Substrate thermodynamics control growth and spin coupling in flexible cobalt thin films

Abstract

Interfacial engineering remains a critical challenge in flexible spintronics where simultaneously optimizing crystalline quality, magnetic robustness, and proximity effects is difficult. By depositing cobalt films under constant adatom kinetic energy onto flexible substrates with contrasting enthalpies of fusion—muscovite mica (high ΔH_f) and perfluoroalkoxy alkane (PFA, low ΔH_f)—we demonstrate a thermodynamics-driven strategy to control growth mode, surface roughness, microstructure, and spin coupling. Atomic force microscopy and X-ray diffraction reveal layer-by-layer growth with low roughness on mica (R_a ≈ 1.7–2.3 nm) versus island-like rough morphologies on PFA (R_a up to 47.7 nm). Magnetic measurements show a 50% enhancement of coercive force and mechanical flexibility on PFA, while Pt capping layers amplify magnetic proximity effects more significantly on rougher PFA interfaces. We introduce the Thermal-Informed Roughness Activation (TIRA) model, linking substrate enthalpy and adatom energy to interfacial roughness and spintronic properties. This framework offers practical design rules for optimizing flexible spintronic devices by balancing crystallinity, magnetic coupling, and bendability.

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Introduction

As applications of spintronics develop towards soft and wearable devices, interfacial engineering has become a key issue for simultaneously enhancing the stability and functionality of devices.^1–3 Under depositing conditions of constant or slightly varying kinetic energies for incident atoms, the competition of thermal physical properties between adatoms and the substrate will be the key factor determining the occurrence of interfacial micro-reconstruction and roughening, which influences the crystalline orientation, magnetic anisotropy, and spintronic viability.^4–6 Therefore, it is necessary to construct a functional description covering thermodynamics and deposition kinetics to establish a quantifiable relationship linking energy incidence, the material energy barrier, surface morphology evolution, and interface effects. Previous research mainly focuses on the mechanism between diffusion and chemical bonding.^7–10 However, from previous experience and reports, the thermal stability, flexibility, and crystallinity may dominate the switch of growth modes between the Frank van der Merwe (FvM, layer by layer) growth mode with low roughness and the Volmer Weber (VW, island type) growth mode with high roughness. This trade-off is the main reason that the crystalline quality, magnetic proximity effect (MPE) and bending endurance of flexible devices cannot be simultaneously optimized.^7,8 This mechanism transition makes it impossible for a single process to address multi-objective design, leading to a bottleneck in the material choice and process pathway. In this report, we adopt a controlled design choosing two flexible substrates with significant differences in their enthalpy of fusion (ΔH_f). Under constant kinetic energy of incident atoms, we deposit cobalt (Co) on mica with high ΔH_f and perfluoroalkoxy alkane (PFA) with low ΔH_f and set the substrate's enthalpy of fusion as the main factor constructing a thermal-informed roughness activation (TIRA) model. We assume that a dimensionless sensitivity parameter (χ) and an activation nucleus can quantify the initiating conditions of interfacial micro-reconstruction and roughening. Combining the measurement of Atomic Force Microscopy (AFM), X-Ray Diffraction (XRD), a Superconducting Quantum Interference Device (SQUID) and Secondary Ion Mass Spectrometry (SIMS), we systematically investigate the surface morphologies, crystallinity, magnetic properties, and chemical depth profiling. The experimental results imply that the substrate with low ΔH_f can promote larger surface arithmetic mean roughness (R_a) and VW growth mode, which can enhance the MPE by increasing the contact area between Pt/Co interfaces. Conversely, the substrate with high ΔH_f can retain the low roughness from FvM growth mode and has a relatively controllable crystalline characteristic. These results suggest a connection between the kinetic energy of adatoms, surface morphologies, and spintronic coupling within a single thermodynamic framework, indicating possible tunable factors. Based on the proposed TIRA model, the interfacial roughening and the corresponding spin coupling can be effectively tuned through the competition between the substrate enthalpy of fusion and the incident adatom kinetic energy. When the system operates in the high-sensitivity regime (χ ≈ 1), an optimized balance among crystallinity, interfacial MPE, and mechanical endurance can be achieved. This thermodynamic–kinetic strategy not only elucidates the mechanism governing interface evolution but also provides a practical route toward functional spintronic systems that remain magnetically stable under large curvature, as shown in Fig. 1. Such characteristics make the approach particularly suitable for the development of wearable magnetic sensors, low-power spin–orbit torque memory, and bendable non-volatile spin arrays integrated within flexible electronic packaging. Consequently, the TIRA model provides a physically grounded framework that may bridge fundamental interfacial physics with applied device engineering in flexible spintronic platforms.

