along with the objective lens field which is in the z-direction. The geometry of NiFe strips used for the study is shown in Fig. 1b. We have discussed the fabrication of the TEM chips used in this study, in Supplementary Note S2. The magnetic field values given in the inset of Fig. 1e are the in-plane magnetic fields for the given objective lens value and tilt conditions.

Fig. 1: In-situ TEM experiments on NiFe strips.
figure 1

a Schematic of the sample holder and the mechanism for introducing in-plane fields. In-plane magnetic fields are generated using α and β tilt of the holder in a controlled out-of-plane objective lens field. b Geometry of the NiFe strips deposited on the MEMS chip. c Out-of-focus TEM image of the NiFe strip showing ___domain walls. d (i) \({M}_{x}\) and (ii) \({M}_{y}\) of the initial magnetization. e Color map of the in-plain domains in the NiFe strips with an in-situ magnetic field applied along x-direction from (i–vi) 0 to 80.5 Oe.

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The initial magnetic ___domain structure was created by first saturating the NiFe strips through a small alpha tilt (1.9°) and applying a large objective lens field which is gradually reduced to zero. The normalized \({M}_{x}\) and \({M}_{y}\) of the NiFe layer, calculated from defocused images [described in methods, Modified Transport of Intensity Equations (MTIE), equations (3) and (4)] are given in Fig. 1d (i) and (ii) respectively. The same area was illuminated throughout the measurements with varying in-situ magnetic fields. Distortions were introduced due to the change in focus (objective mini lens) and the objective lens fields used to magnetize the sample. These were compensated by finding a homography transformation matrix22 to match the distorted image to the in-focus image. A color map of the magnetic signal was then calculated, and the corresponding map for Fig. 1d (i–ii) is given in 1e (i). The different domains present in the NiFe can be easily distinguished after the MTIE calculations. The red contrast seen at the edges of the NiFe strip (in Fig. 1e) is the measurement error. This is caused by the improper matching between the in-focus and out-of-focus images due to the Fresnel fringes at the sample edges produced by the defocusing.

Results

In-situ magnetization studies of NiFe

The spatial evolution of magnetization of NiFe was conducted by applying an external field as shown in Fig. 1e. At 0 Oe, the blue domains (along ~−x direction) and the green domains (along ~+x direction) occupy almost equal area on the NiFe strip. The magnetization of the NiFe strip also displays magnetic ripple contrast, indicating the polycrystalline nature of NiFe layer23. The direction of the electron beam is along z-axis as shown in Fig. 1a. The in-situ magnetic field along the x-direction was applied by tilting the TEM chip (alpha tilt) by 1.9° and gradually increasing magnetic field by the objective lens field of the TEM using the free lens controller (co-ordinate system and tilt directions with respect to the holder are shown in Fig. 1a). The shrinking of the blue domains with increasing in-plane external field is clearly observed. At 80.5 Oe, the strip is almost completely magnetized along the direction of the green domains (which is the direction of the in-plane field induced by the sample tilt), and the NiFe strip effectively becomes a single ___domain with in-plane magnetization. The presence of the magnetic ripple contrast arising from local variation in magnetization due to the presence of grains may have increased the saturation field which is comparable with NiFe wires reported in literature24,25. The raw images used for the calculation are given in supplementary information, Fig. S6 in Supplementary Note 4.

Domain wall motion at the Gr/NiFe interface

The next step is to study the ___domain wall propagation in the vicinity of the Gr/NiFe interface. The preparation of the Gr/NiFe interface is discussed in Supplementary Note S3. The ___location of the graphene flake and an image of the Gr/NiFe interface taken in the Lorentz mode are shown in Fig. 2a, b. The quality of the Gr/NiFe interface was studied using the cross-section TEM after the experiments were done, are shown in Supplementary Note S3. The thickness of the graphene was ~2 nm indicating about 10 layers. The TEM of graphene showed 6-member carbon rings (refer to Fig. S4 in Supplementary Information) with the absence of atomistic defects. No amorphous layer was observed between graphene and the polycrystalline NiFe, as shown in Fig. S5 of Supplementary Information, indicating a clean VdW/FM interface. The DMI interaction between the NiFe and graphene is short-ranged to <3 nm of the interface26. Any small amorphous deposits between the two layers can reduce the strength of the interaction, and thus, the influence on the ___domain wall dynamics becomes substantially low.

