Unveiling Spin Dependent Effectiveness of Strain Engineering in Metal Catalysts

Abstract

Strain engineering has emerged as a powerful strategy to modulate catalytic activity, yet its general applicability remains uncertain, especially for magnetic catalysts where spin effect also plays a critical role in governing reactivity. Here, we reveal a metal-dependent modulation on adsorbate chemisorption to strain, with magnetic metals exhibiting reduced strain sensitivity compared to non-magnetic metals. Using ammonia synthesis as a model reaction, we attribute this behavior to an antagonistic interaction between strain and spin, wherein spin effect counteracts strain-induced chemisorption modulation and becomes stronger with increasing magnetism, originating from the varying shift of d-band center under the combined effects. Kinetic analysis further confirms that strain engineering markedly modulates the reactivity of weakly magnetic or non-magnetic metals by reshaping traditional scaling relations under strain-free conditions, while offering marginal impact to strongly magnetic metals. Accordingly, we propose a practical strain-based strategy to enhance the activity of representative ammonia synthesis catalysts, including Fe, Co, Ni and Ru. Moreover, the metal-dependent strain effect can be extended to key intermediates in other reactions, indicating a general phenomenon and establishing a conditional principle for applying strain engineering in metal catalysts design.

Changing a catalyst’s surface via strain can alter how strongly it binds reacting molecules, but this does not help every metal equally. This study shows that magnetism can offset strain, limiting gains in strongly magnetic metals and guiding better catalyst design.

Introduction

Enhancing catalyst reactivity remains a central challenge in advancing heterogeneous catalysis, given the pivotal role catalysts play in modern chemical industries^1–3. Among various approaches, strain engineering has emerged as a powerful method to tune catalytic activity by modifying the geometric and electronic structure of active sites^4,5. For instance, compressive or tensile stress applied to Pt, Ru, or Cu surfaces has been shown to significantly enhance the catalytic activity in reactions such as oxygen reduction⁶, ammonia synthesis^7,8, and CO₂ electroreduction⁹. Notably, a mere 1% compressive stress exerted on a pure Pt catalyst can increase its oxygen reduction activity by more than 300%⁶. The underlying mechanism for the improvements lies in the strain-induced regulation in chemisorption of key intermediates^10,11, as catalytic activity exhibits a volcano-shaped dependence on the adsorption energy of intermediates based on the Sabatier principle^12–14. Therefore, by precisely controlling strain, the adsorption energy can be modulated to drive the system toward the peak of the volcano, thereby maximizing catalytic efficiency.

Beyond strain engineering, recent studies have demonstrated that spin engineering is another effective approach for modulating catalytic activity, especially for magnetic catalysts^15–17. Unlike traditional strain engineering that focuses on structural modification, spin engineering specifically targets the spin state of metal centers¹⁸. For instance, Yang et al. found that tuning the e_g electron occupancy of transition metal cations in perovskite oxides enhances the activity of oxygen evolution reaction by optimizing the spin-related electronic structure and increasing metal-oxygen covalency^19,20. Xu et al. also pioneered spin-related electrocatalysis by leveraging spin polarization to regulate reaction pathways and enhance the catalytic performance of H₂O splitting^21,22. Additionally, our previous works revealed a spin-mediated promotion effect that activates traditionally unreactive cobalt catalysts by introducing a promoter to reduce the spin moment of Co atoms, and on that basis, proposed La and NbN as highly effective spin promoters for Co in ammonia synthesis^23–25. We further preliminarily demonstrated that spin engineering can improve catalytic activity in many reactions, based on the close correlation between the surface spin state and the adsorption energy of various intermediates^26,27.

Both strain engineering and spin engineering have independently demonstrated significant impacts on the reactivity, promoting growing interest in their combined application, such as applying strain to magnetic materials to modulate the catalytic activity^28,29. For instance, in Fe-based catalysts, strain can trigger a transition from low-spin (LS) to a high-spin (HS) state, with HS Fe sites identified as the primary active sites for oxygen reduction reaction³⁰. Likewise, comparative studies across transition metals have revealed distinct strain responses in catalytic enhancement, with a 3% tensile strain applied to Cu yielding a current density comparable to that achieved with 4% strain on Ni³¹.

The above findings suggest that applying strain to magnetic catalysts may provide a versatile route to tune reactivity through coupled strain and spin effects, as strain alters not only the lattice geometry but also the spin state of surface metal atoms^32,33. This dual modulation raises fundamental questions: Does strain engineering exhibit the same effectiveness in both magnetic and non-magnetic catalysts? And when stress engineering is applied to magnetic systems, how do strain and spin effects respectively function in governing catalytic behavior? Given the growing importance of strain in catalyst design, a clear understanding of how strain interacts with spin is essential to the predictive power and generalizability of strain engineering, particularly for magnetic materials.