Fig. 1 Thermal-Informed Roughness Activation (TIRA) concept and device implications.

Experimental methods

In this report, we chose two flexible substrates, muscovite mica and PFA. Substrates were cleaved into flat coupons and handled exclusively with non-metallic tweezers. Prior to film deposition, each substrate was cleaned in an ultrasonic bath of isopropyl alcohol (IPA), rinsed with deionized water, blown dry with high-purity nitrogen, and immediately loaded under vacuum to minimize re-adsorption of surface contaminants.^11,12

Thin films were prepared in an ultrahigh-vacuum system with a base pressure of approximately 6 × 10⁻¹⁰ Torr. Substrates were mounted on an unheated stage without intentional substrate bias so that the incident kinetic energy of adatoms remained comparable across all trials. Co was deposited by electron-beam evaporation from a Co source with a purity of 99.99%. During Co deposition, the working pressure was in the 10⁻⁹ Torr range. The nominal deposition rate was controlled between 0.03 and 0.10 nm s⁻¹ and monitored in real time with a quartz crystal microbalance (QCM). To ensure accuracy regarding the nominal thickness, the cumulative thickness indicated by the QCM was cross-checked ex situ by X-ray fluorescence (XRF) on representative samples to establish a single-point calibration factor that was used for all thicknesses in this report. The nominal thickness reported herein represents the mass-equivalent thickness of the deposited material. After Co deposition, platinum (Pt) capping layers were deposited in the same vacuum line by magnetron sputtering without breaking vacuum. High-purity argon gas (Ar) served as the sputtering gas. The Ar working pressure and target power were adjusted to obtain a stable rate near 0.10 nm s⁻¹, and a low ion energy was maintained to avoid damage to the Co surface. A Pt thickness series was prepared on both substrate types under identical process conditions for direct comparison.^13,14

The surface morphology was characterized by AFM in contact mode using silicon cantilevers. Large-area surveys used 25 × 25 μm² frames to capture mesoscale clustering on PFA and terrace-flat growth on mica, complemented by smaller frames when we needed to resolve nanoscale features. The arithmetic mean roughness R_a reported here is the average roughness over all frames for a given sample after background plane subtraction and line-by-line de-striping. The crystal structure was examined by XRD using common θ–2θ scans. Co/mica and Co/PFA samples were measured under identical geometrical conditions. Chemical depth distributions were analyzed by SIMS. Depth profiling targeted elemental Co and Pt and characteristic Pt–Co alloy signals. Primary-ion conditions were selected to minimize preferential sputtering and to maintain an approximately linear erosion rate through the film stack. The sputtering time was converted to an approximate depth using calibrated crater depths on the companion samples, enabling qualitative comparison between mica-based and PFA-based stacks. The integrated Pt–Co signal was used as a semi-quantitative proxy for the extent of interfacial alloying. Magnetic measurements were conducted using a SQUID magnetometer at room temperature. Hysteresis loops were obtained with the magnetic field applied in the film plane unless stated otherwise. The coercive force (H_c) was defined from the zero crossings of magnetization (M) in the major loop after background subtraction, and the saturation magnetization (M_s) was obtained from the steady region of the high magnetic field (H) region. To evaluate mechanical flexibility and magneto-mechanical robustness, bending tests were performed by conformally mounting the samples on cylindrical mandrels with different radii (r); the curvature was quantified as 1/r. For each curvature, three bend-and-release cycles were applied prior to magnetic measurements to eliminate transient seating effects. Hysteresis loops were then re-measured without removing the sample from the mandrel to avoid relaxation. Optical photographs recorded the maximum sustainable curvature for each substrate to confirm the absence or presence of cracking and delamination. Details of the instrumentation and equipment omitted here can be found in our previous work.^15–17