Fig. 2: Domain wall propagation with magnetic field in the Gr/NiFe device.
figure 2

a Image of the TEM chip showing the ___location of the Gr/NiFe interface, b high-resolution TEM image of the Graphene placed on permalloy. Domain wall expansion near the Gr/NiFe interface with in-situ magnetic fields along the c (i–v) +x field sweep and d (i–v) −x field sweep.

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The initial ___domain wall configuration was produced by introducing both alpha (±5°) and beta (±5°) tilts, saturating the magnetization using a large objective field and subsequently reducing the magnetic field and the tilts back to 0. The calculated magnetization overlayed onto the in-focus L-TEM images near the Gr/NiFe interface when magnetized along +x and −x directions are given in Fig. 2c, d(i–v) respectively. The magnetic field values given in Fig. 2c, d are the effective in-plane magnetic fields acting on the sample. The ___domain walls outside graphene are marked using a white arrow, while the ___domain walls under graphene are marked using a yellow arrow. The defocused LTEM images acquired for different field conditions are given in Supplementary Note S4.

The initial magnetization conditions, characterized by the presence of one ___domain wall located outside the graphene area and another beneath the graphene, were similar for both field sweeps. The ___domain walls were subsequently moved by the in-situ magnetic fields generated by the objective lens field and the alpha tilt. The field direction was set to move the ___domain wall to the right (+x direction, 1° alpha tilt), as shown in Fig. 2a(i–v). Increasing the magnetic field to 15 Oe moved the ___domain wall in uncovered NiFe to the right while the ___domain wall under graphene remained stationary. Increasing the field even further to 25 Oe deformed the ___domain wall under the graphene region slightly, but the uncovered ___domain wall moved further along the NiFe strip. Thus, there is an asymmetry in the motion of the ___domain walls with magnetic fields under and outside the graphene which is observed for both +x and −x directions. For the −x field sweep, the ___domain under the graphene switched instantaneously after the in-situ magnetic field of 30 Oe. Similar to the measurements on the NiFe strip (Fig. 1e), magnetic ripple contrast from the polycrystalline NiFe grains of varying magnetization has been observed in this case as well.

Effect of different magnetic energies

The asymmetry in the motion of the NiFe ___domain wall under and outside graphene is due to the local modification in the energy density landscape induced by the Gr/NiFe interface. The presence of DMI19 and PMA17 at graphene/FM interfaces has been demonstrated using first principle calculations and spin-polarized low-energy electron microscopy (SPLEEM). Considering these possible interfacial effects, the total magnetic energy density of the NiFe strip in the presence of the Gr/NiFe interface can be expressed as follows,

$${E}_{{Total}}={E}_{{Zeeman}}+{E}_{\rm{exchange}}+{E}_{{magnetostatic}}+{E}_{{PMA}}+{E}_{{DMI}}$$
(1)

In the presence of external magnetic fields, the sizes of the domains are determined in such a way that the total energy of the NiFe strip is minimized. Hence, we carried out a micromagnetic simulation in MuMax327 following the energy minimization routine to understand the possible effect of iDMI and PMA at the Gr/NiFe interface. We model a similar NiFe strip, partially covered with a graphene flake as observed in the L-TEM. The presence of graphene is implicitly modeled by defining a finite DMI and/or PMA only in that particular region which represents the area under the graphene. Detailed methodology of micromagnetic simulation is discussed in the supplementary information, Supplementary Note S5.

We conducted an L-TEM study with a finer in-situ magnetic field step size of 0.25 Oe to compare the results with micromagnetic simulations. The rate of ___domain expansion has been quantified by calculating the ___domain expansion factor, \(\epsilon\) which was defined as,

$$\epsilon =\frac{{A}_{{Domain}1}}{{A}_{{Domain}1}+{A}_{{Domain}2}}$$
(2)

where A(Domain 1 (2) is the area under the ___domain 1 (2).

The ___domain expansion factor \(\epsilon\) under graphene and outside graphene is given in the Fig. 3(a-i), for each value of the in-situ magnetic field when the ___domain expands. Note that, both domains are partially covered by the graphene flake. The ___domain expansion rate, as a function of the magnetic field, is staggered up to around 25 Oe. This is possibly due to the presence of geometrical defects at the edges, which act as the pinning sites. The entire plot is given in Supplementary Information, Supplementary Note S4. We observe from Fig. 3a that the slope of the ___domain expansion rate is a linear function of the magnetic field. The rate of ___domain expansion is smaller at the Gr/NiFe interface (black circles) as compared to its counterpart outside the Gr/NiFe interface (red circle). We have estimated the slopes as 0.0485 Oe−1 (from red circles) and 0.0388 Oe−1(from black circles) for the area outside and within the Gr/NiFe interface, respectively. Hence, we conclude that the presence of graphene indeed slows down or “brakes” the ___domain expansion in NiFe.