Motivated by these questions, we performed a detailed theoretical study to elucidate the role of strain in modulating catalytic activity across different metals, combining with density functional theory (DFT) calculations and Micro-kinetics modeling. In this work, spin-polarized (SP) metals with varying magnetic properties (Fe, Co, and Ni), as well as non-spin-polarized (NSP) metals like Ru, Rh, and Pd, were selected as comparisons to first investigate how strain influences the adsorption energy of intermediates on these metals. We reveal a metal-dependent response on adsorbate chemisorption under strain, and show that the efficacy of strain is governed by the surface magnetic state. We then use ammonia synthesis as an example to understand this behavior by disentangling the effects of strain and spin on chemisorption of N and N₂ transition state, uncovering an antagonistic interaction between them (Fe > Co > Ni) and providing a rational explanation via d-band center for this behavior. We further combined kinetic analysis to examine when and how strain modulates catalytic activity, and proposed specific strategies to tune the activity for ammonia synthesis via strain engineering. Finally, we extended this metal-dependent effect to other key intermediates across different catalytic reactions, underscoring its generality. These findings establish that strain engineering is highly effective in low-spin metal catalysts but offers only marginal benefit in high-spin systems, providing a broadly applicable framework for catalyst design by utilizing strain engineering.

Results

Metal-dependent modulation on adsorbate chemisorption under strain

To investigate the effect of strain on the binding strength of adsorbates to metal surfaces, we here considered a range of adsorbates, including N, C, H, O, S, CH, CH₂, NH, and NH₂, which are widely recognized as activity descriptors in various catalytic reactions^34–38. A variety of metals, including Fe, Co, Ni, Ru, Rh, and Pd, was also included to provide a comprehensive evaluation. Biaxial strains ranging from −4% to +4% were applied by symmetrically varying the in-plane lattice constants (Fig. 1a), where the range of strain within ±4% was chosen because it is experimentally accessible³⁹ and theoretically sufficient⁴⁰ to modulate adsorption energies and catalytic activity. The adsorption energies (ΔE) of adsorbates on different metal surfaces under strain were then calculated and are shown in Supplementary Figs. 1–2 and Supplementary Tables 1–2. The relations between adsorption energy and strain for N, C and O are shown in Fig. 1b, while results for other adsorbates are presented in Supplementary Fig. 3.

Fig. 1. Effect of strain on adsorbate chemisorption over various metals.

a Schematic diagram of applying strain on metals. b Relations between adsorption energies (ΔE) of N, C, and O and applied strain for Fe, Co, and Ni, as well as Ru, Rh, and Pd. c The slope of the fitting line between adsorption energy and strain for N, C, and O on 3 d, 4 d, and 5 d metals in groups 8, 9, and 10, with 3 d metals including both spin polarized (SP) and non-spin polarized (NSP) surfaces.

For all studied adsorbates, the applied strain could regulate ΔE across the various metal surfaces, with tensile stress enhancing the adsorption energy while compressive stress weakening it (Fig. 1b). However, the extent of the response to strain varies among metals. Specifically, the strain-induced changes in adsorption energy are relatively small for Fe, Co, and Ni (3 d metals, solid lines in Fig. 1b), whereas much larger variations are found for metals such as Ru, Pd and Rh (4 d metals, dotted lines in Fig. 1b). This trend is more clearly reflected in the normalized fitted lines of adsorption energy versus strain, where the slopes of the three 4 d metals are steeper than those for the three 3 d metals, indicating a stronger strain response (Supplementary Fig. 4).

The above results imply that the effect of strain on ΔE is metal-dependent and may correlate with the metals' periods. To further confirm this observation and elucidate its origin, we calculated adsorption energies of N, C, and O on nine metals from groups 8, 9, and 10 of the 3 d, 4 d, and 5 d periods to make a direct comparison (Supplementary Fig. 5 and Supplementary Table 3). We found that, compared with Fe, Co, and Ni in 3 d series, the effect of strain on ΔE is much larger for the metals in 4 d and 5 d series, as indicated by their higher absolute slopes (Fig. 1c). Additionally, across the periods from left to right, the slopes of metals in group 9 and 10 gradually flatten (decrease), whereas the slopes for Fe, Co, and Ni become steeper (increase). This proves that the impact of strain on Fe, Co, and Ni differs fundamentally from that on other metals. Considering that the principal distinction of Fe, Co, and Ni from others is their magnetic character, we therefore hypothesize that the origin of the metal-dependent modulation on adsorbate energy is related to the surface intrinsic spin state.

Surface spin state governs metal-dependent strain response

To further substantiate the correlation between strain effectiveness and surface spin-polarization, we examined adsorbate adsorption on Fe, Co, and Ni surfaces under NSP conditions. Specifically, the calculations under NSP conditions were performed by artificially setting the total magnetic moment on SP surfaces to zero, effectively removing surface magnetism while preserving the original lattice structure, thereby enabling a direct comparison with the SP counterparts. Here, ammonia synthesis was used as a model reaction, and N adsorption energy (ΔE_N) was employed to clarify the effect of strain on SP and NSP metals and their relative reactivity, as ΔE_N is regarded as one of the descriptors for reflecting the activity of ammonia synthesis³⁹. The variation of ΔE_N on SP and NSP surfaces under strain was compared via the normalized fitting lines at −4% strain (Fig. 2a), showing that the strain-induced change in ΔE_N is greater on the NSP surface than that of the SP surface, as evidenced by the larger slope of the NSP surface (k_NSP) compared with the SP surface (k_SP). Furthermore, this discrepancy increases with the intrinsic magnetic degree of the metal surface (Fe > Co > Ni), demonstrating that the role of strain is strongly dependent on the degree of surface spin state.

