Magnetization Reversal Signatures of Hybrid and Pure N\'eel Skyrmions in Thin Film Multilayers

We report a study of the magnetization reversals and skyrmion configurations in two systems - Pt/Co/MgO and Ir/Fe/Co/Pt multilayers, where magnetic skyrmions are stabilized by a combination of dipolar and Dzyaloshinskii-Moriya interactions (DMI). First Order Reversal Curve (FORC) diagrams of low-DMI Pt/Co/MgO and high-DMI Ir/Fe/Co/Pt exhibit stark differences, which are identified by micromagnetic simulations to be indicative of hybrid and pure N\'eel skyrmions, respectively. Tracking the evolution of FORC features in multilayers with dipolar interactions and DMI, we find that the negative FORC valley, typically accompanying the positive FORC peak near saturation, disappears under both reduced dipolar interactions and enhanced DMI. As these conditions favor the formation of pure Neel skyrmions, we propose that the resultant FORC feature - a single positive FORC peak near saturation - can act as a fingerprint for pure N\'eel skyrmions in multilayers. Our study thus expands on the utility of FORC analysis as a tool for characterizing spin topology in multilayer thin films.


I. Introduction
Magnetic skyrmions have been realized in several material systems, most notably magnetic multilayer thin films which host nanoscale skyrmions at room temperature [1][2][3]. In such multilayers, the Dzyaloshinskii-Moriya interaction (DMI) arising at the ferromagnet (FM)/heavy-metal (HM) interfaces is paramount in stabilizing the Néel spin textures that these skyrmions possess [4,5]. However, the actual spin textures of these skyrmions have recently been proven to be more complex, owing to the competition between DMI and dipolar interactions between the thin film layers [6][7][8]. For most multilayer systems, skyrmions exhibit thickness-dependent magnetization profiles, where a centrallayer Bloch texture is sandwiched between Néel textures of opposite chiralities from the topmost and bottommost layers [7]. These are known as hybrid skyrmions, whereas uniform Néel-texture skyrmions throughout the multilayer, realizable in a high-DMI environment, are known as pure Néel skyrmions [7].
Differences in the spin texture and chirality of skyrmions strongly influence their current-driven dynamics [7,[9][10][11], rendering the knowledge of their complete, three-dimensional spin textures crucial for spintronic material design. Distinguishing between hybrid and pure Néel skyrmions, however, requires sophisticated imaging methods, such as circular dichroism x-ray resonant magnetic scattering [7,8] or nitrogen-vacancy center magnetometry [12] in order to resolve the thicknessdependence of the magnetic textures. These techniques may not always be readily available in most research facilities. On the other hand, the interplay of dipolar interactions and DMI, as well as other ubiquitous and tunable magnetic interactions in multilayers, directly affect the domain size, density, and the level of disorder in the skyrmion configuration [3]. These parameters consequently influence the magnetization reversal processes [13] and hysteretic behaviour of spin textures [14], which may provide indirect clues for inferring the inner complexity of three-dimensional skyrmions.