Fig. 3: Comparison of experimental ___domain wall expansion in Gr/NiFe with micromagnetic simulations.
figure 3

a Domain expansion rate with the magnetic field when the ___domain expands, the inset (i) shows ___domain 1 and ___domain 2 mentioned in Eq. 2 along with the initial ___domain configuration. The error bars are calculated from the width of the ___domain wall measured from the defocused images. b Simulated expansion of ___domain within the plane magnetic field with anisotropy (Ku = 4.021 kJ/m3) and DMI (2.35 mJ/m2) and c simulated rate of ___domain wall expansion for different DMI values (20–60 μJ/m2). The error bars represent the standard deviation of the data extracted from the simulation results.

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The braking of the ___domain expansion can occur only if the mobility of the ___domain wall is different under graphene compared to outside the graphene area. A simple theoretical estimate of the ___domain wall mobility can be obtained using the formula, µ = γΔ/α, where γ is the gyrometric ratio, Δ is the ___domain wall width, and α is the Gilbert’s damping factor. The Gilbert’s damping factor for NiFe/Gr is higher than the bare NiFe films as shown in the FMR measurements in Supplementary Information, S1. The relative ___domain wall width measured from the Lorentz TEM images shows that the width reduces under graphene, as shown in Supplementary Note, S6. Thus, the mobility of the ___domain wall under graphene is relatively lower than the bare NiFe layer, which could have resulted in the braking effect observed.

We have performed micromagnetic simulations to understand the origin of such a “braking effect” and reduced mobility on ___domain wall expansion induced by the Gr/NiFe interface. It should be noted that a fully quantitative agreement between the experimental results and simulation could be hardly obtained because of the inevitable mismatch between the simplified micromagnetic model and the real experimental conditions. However, from the qualitative agreement between our experiment and the simulation results, we explain the underlying phenomena. We have first defined a ___domain wall which is partly Bloch and partly Neel type, at the center of a rectangular NiFe strip. In addition, we introduced PMA and DMI locally at the Gr/NiFe interface and varied their strength to observe the ___domain wall motion under the influence of different external magnetic fields. A parametric study with PMA has been performed with Ku ranging from 0.4 to 40.21 kJ/m3 and iDMI strength from 2.3 to 2.5 mJ/m2 at the Gr/NiFe interface to observe the possible pinning effect (due to roughness, see Supplementary Note S7) on the ___domain wall as observed experimentally. This is given in Supplementary Note S5. Softly pinned ___domain walls were observed with a PMA, Ku = 4.021 kJ/m3, or an iDMI strength of 2.35 mJ/m2 at the Gr/NiFe interface. These are investigated in detail and are shown in Fig. 3b. Even though the ___domain structure was initialized with a vertical ___domain wall across the width of the NiFe strip (Supplementary Information, Fig. S9 (a)), the introduction of PMA and iDMI at the interface changed the shape of the ___domain wall similar to those observed experimentally. However, the introduction of PMA at the Gr/NiFe interface did not exhibit any pinning effect of ___domain walls, whereas the iDMI at the interface significantly hindered the ___domain expansion exhibiting the “braking effect”. This indicates that the “braking effect” experimentally observed, is because of the interfacial DMI at the Gr/NiFe interface.

The DMI value of 2.35 = mJ/m² used in the simulation [shown in Fig. 3c] is comparable with values observed by Yang et al.19 and appears higher than other experimental measurements28 on Gr/NiFe interfaces. These experiments report DMI values within the range of 60 μJ/m², with multiple graphene layers reducing the interfacial DMI. This could be because the effect of the polycrystalline nature of our NiFe film was not considered in this simulation. To verify this, we carried out micromagnetic simulations with 40 nm grain size and 10% variation in \({M}_{s}\) using the in-built Voronoi Tessellation functionality of MuMax327 (which was used to obtain Fig. 3a) with an additional iDMI value in the range of 0–60 μJ/m2. The ___domain expansion rate was calculated for different iDMI values and is presented in Fig. 3c. There is a clear reduction in ___domain expansion rate with increasing iDMI, and with an iDMI value of 60 μJ/m2 the ___domain expansion rate was comparable to the experimentally observed values. Thus, we conclude that the soft pinning of ___domain walls observed in the in-situ L-TEM study near the Gr/NiFe interface was due to iDMI introduced at the interface. This could be used to spatially stifle the expansion of domains to control the ___domain wall propagation on demand.

