Modulating spin relaxation at the ferromagnet/molecule interface via anchoring atom engineering

Abstract

Although spintronics has demonstrated potential for high-density, low-power electronic devices, performance often falls short of theoretical predictions owing to challenges in efficient spin injection and transport. Prior research has highlighted the role of molecular design in modulating interfacial properties; nonetheless, the impact of different anchoring atoms on spin relaxation, particularly during tunneling transport, remains largely unexplored. We fabricated Fe₃O₄/molecule hybrid nanoparticles through self-assembly to investigate experimentally and theoretically how different anchoring atoms — S and C (−COOH, −SO₃H, −OSO₃H) — affect the electrical and magneto-transport properties at the Fe₃O₄/molecule interface, as well as intramolecular spin relaxation and the associated physical mechanisms. Electrical transport measurements revealed that the contact resistivity at the Fe₃O₄/molecule interface was highly sensitive to the anchoring groups, in marked contrast to the tunnel attenuation coefficient β. Meanwhile, magneto-transport results demonstrated that replacing the carbon-centered anchoring group (−COOH) with sulfur-centered groups (−SO₃H, −OSO₃H) reduced the magnetoresistance and shortened the intramolecular spin diffusion length by ~69% compared with the carbon-centered anchoring group (−COOH). The theoretical studies clarified the role of orbital hybridization in tuning interfacial spin properties. We also examined the influence of magnetic field and temperature on intramolecular spin relaxation during tunneling and discussed the underlying mechanisms. This study experimentally verified, for the first time, the occurrence of spin relaxation within organic molecules during tunneling.

Graphical abstract

Keywords

organic spintronics / spin-dependent tunneling / spin relaxation / Fe₃O₄/molecule interface / anchoring atom

1 Introduction

Spintronics, a prominent branch of microelectronics, focuses on utilizing electron spins for information storage, transmission, and processing [1, 2]. Compared with conventional electronics, spintronic devices offer significant advantages, including higher storage density and lower energy consumption, and have become one of the most active research frontiers [3-5]. Expanding beyond conventional rigid systems, several studies has shifted towards flexible spintronics for wearable applications [6, 7]. For instance, Fe₃O₄ films prepared at room temperature on polymer substrates not only retain half-metallic properties and high magnetoresistance, but also exhibit excellent mechanical flexibility [8-10]. In spintronics, the representative device structure is the spin valve, composed of two ferromagnetic electrodes sandwiching a non-magnetic layer, which enables spin–charge interaction by combining magnetic response with charge-related properties [11]. A key prerequisite for realizing these functions is the effective injection of spin-polarized charge carriers into non-magnetic spacers [12], followed by their sustained transport while maintaining spin coherence [13]. However, despite extensive research efforts, the performance of spintronic devices remains below theoretical expectations because of persistent challenges in charge and spin injection efficiency [14].

Theoretical studies [15, 16] have demonstrated that unique spin-related functions can be achieved at ferromagnet/molecule interfaces — capabilities unattainable at conventional ferromagnetic/inorganic interfaces — making these interfaces critical platforms for spin injection and manipulation at the molecular scale. The ferromagnet/molecule interface can be engineered to effectively modulate magnetic properties, a prerequisite for enhancing spin injection efficiency and optimizing device performance [17, 18]. Given the chemical diversity of organic molecules, substantial potential exists to regulate spin injection and interfacial properties through molecular design. This capability opens new avenues for information storage and transmission, thereby driving growing research interest in this field [19, 20]. Among several molecular components, the anchoring group serves as a vital bridge between the molecule and ferromagnetic electrode, directly determining the bonding mode, bonding strength, and orbital hybridization at the interface [21], and thus fundamentally influencing interfacial spin injection efficiency and spin transport characteristics in molecular junctions [22]. Zhang et al. [23] employed ab initio theory to investigate the spin characteristics of organic molecules adsorbed on the Ni(111) surface and demonstrated that interfacial spin polarization is highly sensitive to the hybridization of the anchoring atom’s outer orbitals and their energy level alignment relative to the d-orbitals of ferromagnetic atoms. Their study further revealed that spin polarization depends on the atomic species, and that anchoring atoms with high electronegativity can yield enhanced tunneling magnetoresistance and large spin-filtering efficiency. In addition, numerous theoretical works [24, 25] have demonstrated that modifying the anchoring group is among the most direct and effective strategies for tuning spin injection at ferromagnet/molecule interfaces. Collectively, these findings provide crucial insights and guidance for advancing spintronics and optimizing the performance of spin-based devices.