Fig. 2. The interaction between strain and spin effects on magnetic metals.

a Normalized trend line of the relationship between N adsorption energy (ΔE_N) and strain on SP and NSP Fe, Co, and Ni surfaces. The illustration represents the occupation of d electrons in the e_g and t_2g orbitals of metals, representing the degree of metal magnetism (Fe>Co>Ni). b Relations between strain and changes in spin moment on Fe, Co, and Ni. c Relations between spin moment and ΔE_N on Fe, Co, and Ni. d Comparison of individual strain and spin effect on N adsorption energy (ΔΔE) of Fe. e Schematic representation of the antagonistic effects of strain and spin on Ni and Fe, representing low-spin and high-spin metals, respectively.

We then examine why the strain's regulation of N adsorption is highly sensitive to the surface spin state. To this end, the spin moments of metal atoms directly involved at the N adsorption sites under varying strain were calculated (Supplementary Fig. 6) and normalized with respect to the strain-free case in Fig. 2b. Strain can alter the surface spin state, with tensile stress increasing and compressive stress decreasing it. Furthermore, the spin moments exhibit a systematic variation with applied strain, with the effect particularly pronounced in Fe due to its high intrinsic magnetization. It indicates that strain not only perturbs the lattice geometry but also modulates the surface spin state, consistent with previous works⁴¹. To further validate the reliability of the calculated spin state on SP surfaces using the Revised Perdew-Burke-Ernzerhof (RPBE) functional, additional calculations via Heyd-Scuseria-Ernzerhof hybrid functional (HSE06)^42,43 were performed for comparison. Although slight differences in absolute spin moments were observed, both functionals yield consistent strain-induced spin trends, with RPBE results showing a clear linear correlation with HSE06 (Supplementary Figs. 7–8). This demonstrates that the strain-spin relationship is independent of the exchange-correlation functional and that the conclusions are reproducible using both standard and hybrid DFT approaches. Furthermore, spin moments of bulk Fe, Co, and Ni exhibit the same qualitative trends with both functionals, and the RPBE values agree well with experimental data⁴⁴, confirming the robustness of RPBE functional for spin prediction (Supplementary Fig. 9 and Supplementary Table 4).

Note that applied tensile stress on NSP surfaces expands the lattice structure and thus strengthens the adsorption (Fig. 2a), yet on SP surfaces it simultaneously increases the surface spin moment, which also influences ΔE_N (Fig. 2c). It means that both the applied strain and the surface spin moment correlate with ΔE_N, but for SP surfaces the observed ΔE_N reflects a superposition of geometric strain and strain-induced spin effects. Specifically, applying strain on SP surfaces modulates the adsorption energy via the lattice structure-induced strain effect on one hand, and the surface spin state-induced spin effect on the other hand.

We then decouple the strain and spin effects, quantitatively evaluate their individual roles in chemisorption, and, on this basis, further elucidate their underlying origins from perspectives of electronic structure and spin, ultimately developing a mechanistic understanding of the observed metal-dependent strain sensitivity. Notably, from a strict physical perspective, these two effects cannot be completely decoupled. In this work, the separation is not intended as a rigorous physical partition but rather as a controlled analysis that constrains one degree of freedom while monitoring the other to disentangle their relative contributions. A differential descriptor of ΔΔE_x% is defined to capture the net modulation of chemisorption at a given strain level x%, building on widely accepted methodologies for isolating and quantifying the contribution of electronic and spin effects^24,25,27, thereby providing a robust framework to analyze the interplay between strain and spin effects. ΔΔE_x%-strain represents the pure strain effect, calculated on NSP surfaces where magnetism is artificially removed. ΔΔE_{x%-strain & spin} corresponds to the combined effects of strain and spin derived from SP surfaces under identical strain conditions. The spin contribution is therefore defined as ΔΔE_x%-spin = ΔΔE_{x%-strain & spin} – ΔΔE_x%-strain. This comparative framework allows a direct, quantitative assessment of the roles of strain and spin in governing adsorption behavior under otherwise identical conditions.

For Fe, the relative change in adsorption energy induced by strain alone (ΔΔE_x%-strain) alters substantially with strain, the corresponding combined effects of strain and spin (ΔΔE_{x%-strain & spin}) show minimal variation, suggesting that the spin response effectively counteracts the strain effect (Supplementary Fig. 10). The antagonistic interaction is further confirmed by the decoupled pure strain and spin effects (Fig. 2d), where the two contributions exert clearly opposite influences on ΔE_N, and their magnitudes are comparable, resulting in only a minor net change in adsorption energy on SP Fe. Compared with highly magnetic Fe, the spin effect is modest for Co and nearly negligible for Ni, indicating that spin plays a progressively smaller role in adsorption modulation as intrinsic magnetization decreases (Supplementary Figs. 11–13).

Overall, as visualized in Fig. 2e, on low SP metals like Ni, the spin effect induced by mechanical strain exerts minimal influence on adsorption energy, leaving the strain effect as the dominant factor. In such systems, strain engineering remains an effective strategy for tuning adsorption strength. In contrast, on high-spin surfaces like Fe, the antagonistic interplay between strain and spin effects leads to near-cancellation, resulting in negligible net changes in adsorption energy, and the effect of strain engineering in modulating catalytic behavior is thus significantly diminished.