Results and discussion

First, the surface morphologies of Co deposited on mica and PFA substrates were characterized by AFM (Fig. 2). The insets in Fig. 2a and d show the initial roughness of the raw substrates (0.15 nm for mica and 11.7 nm for PFA), confirming that the significant surface evolution is process-induced. For the Co/mica series (Fig. 2a–c), as the nominal thickness increases from 10 to 30 nm, the surface roughness ranges from 1.7 to 2.3 nm. These experimental results are consistent with some common observations in the previous literature, such as Co being deposited on Si substrates showing excellent FvM mode growth. However, in Fig. 2d–f, when the thickness of Co on PFA increases from 10 to 30 nm, the surface roughness increases from 24.4 to 47.7 nm. When comparing the surface roughness of Co/mica with that of Co/PFA, the surface roughness of Co/PFA is an order of magnitude larger than that of Co/mica. Moreover, the roughness of Co/PFA even exceeds the nominal Co thickness, indicating that strong interfacial interactions occur between Co and PFA during deposition. Such an intense interaction leads to the formation of a hybridized interface where the effective surface modulation becomes larger than the deposited Co thickness. In this case, the Co thickness is more appropriately regarded as the coverage of Co on PFA; however, the term thickness is retained here to allow straightforward comparison of the amount of deposited Co among the samples. From previous reports,^18–20 the deposited materials have kinetic energies influencing the interaction between deposited materials and substrates, which is called the molecular-incident reaction effect.

Fig. 2 AFM analysis. (a) 10 nm Co/mica, R_a: 1.7 nm; (b) 20 nm Co/mica, R_a: 2.0 nm; (c) 30 nm Co/mica, R_a: 2.3 nm; (d) 10 nm Co/PFA, R_a: 24.4 nm; (e) 20 nm Co/PFA, R_a: 25.5 nm; and (f) 30 nm Co/PFA, R_a: 47.7 nm (the size of all AFM images is 25 × 25 μm²). The insets in (a) and (d) show the morphologies of the bare mica and bare PFA substrates, respectively, highlighting the initial surface conditions prior to deposition. Note: the nominal thickness represents the mass-equivalent thickness of the deposited material.

This interfacial interaction can be investigated by thermodynamics, which is divided into diffusion, compound, and melting from different energies. There are many reports discussing the interfacial mechanism for diffusion and compound,^7–10 so we aim to focus on the related mechanism of melting in this study. The significantly increased surface roughness of Co/PFA may enhance local thermal activation, potentially approaching conditions relevant to surface melting. It is worth noting that the large roughness of the initial PFA substrate may be a minor factor in growth model transition from the viewpoint of atom diffusion. With regard to the enthalpy of fusion, the enthalpies of fusion for evaporated Co, PFA, and mica are 305, 23.5, and 500 J g⁻¹, respectively.^21–24 Therefore, the evaporated Co atoms can lead to different deposition mechanisms between PFA and mica surfaces.

The large difference in enthalpy of fusion plays a decisive role. When energetic Co adatoms impinge on the low-ΔH_f surface, their kinetic energy is sufficient to induce local thermal activation or softening of the polymer chains. This creates a dynamically unstable interface that inhibits wetting and enhances adatom mobility, driving Co atoms to agglomerate into clusters (Volmer–Weber mode). In contrast, the high-ΔH_f mica surface remains thermodynamically rigid, promoting stable adsorption and layer-by-layer (Frank van der Merwe) growth. Since the typical diffusion-induced interfacial layer is thinner than 1 nm^25–27 and the observed roughness on PFA reaches ∼47.7 nm, the large-scale morphological evolution is attributed to thermodynamic softening or melting instead of atomic diffusion. Therefore, in this study, we will focus on the effect of interfacial melting and won't take the influence of interfacial compounds into account.