Spin relaxation in organic molecules constitutes a critical aspect of spin transport processes. To the best of our knowledge, current research on the mechanisms of spin relaxation predominantly focuses on carrier hopping or diffusion transport within molecules [26, 27], whereas only a few studies have examined tunneling transport in molecules. As one of the principal transport modes in organic spin devices, tunneling is commonly observed at ferromagnet/molecule interfaces and in single-molecule junctions. Consequently, investigating spin relaxation mechanisms in tunneling processes is essential for optimizing spin injection and transport efficiency and for deepening the understanding of organic spintronics. In this work, we fabricated Fe₃O₄/carboxylic acid, Fe₃O₄/sulfonic acid, and Fe₃O₄/sulfuric acid hybrid nanoparticle samples via self-assembly to systematically investigate the effects of different anchoring atoms (C and S) on spin transport at the Fe₃O₄/molecule interface and the mechanisms of intramolecular spin relaxation during tunneling. Electrical transport measurements revealed that the potential barrier at the Fe₃O₄/molecule interface was highly sensitive to the anchoring groups. Furthermore, magneto-transport results demonstrated that replacing replacing the carbon-centered anchoring group (−COOH) with sulfur-centered groups (−SO₃H, −OSO₃H) reduced the magnetoresistance and shortened the intramolecular spin diffusion length by ~69%. The density functional theory (DFT) be incorporated to clarify the role of orbital hybridization in tuning interfacial spin properties. Furthermore, we analyzed the roles of magnetic field and temperature in intramolecular spin relaxation during tunneling and discussed the underlying mechanisms.

2 Experimental methods

The detailed fabrication process of Fe₃O₄/molecule hybrid nanoparticles has been described previously [28], where the average size of the Fe₃O₄ particles was ~10 nm [29]. We selected three categories of molecules with different anchoring groups (−COOH, −SO₃H, −OSO₃H), namely N-alkyl carboxylic acids, N-alkyl sulfonic acids, and N-alkyl sulfuric acids, as shown in Figs. 1(a), (b), and (c), respectively. The N-alkyl carboxylic acids include butanoic acid (CH₃(CH₂)₂COOH), octanoic acid (CH₃(CH₂)₆COOH), dodecanoic acid (CH₃(CH₂)₁₀COOH), and octadecanoic acid (CH₃(CH₂)₁₆COOH), denoted as Cn, where n = 4, 8, 12, and 18, respectively. The N-alkyl sulfonic acids include butane sulfonic acid (CH₃(CH₂)₃SO₃H), octane sulfonic acid (CH₃(CH₂)₇SO₃H), dodecyl sulfonic acid (CH₃(CH₂)₁₁SO₃H), and hexadecyl sulfonic acid (CH₃(CH₂)₁₅SO₃H), denoted as Sn, where n = 4, 8, 12, and 16, respectively. The N-alkyl sulfuric acids include butane sulfate acid (CH₃(CH₂)₃OSO₃H), octane sulfate acid (CH₃(CH₂)₇OSO₃H), dodecyl sulfate acid (CH₃(CH₂)₁₁OSO₃H), and hexadecyl sulfate acid (CH₃(CH₂)₁₅OSO₃H), denoted as SOn, where n = 4, 8, 12, and 16, respectively. Fe₃O₄ nanoparticles coated with Cn, Sn, and SOn were denoted as S(Cn), S(Sn), and S(SOn), respectively. The samples formed a magnetic tunnel junction network in which Fe₃O₄ nanoparticles were coated with monolayer molecules [29, 28], as shown in Fig. 2(a). Electrons preferentially take tunneling paths with the minimum particle-to-particle separation — corresponding to the molecular length — so [30], the transport measurements reflect molecular-scale characteristics. All samples were fabricated in ambient air and measured in a vacuum.