Beyond the studied stepped surfaces, we also examined N adsorption on terraced surfaces of Fe, Co, and Ni under strain, considering that terrace sites typically occupy a much larger fraction of the exposed surface area in practical catalysts. The results in Supplementary Figs. 14–16 and Supplementary Table 5 show that the strain-induced trends on terrace surfaces are consistent with those observed on stepped surfaces, indicating that the strain-dependent adsorption behavior and the antagonistic interplay between strain and spin effects are largely independent of surface structures, further supporting the generality.

Understanding the origin of the strain-spin relationship

Following the identification that the reduced strain response of ΔE_N on magnetic metals arises from an antagonistic interplay between spin and strain effects, we sought to elucidate its underlying origin by examining the surface electronic structure, with a key factor governing adsorbate-metal interactions^45–47. As shown in Fig. 3a and Supplementary Table 6, applied strain induces systematic shifts in the d-band center (ε_d) of surface atoms at the N adsorption sites, with a nearly linear correlation to the strain magnitude. Tensile stress shifts ε_d closer to the Fermi level (E_F), thereby increasing the occupancy of metal d states above the E_F and strengthening the metal-adsorbate bonding, consistent with the trend observed in Fig. 2a. Conversely, compressive stress shifts ε_d away from the E_F, weakening the bonding strength.

Fig. 3. Origin of the antagonistic interaction between strain and spin.

a d-band center (ε_d) as a function of strain for Fe, Co, and Ni. Changes in d-band center (ΔΔε_d) as a function of the variation in ΔE_N when considering b strain (ΔΔε_d-strain) and c spin (ΔΔε_d-spin) effects only for Fe, Co, and Ni. d Computed projected density of states (PDOS) and d-band center positions for NSP and SP Fe with and without strain, the illustration clearly shows the shift of ε_d under ±4% strain, compared to strain-free. e Schematic illustration of how tensile stress modulates surface spin state, incorporating changes in bond length, electron localization function (ELF), e_g and t_2g orbital energy change, electronic occupancy state, and spin density. The colorbar in both ELF and spin density maps ranges from 0 to 1. In the ELF plots, blue indicates electron delocalization, while red denotes electron localization. In the spin density maps, blue indicates low spin density and yellow indicates high spin density.

Importantly, the extent of strain-induced modulation of ε_d varies across different metal surfaces. As reflected by the differences in slope, ε_d of NSP Fe shifts much more significantly under strain compared to that of SP Fe. In contrast, this discrepancy nearly vanishes for Ni, where slopes for SP and NSP surfaces are nearly identical. This trend in ε_d sensitivity to strain exactly accounts for the more pronounced variation in ΔE_N on NSP surface than on SP surface, and the magnitude of this discrepancy correlates with the intrinsic magnetic moment of the metal surface as shown in Fig. 2b.

To more directly clarify the role of ε_d on strain and spin, we introduce a differential descriptor of ΔΔε_d-x%, analogous to ΔΔE_x%, representing the net modulation of d-band center at a given strain level x%. The spin contribution on ε_d is therefore defined as ΔΔε_d-spin = ΔΔε_{d-strain & spin} – ΔΔε_d-strain. As shown in Fig. 3b, pure strain induced changes in d-band center (ΔΔε_d-strain) scales well with the corresponding change in N adsorption energy (ΔΔE_x%-strain), directly confirming that strain-driven shifts in the ε_d is the origin of adsorption energy modulation. A similar correlation is observed upon pure spin effect (Fig. 3c), indicating that spin also influences adsorption by altering the position of ε_d. Therefore, ε_d underlies the spin-dependent strain sensitivity in adsorption energy, which can directly reflect ΔΔE regulated by strain for metals with different intrinsic magnetization (Supplementary Fig. 17).

We next investigate how the d-band center reflects the adsorption energy for different magnetic metals under strain, using Fe and Ni as representatives of high-spin and low-spin, respectively. For high-spin Fe, the strong exchange splitting leads to the spin-up d-band is largely occupied and located predominantly below E_F, whereas the spin-down d-band is partially occupied. The exchange splitting will be enhanced under tensile stress, causing the spin-up d states to shift downward in energy and the spin-down d states to shift upward relative to E_F, leading to opposite responses of spin-up and spin-down d states to strain. Thus, in highly SP Fe, these opposing contributions of ε_d splitting largely cancel out, leading to minimal net shifts in ε_d and correspondingly minor changes in adsorption energy (Fig. 3d). For low spin Ni, the spin contribution is small as ε_d splits to a lesser extent and all lie below the E_F, allowing strain to dominate and lead to a more substantial shift of total ε_d compared to Fe and thus a stronger adsorption (Supplementary Fig. 18).