Considering the applications of Co on spintronic devices, in addition to the surface morphologies and roughness, the crystallinity of Co is of the utmost importance. In particular, the structure of hexagonal close packed Co (hcp-Co) can exhibit stable ferromagnetism. Therefore, XRD was employed to investigate the crystallinity of Co/mica and Co/PFA, and the results are shown in Fig. 3a and b, respectively. In Fig. 3a, Co/mica obviously shows the diffraction peak of hcp(002) (black club), which agrees with the previous literature for Co/Si,^19,20,28 and the diffraction peaks of mica (black diamonds) can also be clearly observed.^29,30 In Fig. 3b, there is no diffraction peak for Co/PFA, which can be attributed to the interfacial interaction. In the previous literature,^19,20,31 the crystalline structure can't be measured when Co is deposited on substrates with a low enthalpy of fusion. Considering the great mobility and degree of freedom for the PFA interfaces, Co is epitaxially deposited with difficulty and can only be accumulated in VW mode on PFA, resulting in the absence of any ordered alignment by XRD. This highlights that the thermodynamically unstable PFA interface prevents the stable nucleation required for hcp-phase formation.

Fig. 3 The XRD patterns of 10, 20 and 30 nm Co on (a) mica and (b) PFA.

After analyzing the surface morphologies and crystalline structures of the dynamic interfaces between Co deposition and the substrate corresponding to the magnetic anisotropy energy (MAE) and defects, the magnetic properties of Co can be investigated. The evolution of coercive force for the Co thickness from 10 to 30 nm on mica (black squares) and PFA (red circles) is shown in Fig. 4a. For both series, the coercive force gradually decreases as the Co thickness increases. From the previous literature, because of the transition from Néel wall to Bloch wall from the magnetization reversal mechanism when depositing ferromagnetic thin films, the coercive force will first increase and then decrease.^19,20,32 At the turning point, the Bloch wall gradually replaces the Néel wall and the energy of magnetization reversal decreases due to the increase in thickness of the domain wall, resulting in a decrease of coercive force.

Fig. 4 (a) The coercive force of x nm Co on PFA (red circles) and mica (black squares). (b) The schematic plot for the radius of curvature (r) of the sample. (c) The coercive force of 18 nm Co on PFA (red circles) and mica (black squares) with different curvatures and the photos are samples with extremely large curvatures.

Furthermore, the coercive force of Co/PFA is larger than that of Co/mica by 50% and the curve exhibits an upper-right shift. Considering that the origins of coercive force are MAE and the barrier to domain wall motion, there are more interfacial interactions of Co/PFA because of different substrate properties corresponding to the structures in Fig. 2. The Co thin films exhibit stable but disordered large-sized clusters, and there obviously exist more boundary defects and bigger surface roughness that act as pinning sites for domain walls, resulting in a larger coercive force and the observed delay in the Néel-to-Bloch transition. Simultaneously, because there are more boundary defects, the magnetic domain is separated and the transition from Néel wall to Bloch wall is delayed.^19,20,32 Therefore, the behavior of coercive force shifts to the region of larger thickness.

For flexible materials, we investigated the effect of coercive force versus curvature (in Fig. 4b) on magnetic thin films, as shown in Fig. 4c. We can see that there is no obvious influence of slightly bending the sample on coercive force. However, as mica is a crystalline and layered-accumulation substrate, it is hard and brittle; visual inspection confirmed that even slight bending resulted in visible cracking and delamination. On the other hand, no such defects were observed on the Co/PFA films, indicating their superior mechanical robustness. Surprisingly, Co thin films are also flexible on the surface of PFA with stable magnetic properties. Considering that Co follows the FvM mode growth, the magnetic properties are usually influenced by stress, as reported in the previous literature.^33–35 Developing magnetic thin films that are not influenced by stress may offer a new route for flexible spintronic applications. It is assumed that the interfaces between Co and PFA shown in Fig. 2 allow Co to be deposited by huge clusters and weaken the interaction between clusters, improving the tolerance to stress changes. This is the first publication of magnetic thin film devices with high flexibility (1/r ≫ 0.5 mm⁻¹).^36–38