The ability to identify these subtle processes has been demonstrated by the First Order Reversal Curve (FORC) technique, which provides a magnetic fingerprint of the interactions and reversal processes occuring in magnetic materials [15,16]. Recent studies have begun utilizing FORC in skyrmion-hosting multilayers to study field history control of zero-field skyrmion population [17,18], while simultaneously revealing magnetic reversal mechanisms influenced by the skyrmion configuration [17]. Indeed, the variety of magnetic interactions and skyrmion configurations realizable in different thin film heterostructures offer a rich resource for FORC studies. , suggesting that their stability results primarily from magnetic dipolar interactions [19], while the latter shows smaller 46 ± 12 skyrmions, indicating the more dominant role played by the DMI (D) in skyrmion formation [19]. FORC analysis and MFM imaging reveal distinct irreversibility features in these two material systems. Using micromagnetic simulations, we show these two multilayers stabilize hybrid and pure Néel skyrmions, respectively, which may account for their distinct FORC features. To support this hypothesis, we apply our analysis to Pt/Co/MgO samples with different numbers of layer repetitions, and also to Fe/Co multilayers with different ferromagnetic compositions. Again, we observe a correlation between FORC features and the relative strengths of dipolar interactions and DMI, which faciliate the transition from a hybrid to a pure Néel skyrmion texture [7]. This points towards a possible thermodynamic signature for high-D multilayers, which can stabilize pure Néel skyrmions.  (4) were deposited on thermally oxidized silicon wafers at room temperature (numbers in parentheses refer to the layer thickness in nm). Ir/Fe/Co/Pt samples were deposited using a Chiron ultra-high vacuum multi-source sputter tool, while Pt/Co/MgO samples were deposited using a Singulus Timaris ultra-high vacuum multi-target sputter tool. The base vacuum in each case is 1×10 -8 Torr and sputtering is carried out in 1.5×10 -3 Torr of argon gas. Magnetization measurements on these samples were performed using superconducting quantum interference device (SQUID) magnetometry, in a Quantum Design Magnetic Property Measurement System (MPMS), to obtain the saturation magnetization (MS). Out-of-plane and in-plane hysteresis loops were also acquired to determine the uniaxial effective anisotropy values Keff.

Multilayer
FORC measurements were then conducted on as-grown samples using a Vibrating Sample Magnetometer (VSM) at room temperature. Each FORC measurement consists of a two-part sequence: (1) the sample is first saturated at a positive field and then brought to a reversal field , (2) from the magnetization of the sample is measured starting from and ending at 0, as the applied field is reversed. Repeating the sequence for multiple values of , we obtain a family of FORCs ( Figure 1(a),(b)), used to compute the FORC distribution defined as: Plotting as a density plot against and produces a FORC diagram ( Figure 1(c), (g)), which quantifies the degree of magnetic irreversibility for the magnetic field histories of the measured sample. Each FORC diagram is studied by complementary MFM images, which capture the magnetic textures obtained by different field histories. The method used for acquiring and analyzing MFM images is similar to that described in Ref. [3].
Micromagnetic computations were performed by means of a state-of-the-art micromagnetic solver, PETASPIN, which numerically integrates the Landau-Lifshitz-Gilbert (LLG) equation by applying the Adams-Bashforth time solver scheme [20]: where G α is the Gilbert damping, is the normalized magnetization, and  h is the normalized effective magnetic field, which includes the exchange, interfacial DMI, uniaxial anisotropy, and Zeeman fields, as well as the magnetostatic field computed by solving the magnetostatic problem of the whole system [8,21].

III.
Results and discussion We first focus on the FORC diagram of Pt/Co/MgO, which has an estimated (Refs. [2,7]) D value of 0.5 mJ/m 2 . For this sample, we observe large regions of irreversibility extending all the way from = 0 mT to ≈ −180 mT. The first feature is a wide, positive-valued ridge from ! = 0 " to ! ≈ −125 " (Figure 1(c)), coinciding with the transition from labyrinthine stripes to the skyrmion phase (Figure 1(d)-(f)), where approximately 100 nm-diameter skyrmions emerge in a disordered configuration at ! = ! = −110 " (Figure 1(f)). Based on the interpretation of Ref. [17], we deduce that the large, positive-valued region of irreversibility for | | ≤ | | in this range corresponds to skyrmion and stripe mergers taking place as the applied field decreases. As | ! | increases from 125 " to 180 ", a pair of irreversible regions consisting of a negative-valley (blue) and positive-peak (red) emerges (Figure 1(c)). This familiar pair feature arises from the sign change in the second derivative of the magnetization as neighboring reversal curves diverge and then converge in the high field regime (dashed circles in Figure 1(a)). The feature, which was observed near the out-of-plane saturation fields in FORC studies of other magnetic multilayers [15][16][17], signifies the onset of skyrmion annihilation as the applied field increases along the diagonal edge, followed by skyrmion and stripe nucleation as the field is reduced along the H axis.