Building on this, we further provide an overall rationale for how strain influences the surface spin state through modulation of the electronic structure, taking tensile stress as an example (Fig. 3e). As the applied tensile stress increases from 0% to 4%, the expanded interatomic distances reduce orbital overlap and suppress d orbital hybridization, leading to enhanced electron localization. This localization strengthens exchange interactions among d electrons, and the concurrently reduced crystal field splitting further narrows the energy gap between e_g and t_2g orbitals. Analysis of the occupancy of electrons in the d orbital, obtained from the integral of the density of states (DOS) of the d orbital (Supplementary Figs. 19–20), shows that tensile stress increases the occupancy of electrons in the e_g orbital (d_z2 and d_x2-y2), while reducing the occupancy of electrons in the t_2g orbital (d_xy, d_yz, and d_xz). Therefore, the localized electrons preferentially occupy the e_g orbitals rather than pairing with existing electrons in the t_2g orbitals, resulting in larger spin splitting and enhanced surface spin polarization.

Kinetic validation of metal-dependent modulation in activity under strain

The above findings on the interplay between strain and spin effects in modulating adsorption energy highlight that the efficacy of strain engineering is intrinsically dependent on the surface magnetic state. In strongly magnetic systems, the spin-strain antagonism imposes a fundamental limitation on the strain-induced activity modulation. By contrast, in weakly magnetic or non-magnetic catalysts, where spin contributions are minimal, strain remains a robust and effective means of tuning adsorption. This insight has important implications for screening catalyst materials, where strain engineering is expected to be most effective.

To validate this, we continued taking ammonia synthesis as an example and performed kinetic analysis to evaluate the effect of strain on the activity beyond thermodynamics. Herein, the N₂ dissociation energy (ΔE_N-N) was calculated as the criterion (Fig. 4a and Supplementary Table 7), as N₂ dissociation is generally regarded as another key descriptor for catalytic activity evaluation in ammonia synthesis in addition to N adsorption energy^23,27,38. Consistent with the trend in N adsorption, applied strain could tune ΔE_N-N on both SP and NSP surfaces, with relatively minor variations on high-spin metals and larger changes on low-spin metals, and the modulation being substantially more pronounced on NSP Fe and Ni surfaces (Fig. 4a, b). This result provides a valuable probe to determine whether the observed metal-dependent modulation in chemisorption can be extended to the transition-state region.

Fig. 4. Metal-dependent response to strain engineering on activity.

a Activation barrier of N-N dissociation transition state (N-N TS) on Fe and Ni with and without strain of ±4%. b Normalized trend line of the relationship between N-N dissociation transition state energies (ΔE_N-N) as a function of strain on SP and NSP surfaces of Fe and Ni. c Two-dimensional (2D) activity heatmap illustrating the theoretically calculated steady-state rate per site for ammonia synthesis as a function of N-N dissociation transition state energy and N adsorption energy (ΔE_N). The dashed scaling line indicates the corresponding scaling relations within the strain range of −4% to +4% on NSP metal surfaces. d The enlarged perspectives of ΔE_N-N as a function of ΔE_N for Fe, Ru, and Ni under strain, where Fe continues to follow the strain-free linear scaling relationship, whereas Ru and Ni deviate from it. e Activity span for ammonia formation as a function of ΔE_N under different strain conditions, with the position of Fe, Co, Ni, and Ru clearly marked. f Activity for ammonia synthesis (turnover frequency, TOF) as a function of strain for Fe, Co, Ni, and Ru.

Notably, without explicitly examining the strain on ΔE_N-N, it is incomplete to infer the impact of strain on activity via its effect on ΔE_N, such as concluding that strain induces only a small change in ΔE_N and thus a minor effect on catalytic activity based on the volcano as a function of ΔE_N. Because this conclusion relies on a critical premise that ∆E_N and ∆E_N-N obey the same scaling relationship on all surfaces, as different scaling relationships correspond to different volcano plots and activity trends. This is precisely why a dual activity descriptor combining ∆E_N and ∆E_N-N was introduced later, rather than relying solely on ∆E_N.

We then illustrate how strain affects activity and further outline strategies to improve the ammonia synthesis activity of metal catalysts, including SP surfaces (Fe, Co, Ni), as well as the widely used Ru catalyst, as a representative NSP case. To evaluate the activity of metals under strain, the 2D activity volcano under strain-free conditions as a function of N and N-N binding energies (Fig. 4c) was constructed employing the mean-field microkinetic model^27,38, with the used scaling relations between Ε_Ν and all relevant intermediates and transition states as shown in Supplementary Figs. 21–26. The five dashed lines represent the different scaling relations between ∆E_N and ∆E_N-N on NSP metals (see Supplementary Figs. 27–30 and Supplementary Table 8 for computational details), reflecting how these linear relationships change under varying strains. In particular, strain can break the scaling relationship on NSP surfaces, whereas it has a smaller effect on magnetic surfaces, as exemplified by the comparison between Fe, Ru, and Ni shown in Fig. 4d. Fe displays localized displacement and largely continues to follow the strain-free linear scaling relationship even under different strains, while Ni shows a slightly stronger response than Fe. In contrast, Ru exhibits a much more pronounced deviation from the original strain-free scaling and instead follows new strain-dependent linear relations, indicating a greater strain sensitivity of its activity.