Then, adding Pt with strong SOC and SHE effects at vacuum/Co interfaces,^39–41 we want to realize the boundary conditions at the interfaces between Pt and Co. From the previous literature, the SOC effect will be provided by the single lattice of FvM mode-grown Pt/Co for the interaction between Pt and Co, and it shows the MPE.^42,43 The saturation magnetization of Co films without Pt is defined as M⁰_s ≡ M^Pt_s (Pt thickness, t_Pt = 0). As Pt is gradually deposited on top of Co, the saturation magnetization turns out to be M^Pt_s (t_Pt). When the value of is bigger than 1, the additional magnetic moments from the MPE and the SOC effect at Pt/Co interfaces can be confirmed. In Fig. 5a, for Pt/Co interfaces on both mica and PFA substrates, a significant MPE will be observed (δ ≥ 1). However, when the thickness of Pt is between 10 and 20 nm, there are different observations for the magnetization of Pt/Co interfaces between the mica and PFA substrates. The intensity of the MPE will be enhanced as the Pt thickness increases for Pt/Co on the PFA substrate, while a significant weakening of the intensity of the MPE will be observed for Pt/Co on mica.

Fig. 5 The enhancement of (a) magnetization and (b) coercive force of x nm Pt on 30 nm Co/PFA (red circles) and 30 nm Co/mica (black squares).

Considering the surface roughness from Co deposition shown in Fig. 2, when Pt is deposited on top of rougher Co/PFA surfaces, the amount of Pt/Co interfaces is expected to be larger, resulting in a stronger interaction between Pt and Co. However, for the Co/mica system, Co is almost grown in FvM mode on mica, so the Pt/Co interfaces will be limited. Furthermore, as the Pt thickness increases, the competition between the Pt–Pt bond and the Pt–Co bond will be enhanced, resulting in weakening of the MPE from Pt–Co.

On the other hand, the rougher Co/PFA interfaces convert additional Pt into stronger interfacial spin–orbit coupling (SOC)/MPE and enhanced pinning, leading to a gradual increase in coercive force as shown in Fig. 5b. On the other hand, the smoother Co/mica interfaces lead to weakening of the MPE at larger Pt thickness due to Pt–Pt bonding dominance, resulting in a slight increase or saturation of H_c.

In order to confirm that the chemical composition distributions for Pt/Co on mica and PFA are the same as what we expect, depth profiling experiments for Pt/Co on mica and PFA were performed by SIMS as shown in Fig. 6a and b, respectively. We focus on the evolution of Pt, Co, and a Pt–Co alloy as the sputtering time increases. In Fig. 6a, for the chemical composition of Pt/Co on mica, Pt is the richest on the topmost surface, and we can also find the existence of the Pt–Co alloy. As the sputtering time increases, we can find a slight decrease in Pt intensity while the intensities of Co and the Pt–Co alloy increase. This reveals that the vertical chemical distribution comprises a topmost Pt layer, an interfacial Pt–Co alloy, and a bottom Co layer. This is consistent with the thin film deposition. Because Co is first deposited on mica and Pt is deposited on top of Co, the observations of Pt, the Pt–Co alloy, and the Co layer can be predicted. In Fig. 6b, we only replace the mica substrate with PFA, and the depth profiling results are almost the same as those on the mica substrate.

Fig. 6 The SIMS intensities of Co, Pt and Pt–Co for 20 nm Pt/30 nm Co on (a) mica and (b) PFA with different sputtering times. The SIMS intensities of (c) Pt–Co and (d) Co for 20 nm Pt/30 nm Co on mica (black) and PFA (red) with different sputtering times.

In order to confirm the MPE shown in Fig. 5 results precisely from the evolution of the Pt–Co alloy, we combined the intensities of the Pt–Co alloy in Fig. 6a and b and the result is shown in Fig. 6c. We can determine the maximum intensities of Pt–Co bonding in the series of Pt/Co on the mica and PFA substrates, which are almost the same. However, in the analysis of depth profiling experiments, the intensities of Pt–Co bonding on PFA are obviously larger than those on mica. After integration, the integrated intensity ratio of Pt–Co bonding on PFA and mica is close to 2.0. In Fig. 5a, the enhancements of saturation magnetization (M_s) for Pt/Co on PFA and mica are 40% and 20%, respectively. The ratio between the enhancements of M_s for Pt/Co on PFA and mica is also 2.0. Therefore, we can assume that the enhancements of M_s can be attributed to the Pt–Co bonding, which is consistent with the previous literature on MPE.^42,43