3 Results and discussion

3.1 Electrical transport

First, we investigated the electrical transport properties of these samples, as shown in Fig. 2(b), which depicts the dependence of resistivity (ρ) on molecular length (d) for S(Cn), S(Sn), and S(SOn). All curves followed \rho \sim {\mathrm{e}}^{-\beta d}(β is the attenuation coefficient), indicating that carriers tunnel through the molecules from one Fe₃O₄ particle to another, as previously demonstrated [28]. The temperature-independent β further supports the tunneling transport characteristics. The measured values were β_C = 0.21 Å⁻¹, β_S = 0.26 Å⁻¹, and β_SO = 0.23 Å⁻¹, showing subtle differences among samples with different anchoring groups. In addition, the relationship β_S > β_SO > β_C suggests that the dominant carrier transport mechanism within the molecules is unlikely to be intermolecular tunneling [31], further discussion can be found in Part 2 of the Supplementary Materials.

As shown in Fig. 3(a), the ultraviolet photoelectron spectroscopy (UPS) measurements show that the work function of bare Fe₃O₄ is 5.65 eV, whereas those of S(C12), S(S12), and S(SO12) are 7.22, 6.95, and 7.10 eV, respectively, which are 1.57, 1.30, and 1.45 eV higher than that of Fe₃O₄, respectively. This increase in the work functions is attributed to the formation of a dipole moment at the Fe₃O₄/molecule interface; owing to this dipole moment, the fermi level (E_F) of Fe₃O₄ moves further away from the vacuum energy level. The calculated energy levels and lengths of these molecules are shown in Table 1. Compared to the lowest occupied molecular orbitals (LUMO) of these molecules, their highest occupied molecular orbitals (HOMO) are closer to E_F of Fe₃O₄, indicating that the HOMO mainly participates in the tunneling transport. Combining the UPS measurements results and the calculated molecular energy levels indicates that the energy level differences ΔE between the Fermi surface and molecular HOMOs are as follows: ΔE(C) = 0.69 eV, ΔE(S) = 1.35 eV, and ΔE(SO) = 1.21 eV. The observed trend ΔE(S) > ΔE(SO) > ΔE(C) could possibly explain the weak correlation between the anchoring groups and β values (β_S > β_SO > β_C) [32].

The DFT calculations for these complexes were performed using the Guassian16 package [33]. The geometry optimizations and frequency calculations were conducted using the B3LYP/6-311+G(d, p) basis sets [34, 35]. For more calculated molecular energy level, please refer to Part 1 of the Electronic Supplementary Materials.