To evaluate the impact of strain on activity clearly, the 1D volcano plot (Fig. 4e) derived from the five scaling relations in Fig. 4c was constructed as a function of ∆E_N under different strain conditions, with blue shading activity span reflecting variations in activity under strain. The activities of Fe, Co, Ni, as well as Ru, a representative catalyst for ammonia synthesis, were also mapped in Fig. 4e and further hightlighted in the enlarged Supplementary Fig. 31. For the high-spin Fe, the variation in activity is minimal, with all data points clustering within a narrow region of the volcano plot, while the activity exhibits a much broader distribution for low- or non-spin metals. Collectively, strain engineering is highly effective in weakly magnetic or non-magnetic metals like Ni and Ru, yet offers only marginal benefit in high-magnetic metals like Fe, supported by the activity trend of Fe, Co, Ni, and Ru under strain in Fig. 4e.

The above indicates that the extent to which strain modulates catalytic activity varies among different metals, and we next illustrate how it can be used to enhance catalytic activity. As metals are located at distinct positions on the activity volcano (Fig. 4f), in addition to the degree of intrinsic activity tuning by strain, this primarily determines the type of strain that should be applied to enhance activity, namely compressive for left-side metals and tensile for right-side metals. Specifically, metals on the left leg, such as Fe, require compressive strain to weaken N adsorption and improve activity, while metals on the right leg, such as Co and Ni, require tensile strain to enhance by strengthening N adsorption. Accordingly, Fe activity increases by about 1.6-fold at −4% compressive strain, whereas Co and Ni increase by approximately over 100-fold at +4% tensile strain. In particular, Co could reach the volcano top at around +12% tensile strain through support engineering, approaching the best Ru (Supplementary Fig. 32). By contrast, Ru, already near the top, is indeed highly strain-sensitive, but both tensile and compressive strains reduce its activity, in good agreement with ref. ⁴⁸.

It should be noted that all activity results shown in Fig. 4c, e, and f are projected from the unstrained system (0%). To further assess their validity, activity volcano plots were constructed under various conditions ( − 4%, −2%, +2%, and +4%) for comparison. We find that the 2D volcano plots exhibit the same trends across the strain range from −4% to +4% (Supplementary Fig. 33), and the corresponding 1D activity plots are nearly identical, with only negligible variations at the peak region (Supplementary Fig. 34), thereby confirming the robustness of the results.

Exploring the universality of metal-dependent response to strain in catalysis

The preceding metal-dependent effect of strain on ammonia synthesis reveals that strain plays a weaker role in modulating adsorption of N and N₂ transition state with increasing surface spin, thereby limiting the effectiveness in enhancing the activity of high magnetic metals. This raises a broader question: is this metal-dependent behavior unique to ammonia synthesis, or does it represent a general constraint across other catalytic reactions involving magnetic surfaces?

To address this, we extended our analysis to a series of key intermediates widely recognized as activity descriptors in diverse catalytic reactions, such as H and O intermediates for H₂O splitting related oxygen evolution/reduction reaction (OER/ORR) and hydrogen evolution reaction (HER)^49,50, and CO and COOH for CO₂ reduction reaction (CO₂RR)^35,51, among others^34,36–38. Using the same computational protocol as employed for N adsorption, we calculate the strain-dependent adsorption energies of these intermediates on both SP and NSP Fe surfaces representing different spin degrees (Supplementary Table 9). A number of configurations of representative intermediates are illustrated in Supplementary Figs. 35–36, and the corresponding adsorption energies as a function of strain are shown in Fig. 5a, revealing a stronger strain response on NSP Fe than on SP Fe.

Fig. 5. Extension of metal-dependent strain effects to other intermediates.

a The normalized trend line of the relationship between the adsorption energy and strain on Fe, including C, H, O, S, CH, CH₂, NH, NH₂, CO, and COOH adsorbates with adsorption configurations in panel (c). b Two-dimensional heatmap describing the strain sensitivity for Fe and Ni. The colorbar refers to the ratio of slope of NSP (k_NSP) and SP (k_SP) surfaces, with a ratio greater than 1 indicating a more pronounced strain effect on the surface species of the NSP surface. c Schematic illustration of the metal-dependent strain response to chemisorption across various adsorbates.

In addition to the SP and NSP cases, we further consider low-spin Ni and high-spin Fe as comparative systems to validate the metal-dependent adsorption under strain. The strain sensitivity is defined as the slope (k) of adsorption energy with respect to applied strain, and the ratio of k_NSP/k_SP is used to quantify the relative response. As shown in Supplementary Figs. 37–38, k_NSP is consistently larger than k_SP, confirming a stronger strain response on NSP than on SP for both Fe and Ni. However, the ratio of k_NSP/k_SP on low spin Ni is close to 1 while it is much larger on high spin Fe (Fig. 5b), confirming a consistent trend across all studied intermediates that strain-induced changes in adsorption energy are more substantial on less magnetic surfaces due to the spin-strain antagonism. Specifically, for high-spin Fe, the slope on the NSP surface is significantly larger than on the SP surface, indicating that spin effects suppress the strain-induced modulation of adsorption energy, thereby weakening the influence of strain on strongly magnetic surfaces. In contrast, for low-spin Ni, the slopes on SP and NSP surfaces are similar, showing that spin effects play a much smaller role in modulating the strain response, and thus, strain can more effectively tune adsorption energies on less magnetic metals.