In Fig. 6d, the depth profiling of Co intensities of on PFA and mica can be clearly observed. We can find an obvious difference between the Co layer removal of Co/PFA and Co/mica interfaces. From the previous literature, the change in interfacial properties for the two heterogeneous materials can be simply categorized into clear and fuzzy change types.^43–45 If there is no diffusion and mixing occurring at the interfaces between heterogeneous materials resulting in a clear interface, the intensity evolution in depth profiling experiments will exhibit an exponential change.^43,44 Conversely, if there is some diffusion or mixing at the heterogeneous interfaces resulting in fuzzy interfaces, the intensity evolution in depth profiling experiments will exhibit a linear-like change.^44,45 According to the previous literature, the Co intensity evolution in depth profiling experiments shown in Fig. 6d can help us confirm a clear interfacial property without mixing for Co/mica and a fuzzy interfacial property with mixing for Co/PFA, which are in agreement with the AFM images shown in Fig. 2.

The degree of change in interfacial properties is decided by the interaction between the kinetic energy of adatoms and the enthalpy of substrate fusion, resulting in an increase of the contact area and an enhancement of surface reactivity. In order to demonstrate this mechanism, we propose a novel model called the Thermal-Informed Roughness Activation (TIRA) model. From the TIRA model, the surface roughness can be controlled by the interaction between the enthalpy of substrate fusion (ΔH_f) and the kinetic energy of adatoms (E_k). When the deposited atoms impinge on different substrates with constant kinetic energy, the interfacial roughness can be expressed by the average roughness (R_a) and decided by the competition between the incident kinetic energy and surface micro-reconstruction of the substrate.

The competition can be described by the TIRA model with a dimensionless activation eqn (1):

χ ≡ E_k/αΔH_f (1)

where ΔH_f is the enthalpy of substrate fusion per atom and α is a composite factor including geometry, thermal conductivity, and crystallographic orientation whose value is between 0 and 1, being used for transforming ΔH_f into the effective energy barrier of surface micro-reconstruction. The probability of micro-reconstruction can be expressed as a saturated eqn (2):

A(χ) = 1 − e^−χn (2)

When χ is much smaller than 1, the probability A(χ) is close to χn, showing that the energy isn't enough to roughen the substrate surface. However, when χ is much larger than 1, the probability A(χ) is close to 1, representing a completely activated substrate surface, which is consistent with the phenomenon of the substrate with low ΔH_f being more easily roughened. We assume F to be the flux of particles arriving at the substrate surface per second in 1 cm². The competition between the increase of surface roughness by first-order kinetic approximation^46,47 and the mechanism of surface smoothness can be expressed by eqn (3):where k₀ is the effective enhancing constant on roughness per bumping, R_a,sat is the maximum roughness, and k_s is the constant of smoothing speed. With constant E_k, ΔH_f and F, we can solve eqn (3) and obtain a solution of time analysis, which can be expressed by eqn (4):

R_a(t) = R_a,∞(1 − e^−t/τ) (4)

When the roughness is far from saturated and the smoothing effect is extremely weak, which means R_a ≪ R_a,sat and k_s ≪ k₀FA, we can obtain the relationship between scale and sensitivity, which can be expressed by eqn (5):

Predicting simply using eqn (5), R_a,∞ will increase with the inverse of αΔH_f with constant E_k representing the substrate with low ΔH_f being more easily roughened, which is consistent with the experimental results. The quantitative consistency between the experimental data and the TIRA scaling directly validates the effectiveness of the model. Under comparable adatom kinetic energy and flux, the TIRA framework predicts that the R_a is inversely proportional to the substrate ΔH_f. Using the reported ΔH_f values for mica (∼ 500 J g⁻¹) and PFA (∼ 23.5 J g⁻¹),^21–24 and the AFM roughness data obtained at equivalent Co thickness, the cross-substrate roughness ratio (PFA/mica = 21 at Co = 30 nm) precisely matches the ΔH_f ratio (∼ 21). This one-to-one correspondence without any adjustable parameters suggests that R_a ∝ 1/ΔH_f, indicating that the interfacial morphology is thermodynamically governed by ΔH_f. Moreover, the complementary SIMS and SQUID results exhibit quantitative scaling with the same trend—where the twofold enhancement in the intensity of the Pt–Co alloy and the corresponding twofold increase in the M_s of Co/PFA further demonstrate that the roughness-activated contact area predicted using the TIRA model directly translates into measurable interfacial and magnetic amplification. To summarize, these findings support that the TIRA model can qualitatively describe and quantitatively predict the evolution of interfacial roughness and its functional consequences for the studied thermodynamic substrates.