While the negative-positive pair feature frequently appears in magnetic multilayers, including the Ir/Fe(x)/Co(y)/Pt stacks, it does not appear for Fe(0.4)/Co(0.4), where D=2.1 mJ/m 2 . No sign change in the second derivative of the magnetization is observed, and hence only a single positive peak is seen as the system approaches saturation, i.e. from ! ≈ −150 mT to ! ≈ −225 mT ( Figure  1(g)). This feature is preceded by an elongated irreversible ridge extending from ! ≈ −50 " to ! ≈ −150 " (Figure 1(g)). Unlike the sprawling irreversible feature in Pt/Co/MgO, the irreversible ridge for Fe(0.4)/Co(0.4) is narrower and localized around the diagonal edge of the FORC diagram. This indicates the presence of a large population of skyrmions, whose repulsive interaction at the short range precludes skyrmion merger, thus resulting in less irreversible activity taking place as the applied field reverses from . Indeed, high-density skyrmions appear as early as ! ≈ −50 " (Figure 1(h)) and quickly transform into a dense array of small skyrmions (≈ 50 nm in diameter) as the applied field increases (Figure 1(i)).
This configuration stands in sharp contrast to the sparse array of larger skyrmions (≈ 100 in diameter) observed in Pt/Co/MgO. Due to their larger size, the latter are likely to be strongly stabilized by dipolar interactions, thus exhibiting hybrid magnetization profiles. The appearance of these hybrid spin textures may be linked to our observed differences in FORC features. To test this hypothesis, we performed micromagnetic simulations of the two systems and extracted their thickness-dependent spin textures. Figure 2 summarizes micromagnetic simulations for the two multilayers. In both cases, the skyrmion diameter is thickness-dependent, being larger in the middle layer and smaller in the external layers. This is attributed to the z-component of the magnetostatic field [7]. The size of the skyrmion is larger in the Pt/Co/MgO sample than in Fe(0.4)/Co(0.4), in qualitative agreement with experimental measurements. A crucial difference between the two cases lies in the thickness-dependence of their respective spin textures. In Fe(0.4)/Co(0.4), the spin chirality is independent of the layer position and a pure Néel skyrmion is obtained in all the layers. This can be attributed to the strong DMI in Fe(0.4)/Co(0.4), which, by overcoming the magnetostatic field dictates the skyrmion texture in all the layers, in agreement with previous theoretical results [7].
On the other hand, a skyrmion in the Pt/Co/MgO exhibits a layer-dependent chirality (hybrid skyrmion), which gradually changes from Néel with an outward spin chirality at the bottom layer, to an intermediate skyrmion mixing Néel-outward and Bloch-clockwise chiralities in the middle layer, and eventually to a Néel skyrmion with inward chirality at the top layer. This is ascribed to the small DMI value in Pt/Co/MgO, thus allowing the magnetostatic field to be dominant. The small DMI only affects the position of the Bloch skyrmion, which is not located in the middle layer, as expected from the magnetostatic field, but is shifted upward to the 10 th layer, consistent with previous findings [7,8].
Comparing our micromagnetic simulations with the FORC features in Fig. 1(c),(g), we found that the coexistence of a positive peak and negative valley of the irreversibility coincides with the stabilization of hybrid skyrmions, stabilized by a combination of DMI and dipolar interactions. On the other hand, the presence of a single positive peak coincides with the presence of pure Néel skyrmions, stabilized primarily by interfacial DMI interactions. The distinct FORC features observed in Fig.1 and the hybrid and pure Néel skyrmion textures suggested by micromagnetic simulations thus suggest a potential correlation between FORC distribution features and the strengths of dipolar interactions and DMI, which influence the thickness-dependent skyrmion textures.