The above results imply that the metal-dependent response to strain observed in ammonia synthesis is not reaction-specific, but rather a general phenomenon that may impose intrinsic limitations on the applicability of strain engineering for regulating the activity of magnetic catalysts in many reactions, as illustrated in Fig. 5c and exemplified by the oxygen evolution reaction (details in Supplementary Fig. 39 and the accompanying discussion). The generality of this sensitivity underscores the importance of considering spin effects when applying strain-engineering strategies, especially in the design of catalysts based on magnetic metals.

Discussion

Through systematic theoretical analysis on adsorbate chemisorption under strain, using ammonia synthesis as a model reaction, we reveal that strain-induced modulation on chemisorption varies with the magnetic character of the metal, arising from an inherent antagonism between strain and spin effects. Kinetic analysis further proves that strain can significantly regulate the activity in low- or non-spin systems, but has a limited effect in high-spin cases. Such as, Fe activity increases by about 1.6-fold at −4% compressive strain, while Co and Ni increase by approximately over 100-fold at +4% tensile strain. Importantly, we find that this metal-dependent behavior under strain is not specific to ammonia synthesis, but extends to key intermediates across diverse catalytic systems, indicating a general phenomenon.

Overall, these findings underscore the necessary to account for spin when applying strain engineering, and suggest that the most promising candidates for strain engineering lie in catalysts with non-spin or low-spin character. This insight clarifies when and how strain can serve as an effective design strategy, helping guide experiments and avoid unproductive trial-and-error, as currently a substantial number of experimental studies continue to invest significant effort in applying strain to magnetic metals. Notably, this work focuses on metal catalysts, and the applicability of strain engineering to other magnetic catalysts, such as oxides and 2D materials, warrants case-by-case evaluation and should be explored in future studies.

Methods

Density functional theory (DFT) calculation method

All theoretical calculations were performed utilizing density functional theory (DFT) within the Vienna Ab initio Simulation Package (VASP 5.4.4)^52,53. The electronic exchange-correlation energy was described using the generalized gradient approximation (GGA)⁵⁴ in the form of the Revised Perdew-Burke-Ernzerhof (RPBE) functional⁵⁵. The projector augmented wave (PAW)⁵⁶ pseudopotentials method was chosen to describe the effective potential between ionic cores and electrons.

Brillouin zone integrations were achieved using a k-point grid of 12 × 12 × 12 for bulk calculations and 3 × 3 × 1 for slab, with the Monkhorst-Pack grid applied for orthogonal lattices and the Gamma grid for hexagonal lattices⁵⁷. Lattice constants optimization were performed on the bulk structure of Body-Centered Cubic (BCC) Fe and hexagonal close-packed (HCP) Co, face-centered cubic (FCC) Ni, as well as other stable phase metals including Cu, Ru, Rh, Pd, Os, Ir, Pt, and Mo. Strain was applied by varying the in-plane lattice constant from −4% to +4% in increments of 2%. The stepped (211) and (10-15) surfaces were modeled using four-layer 2 × 3 supercells. Both spin-polarized (SP) and non-spin-polarized (NSP) DFT calculations on magnetic metals of Fe, Co, and Ni were utilized to assess spin effects on catalysts, where the NSP surface was obtained by artificially setting the total spin moment to zero on SP surfaces. To prevent interactions between periodic images, a vacuum space of 15 Å was introduced along the z-direction, and dipole correction was applied. A kinetic cutoff energy of 450 eV was set for the plane-wave description of valence electrons to ensure convergence. In self-consistent field calculations, all slab and bulk structures were relaxed until the residual force and energy reached convergence thresholds of 0.05 eV/Å and 10⁻⁵eV, respectively.

Transition states (TS) for the reactions were identified using the Dimer⁵⁸ and climbing image nudged elastic band (Cl-NEB) method in its dynamical formulation⁵⁹. Microkinetic modeling was performed using the CATMAP code, based on the mean-field approach and the steady-state approximation^38,60. The activity heatmap was computed at a temperature of 673 K, a stoichiometric ratio of H₂ to N₂ (3:1), a total pressure of 1 bar, corresponding to 0.2% of N₂ conversion respectively, same from the activity volcano published in ref. ²⁷.

The chemisorption energy of N (ΔE_N) and transition state energy of N-N (ΔE_N-N) dissociation are calculated as follows:

$$\mathrm{\Delta }{\mathrm{E}}_{\mathrm{N}}={\mathrm{E}}_{\mathrm{N}}-{\mathrm{E}}_{\mathrm{slab}}-{1/2\mathrm{E}}_{\mathrm{N}2}$$ 1

$$\mathrm{\Delta }{\mathrm{E}}_{\mathrm{N}-\mathrm{N}}={\mathrm{E}}_{\mathrm{N}-\mathrm{N}}-{\mathrm{E}}_{\mathrm{slab}}-{\mathrm{E}}_{\mathrm{N}2}$$ 2

where E_N, E_slab and E_N-N represent the total energy of the N atom adsorbed on the metal surface, the total energy of the pristine metal surface, and the metal surface with the transition state of N₂ dissociation, and E_N2 means the energy of the N₂ gas phase.