In Fig. 7, the schematic plots show the interaction between interfaces and magnetic properties as mentioned in the previous paragraph. According to the TIRA model, when the kinetic energy of deposited atoms is nearly constant, Co follows FvM mode growth on mica, which is the substrate with the higher ΔH_f as shown in Fig. 7a and b. The AFM image in Fig. 2a–c implies a low roughness (R_a), whose value is between 1.7 and 2.3 nm, and the XRD patterns in Fig. 3a exactly show the peaks of hcp-Co(002), resulting in a smaller coercive force and earlier transition from Néel wall to Bloch wall as shown in Fig. 4a and limited bending endurance as shown in Fig. 4c. Because the Pt/Co interfaces are smoother, resulting in the smaller effective contact area shown in Fig. 7c, the enhancement of the MPE as the Pt thickness increases is slight, as shown in Fig. 5. The SIMS results reveal the well-defined Pt/Co/mica layering shown in Fig. 6a.

Fig. 7 The schematic plots of surface evolution for Pt/Co deposited on (a)–(c) mica and (d)–(f) PFA.

On the other hand, Co is grown in VW mode on PFA as shown in Fig. 7d and e because PFA is the substrate of lower ΔH_f, resulting in an enhancement of A(χ) and interface roughening from 24 to 48 nm as shown in Fig. 2. No peaks can be observed in the XRD patterns shown in Fig. 3b. The coercive force for Co/PFA is higher than that for Co/mica by 50% for every thickness and the transition from Néel wall to Bloch wall is postponed as shown in Fig. 4a. The samples still remain stable under bending with a large curvature as shown in Fig. 4c. The rougher Pt/Co interfaces increase the effective contact area as shown in Fig. 7f, resulting in a continuous enhancement of the MPE as the Pt thickness increases, as shown in Fig. 5. The SIMS results reveal a broader depth distribution and an increased integrated intensity of the Pt–Co alloy signal, as shown in Fig. 6. Therefore, these results indicate that the TIRA model may be used to tune ΔH_f or increase E_k in order to control A(χ) and R_a, which could be relevant for applications in flexible electronic devices.

Conclusions

We established a substrate thermodynamics-driven strategy to steer Co thin-film growth and spin coupling on flexible platforms. High-ΔH_f mica supports layer-by-layer growth, low R_a, and clear hcp(002) texture, whereas low-ΔH_f PFA triggers rough, cluster-like morphologies, elevates coercive force, and, critically, preserves magnetic functionality under large curvature, aligning with the needs of wearable and deformable devices. Introducing Pt at the top interface converts geometric roughness into an enhanced magnetic proximity effect, with the twofold increase of the integrated Pt–Co alloy signal on PFA quantitatively mirroring the twofold larger M_s enhancement, thereby tying the chemical intermixing/contact area to magnetic amplification. Finally, the Thermal-Informed Roughness Activation (TIRA) model—expressed via a dimensionless roughness-activation term and saturation kinetics—captures how ΔH_f and adatom energy set the onset and scale of interfacial micro-reconstruction, offering actionable design rules for targeting specific combinations of crystallinity, proximity coupling, and bend endurance in future flexible spintronic stacks.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting the findings of this study are available within the article.

Acknowledgements

We gratefully acknowledge financial support from the National Science and Technology Council (NSTC), Taiwan, under Grant No. 114-2112-M-159-001, 111-2112-M-159-001-MY3, and 111-2112-M-159-002-MY2.

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