Interestingly, the contact resistivity ρ_c of three categories of samples is more sensitive to anchoring group, as depicted in Fig. 2(b), ρ_c(−COOH) > ρ_c(−OSO₃H) > ρ_c(−SO₃H). Among these three categories of samples, the Fe₃O₄/sulfonic acid interface exhibits a relatively smaller hindrance effect on carrier transport, which was more conducive to charge injection, followed by the Fe₃O₄/sulfuric acid. However, the order of contact resistivity magnitudes is opposite to that of the contact barrier (ΔE(S) > ΔE(SO) > ΔE(C)). This result suggests that in our system, the barrier is not the dominant factor governing the contact resistivity. Xie et al. [36-38] systematically studied the factors governing tunneling resistance in molecular junctions, and proposed a single-level model to explain the phenomenon. Their work demonstrates that interfacial contact resistance primarily depends on the coupling strength between ferromagnetic electrode and organic molecules; the stronger the coupling, the lower would be the interfacial contact resistance. Figure 3(b) depicts the spatial distribution of the HOMO of S12 throughout the molecular framework, along with the HOMO of SO12 concentrated at the end of the alkyl chain and that of C12 concentrated at opposite molecular ends (the anchoring group). Therefore, the spatial distributions of the HOMOs in C12 and SO12 are localized farther from the ends of the molecules and may cause weaker contact coupling at the interface. Therefore, the spatial distributions of the HOMOs in C12 and SO12 are localized farther from the ends of the molecules and may cause weaker contact coupling at the interface. The spatial distributions of HOMO in the three categories of molecule (n = 4, 8, or 16/18) exhibit similar localization. Consequently, the contact resistivity of S(Sn) is significantly lower than those of S(Cn) and S(SOn), resulting in reduced resistivity for S(Sn) as well. As discussed below, the adsorption energy and bond strength derived from theoretical simulations can quantitatively confirm the coupling strength between Fe₃O₄ and the molecules. Strong interfacial coupling effectively reduces the contact resistivity and enhances carrier transport [32]. Thus, selecting an appropriate anchor group is the most direct and effective strategy for modulating carrier transport at the ferromagnet/molecule interface in device design.

3.2 Spin-dependent properties at Fe₃O₄/molecule interface

In addition to electrical transport, we examined the influence of anchoring groups on the magnetic properties and spin transport of the samples. Figure 4(a) shows the magnetization curves of S(C12), S(S12), S(SO12), and bare Fe₃O₄ at 300 K, all of which exhibit superparamagnetic behavior. The saturation magnetization (M_S) of bare Fe₃O₄ was 61.8 emu/g at 1 T, whereas M_S decreased for Fe₃O₄ coated with molecules. As demonstrated below, this reduction can be attributed to two primary factors. First, the mass fraction of organic molecules and residual moisture in the sample contribute to this reduction. To exclude the molecular mass contribution, thermogravimetric analysis (TGA) was conducted on these four samples. The S(C12), S(S12), S(SO12), and bare Fe₃O₄ fine powder samples were gradually heated from 30 °C to 600 °C at a rate of 5 °C/min in a high-purity nitrogen (99%) atmosphere respectively. The results indicated that the contents of organic molecules and moisture in the sample led to low saturation magnetization (M_S) (Table 2).

After excluding this effect, the intrinsic saturation magnetization (M_S1) of Fe₃O₄ in the four samples is shown in Fig. 4(b), M_S1 for bare Fe₃O₄ remains higher than that of the coated samples, indicating that other factors also contribute. Secondly, surface modification of Fe₃O₄ nanoparticles by the coated molecules induces interfacial orbital hybridization, which modifies the surface magnetic moment and consequently influences the nanoparticle’s saturation magnetization [39]. A similar effect has been observed when surfactants were coated on Fe₃O₄ nanoparticles [40]. The order M_S1(Fe₃O₄) > M_S1(C12) > M_S1(S12) > M_S1(SO12) demonstrated that altering the anchoring groups can effectively tune the magnetic properties of the Fe₃O₄ nanoparticle surface.

To thoroughly analyze the variation in the magnetic moment on the Fe₃O₄ surface upon molecular adsorption, theoretical studies based on DFT were conducted. For the adsorption model, Fe₃O₄ slabs with saturated adsorption of −COOH, −SO₃H, and −OSO₃H groups were constructed for simulations [Figs. 5(a)−(c)], where the O atoms of the adsorbates form bonds with Fe atoms to stabilize the adsorption structure. Analysis of the magnetic moment distribution reveals that the Fe atoms involved in the adsorption exhibit an opposite spin state compared to those in pure Fe₃O₄ [Figs. 6(a), (c), (e)]. These results indicate that molecular adsorption induces an antiparallel spin arrangement of Fe atoms, thereby reducing the total magnetic moment of Fe₃O₄. This theoretical finding is in good agreement with our experimental results.