The decoupling mechanism was involved the calculation of the spin effect (ΔΔE_x%-spin) and the strain effect (ΔΔE_x%-strain) on adsorption from the following formula:

$$\mathrm{\Delta }\mathrm{\Delta }{\mathrm{E}}_{\mathrm{x}\%}=\mathrm{\Delta }{\mathrm{E}}_{\mathrm{x}\%}-\mathrm{\Delta }{\mathrm{E}}_{0\%}$$ 3

where ΔE_x% and ΔE_0% refer to the chemisorption energies under strain of x% (x = ±2, ±4) and strain-free, respectively. The N-chemisorption change on NSP surfaces with the applied strain defined as strain effect (ΔΔE_x%-strain), while the change on SP surfaces is defined as the combined effect of strain and spin (ΔΔE_{x%-strain & spin}). Lastly, the spin effect is defined as:

$$\mathrm{\Delta }\mathrm{\Delta }{\mathrm{E}}_{\mathrm{x}\%-\mathrm{spin}}=\mathrm{\Delta }\mathrm{\Delta }{\mathrm{E}}_{\mathrm{x}\%-\mathrm{strain\&spin}}-\mathrm{\Delta }\mathrm{\Delta }{\mathrm{E}}_{\mathrm{x}\%-\mathrm{strain}}$$ 4

The d-band center (ε_d) is given by:

$${\mathrm{\epsilon }}_{\mathrm{d}}=\frac{{\int }_{-\infty }^{+\infty }\mathrm{\rho }\left(\mathrm{E}\right)\left(\mathrm{E}-{\mathrm{E}}_{\mathrm{F}}\right)\mathrm{dE}}{{\int }_{-\infty }^{+\infty }\left(\mathrm{E}-{\mathrm{E}}_{\mathrm{F}}\right)\mathrm{dE}}$$ 5

where ρ (E) is the projected density of states on the d-states of the metal atoms, and E_F refers to the Fermi level.

The electron occupation (n_d) of the metal d orbitals (d_xy, d_yz, d_xz, d_z2 and d_x2-y2) was obtained by integrating the projected density of states (PDOS) below the Fermi level:

$${\mathrm{n}}_{\mathrm{d}}={\int }_{-\infty }^{{\mathrm{E}}_{\mathrm{F}}}\mathrm{\rho }\left(\mathrm{E}\right)\mathrm{dE}$$ 6

where the d-electron occupation was calculated as the sum of the spin-up ($\mathrm{\rho }\left(\mathrm{E}\right)\uparrow$) and spin-down ($\mathrm{\rho }\left(\mathrm{E}\right)\downarrow$) contributions for spin-polarized calculations, defined as $\mathrm{\rho }\left(\mathrm{E}\right)=\mathrm{\rho }\left(\mathrm{E}\right)\uparrow +\mathrm{\rho }\left(\mathrm{E}\right)\downarrow$.

The decoupling mechanism was involved the calculation of the spin effect (ΔΔε_x%-spin) and the strain effect (ΔΔε_x%-strain) on d-band center from the following formula:

$$\mathrm{\Delta }\mathrm{\Delta }{\mathrm{\epsilon }}_{\mathrm{x}\%}={\mathrm{\epsilon }}_{\mathrm{x}\%}-{\mathrm{\epsilon }}_{0\%}$$ 7

where ε_x% and ε_0% refer to the chemisorption energies under strain of x% (x = ±2, ±4) and strain-free, respectively. The change of d-band center on NSP surfaces with the applied strain defined as strain effect (ΔΔε_{x %-strain}), while the change on SP surfaces is defined as the combined effect of strain and spin (ΔΔε_{x %-strain & spin}). Lastly, the spin effect is defined as:

$$\mathrm{\Delta }\mathrm{\Delta }{\mathrm{\epsilon }}_{\mathrm{x}\%-\mathrm{spin}}=\mathrm{\Delta }\mathrm{\Delta }{\mathrm{\epsilon }}_{\mathrm{x}\%-\mathrm{strain\&spin}}-\mathrm{\Delta }\mathrm{\Delta }{\mathrm{\epsilon }}_{\mathrm{x}\%-\mathrm{strain}}$$ 8

Author contributions

A.C. conceived and supervised the project. C.Y.F. performed the DFT calculations and data analysis. A.C. provided additional theoretical analysis and drafted the manuscript, with C.Y.F. and Z.Z.F. helping to finalize it. J.H.Y., S.H.L., and Y.T.S. discussed the results and commented on the manuscript.

Peer review

Peer review information

Nature Communications thanks Shaojun Guo, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Funding

A.C. discloses support for the research of this work from the National Key Research and Development Program of China [grant number 2024YFA1509204], the National Natural Science Foundation of China [grant number 22521204], the “Pioneer” and “Leading Goose” R&D Program of Zhejiang Province [grant number 2025C01150], the Challenge and Call project of the Inner Mongolia Autonomous Region [grant number 2024JBGS0033], the Science and Technology Breakthrough project of the Inner Mongolia Autonomous Region [grant number 2024KJTW0013]. C.Y.F., Z.Z.F., Y.T.S., S.H.L., and J.H.Y. declare no relevant funding.

Data availability

All data are available from the corresponding author upon request. The datasets generated in this study are provided in the Supplementary Information Data file. The datasets generated and analyzed during the current work are available at https://github.com/AngLabZJU/strain-and-spin-effects-data.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-026-73254-2.