Discussion

We demonstrate that introducing Graphene onto NiFe can reduce the ___domain expansion rate with a magnetic field. Comparison between the Lorentz TEM imaging on NiFe strips with a local Gr/NiFe interface with in-situ magnetic fields with the micromagnetic simulations indicates the reduction in ___domain wall expansion rate was due to the iDMI introduced by the Gr/NiFe interface. The iDMI strength has been estimated to be around 60 μJ/m2 based on the simulations considering the variation of dipolar interaction and exchange interaction across the grains to incorporate the microcrystals observed in the L-TEM studies. Spatially arranged interfaces along the length of an FM strip can, therefore, control the expansion of domains which is the key to ___domain wall memory systems like ___domain wall logic circuit5,13,29 and racetrack memory1,3,30 schemes.

Methods

Lorentz transmission electron microscopy (LTEM)

The LTEM imaging was done in a double-corrected JEOL ARM 300 microscope in Lorentz mode operated at 300 kV and the objective lens turned off. The probe corrector was turned off as well in this mode, and the image corrector was tuned to obtain a spatial resolution of ~1 nm using a special gold sample of appropriate particle size. For the LTEM imaging, the sample was moved through the focus using the objective mini lens of the image corrector. NiFe devices with and without graphene are prepared on a MEMS chip with a 200 nm thick silicon nitride window which was compatible with a Hennyz TEM holder21. The fabrication of the MEMs chips and the transfer of the graphene is discussed in Supplementary Information S2 and S3. The transfer protocol was optimized using high-resolution transmission electron microscopy to ensure a clean interface between the NiFe and Graphene.

Modified transport of intensity equations

The magnetization mapping of the NiFe sample changes the phase of the electron wave passing through and is observed in Lorentz mode when the image is out of focus. The magnetization of the NiFe strip is calculated using the modified transport of intensity equation (MTIE) based on the difference in intensity between the in-focus and out-of-focus images31. The equations for the same are given below,

$${\rm{\phi }}\left(r\right)={F}^{-1}\left[F\left({k}_{z}{{\rm{\delta }}}_{z}I/I\right)/{k}_{\perp }^{2}\right]$$
(3)
$${tB}=\frac{{{\hslash }}}{e}\left[{n}_{z}\times \Delta {{\phi }}\right]$$
(4)

Where \({\rm{\phi }}\left(r\right)\) is the phase change in the electron wave introduced by the sample, \(F\) and \({F}^{-1}\) denotes the Fourier and inverse Fourier transform, \({k}_{z}\) is the propagation constant of the electron wave in vacuum, \({{\rm{\delta }}}_{z}I\) represents the change in intensity with defocus, \({k}_{\perp }\) is the frequency vector in Fourier space, t is the thickness of the sample, B is the magnetization, \({{\hslash }}\) is reduced plank constant, e is the electronic charge and \({n}_{z}\) is the unit vector along z direction. Equation 2 has a singularity when \({k}_{\perp }\) becomes zero, and a low pass filter is used to get rid of this. The electron phase, \({\rm{\phi }}\left(r\right)\) thus calculated using L-TEM can only provide a relative value for the magnetization of the samples. The code used for the calculation has been uploaded on Github32.

Micromagnetic simulations

The micromagnetic simulation was performed using the open-source software MuMax327 on a rectangular strip of 2048 nm \(\times\) 512 nm \(\times\) 10 nm size, discretized into rectangular cells of 2 nm \(\times\) 2 nm \(\times\) 10 nm. NiFe material parameters derived from the analysis of FMR spectra were used for the simulation. The exchange constant of NiFe was obtained from the literature as \({{A}}_{{\rm{ex}}}=\) 13 pJ/m. The Gr/NiFe interface on the NiFe strip was later defined by importing an image mask of the Graphene patch, scaled in accordance with the dimension of the NiFe strip. The spatial distribution of magnetic moments in each cell was initialized as a two-___domain configuration where, the magnetization at the left and right halves are defined along the x-axis, facing each other (Supplementary Information, Fig. S9a). The ___domain wall (DW) at the middle of the NiFe strip was defined as a mixed state of Bloch wall and Néél wall. DMI and PMA were explicitly defined at the Gr/NiFe interface using the built-in MuMax functions. In each simulation, the final magnetization configuration in the NiFe strip was obtained after relaxing the magnetization to the minimum energy state in the presence of an external magnetic field, followed by solving the Landau–Lifshitz–Gilbert equation. For a detailed discussion on micromagnetic simulation, please see the Supplementary Information, Section S5.