To investigate this correspondence, we track the evolution of FORC distributions and skyrmion diameters in Pt/Co/MgO multilayers with the dipolar interaction strength, by reducing the number of layer repetitions (N) progressively from 15 to 2. The results are encapsulated in Fig 3, where the and axes of the FORC diagrams are normalized to the out-of-plane saturation field, determined as the value at which irreversible features terminate. As interlayer dipolar interaction weakens with reduced N, the FORC distributions transition from a negative-positive peak pair to a single positivepeak. Correspondingly, the observed skyrmion diameter decreases from ≈ 105 nm (for N = 15) to ≈ 80 nm (for N = 4), reflecting a transition from a dipolar-dominant regime to a DMI-dominant regime of skyrmion stability [19]. These observations suggest the disappearance of the negative FORC valley correlates with a reduced dipolar interaction in the multilayer.
Likewise, we also track the evolution of FORC features with the increase in DMI, achieved by varying the Fe/Co compositions of the [Ir(1)/Fe(x)/Co(y)/Pt(1)]20 heterostructure. Raising the Fe/Co composition ratio while keeping their total thickness ≤ 1nm effectively increases the DMI strength while also modifies other magnetic parameters. This results in a variation of the skyrmion size, density, and energetic stability, which can be correlated with key changes in the respective FORC diagrams. The gradual disappearance of the negative-valley, the increase of the DMI strength, and the two-fold decrease in skyrmion diameter [3,17] (Figure 4 (f)) again suggest a transition from a dipolar-dominant to a DMI-dominant regime of skyrmion stability [19], thus hinting at a transition from hybrid to pure Neel skyrmions.
To support this inference, we have performed additional micromagnetic simulations for samples Fe(0.2)/Co(0.8) and Fe(0.5)/Co(0.5), and compared them with the case of Fe(0.4)/Co(0.4). In Fe(0.2)/Co(0.8) with DMI strength of 1.5 mJ/m 2 (Fig. 4(g)), we observe a hybrid skyrmion where the Bloch skyrmion is present in the 17 th ferromagnetic layer. In contrast, the Bloch position for Pt/Co/MgO appears roughly at the center of the stack due to dominant dipolar interaction over DMI. In Fe(0.5)/Co(0.5) (D = 1.9 mJ/m 2 ), no Bloch skyrmion is observed, and the 3D skyrmion profile is almost pure-Néel, with outward chirality in all the layers except for the topmost layer, which hosts a Néel skyrmion with inward chirality (Fig. 4(h)). Eventually, the skyrmion profile achieves a complete pure Néel texture in all the layers in the case of Fe(0.

IV. Conclusion
In summary, we investigated the magnetization reversals and skyrmion configurations for Pt/Co/MgO and Ir/Fe/Co/Pt multilayers, using a combination of FORC measurements, MFM imaging, and micromagnetic simulations. Wide sprawling FORC regions with a characteristic negativevalley/positive-peak pair are indicative of large, hybrid skyrmions in low-D Pt/Co/MgO. In contrast, a single positive FORC distribution peak is indicative of small, pure Néel skyrmions in high-D Fe(0.4)/Co(0.4). By reducing the number of film layer repetitions in Pt/Co/MgO and tuning the thicknesses of Fe and Co in Fe(x)/Co(y) multilayers, we observe a transition of FORC features from a negative-valley/positive-peak pair to a single positive peak in correspondence with a reduction in dipolar interactions and an increase in the DMI strength, respectively. Hence, we propose that the single positive FORC feature can be a useful fingerprint for pure Néel skyrmions in multilayer systems. In addition to providing an indicator for skyrmion spin chirality, the observed FORC features enable a robust assessment of the thermodynamic stability of skyrmions within a particular multilayer: the negative FORC valley vanishes as the stability rises. Whilst additional spin imaging techniques are desirable for microscopically resolving the multitude of complex spin topologies [7,8,12], FORC analysis can play an important role in the analysis of magnetic multilayers. Combining these techniques can efficiently address future challenges in designing and optimizing skyrmionic materials.