To further elucidate the underlying mechanism of this phenomenon, electronic structures, including partial density of states (PDOS), crystal orbital Hamilton population (COHP), and differential charge density, were systematically investigated. The PDOS analysis in Fig. 6(b) reveals that the Fe-3d orbitals strongly hybridize with the O-2p orbitals of C4, forming Fe−O bonds that facilitate adsorption. The COHP results further confirm that the spin-up channel is the major contributor to the Fe−O bond, as evidenced by a higher integrated COHP (ICOHP) value (−1.09) compared to that of the spin-down channel (−0.38). As shown in Figs. 6(d) and (f), the same phenomenon is observed in the −SO₃H and −OSO₃H systems, where the spin-up channel primarily contributes to Fe−O bonding. The ICOHP values follow the order: −SO₃H (−1.39) < −OSO₃H (−1.36) < −COOH (−1.09), the more negative ICOHP values of −SO₃H and −OSO₃H indicate stronger hybridization between the Fe-3d and O-2p orbitals, as reflected in adsorption energy. Specifically, the DFT results show that −SO₃H exhibits the strongest adsorption, with an adsorption energy (ΔE_ads) of −5.22 eV/molecule, followed by −OSO₃H (ΔE_ads = −4.51 eV/molecule) and −COOH (ΔE_ads = −4.09 eV/molecule). The stronger the adsorption or bonding, the greater the interface coupling, which possibly quantitatively explain the interface coupling we mentioned earlier.

A comprehensive analysis suggests that the differences in the saturation magnetization (M_S1) among the three samples [Fig. 4(b)] may be attributed to the chemical bonding strength (ICOHP) and the charge transfer at the Fe₃O₄/molecule interface. As discussed before, strong interfacial bonding (−SO₃H/−OSO₃H) induces severe p−d orbital hybridization, in which spin-up electrons participate in the formation of interfacial Fe−O bonds. Unlike the surface spin-down electrons, these bonding spin-up electrons are effectively ‘pinned’ due to the strong orbital interaction. This asymmetric spin involvement disrupts the intrinsic super-exchange interactions in Fe₃O₄ as well as might rigidly lock the surface Fe spins into a magnetically inactive or antiparallel configuration, thereby impeding their alignment with the external magnetic field [39, 41]. In contrast, weaker bonding (−COOH) likely imposes relatively fewer constraints on the surface spins, thereby posing fewer obstacles to their alignment with the magnetic field, as discussed in Part 5 of the Electronic Supplementary Materials. Furthermore, charge transfer at the Fe₃O₄/molecule interface further modifies the saturation magnetization (M_S1) of these samples. UPS analysis revealed a significant increase in the work function for all samples, indicating charge transfer from Fe₃O₄ to the absorbed molecules, this phenomenon was further supported by theoretical calculations (Part 4 of the Electronic Supplementary Materials). This charge transfer could induce Fe²⁺ oxidation and reduce the interfacial Fe²⁺/Fe³⁺ ratio, thereby lowering the magnetization. Although S(C12) exhibited a slightly larger increase in work function, probably suggesting a more pronounced interfacial charge transfer [42], its significantly weaker “pinning” allows a greater portion of the surface spins to remain responsive to the external magnetic field compared to S(S12) and S(SO12). Ultimately, the saturation magnetization of the samples is codetermined by these two factors.

3.3 Magneto-transport

We investigated the role of anchoring groups in the magneto-transport of the samples. Figure 7(a) shows the magnetoresistance curves of S(C12), S(S12), and S(SO12) at 300 K. Under an applied magnetic field of 5500 Oe, the magnetoresistance (MR) values for these samples were −11.25%, −10.28%, and −10.04%, respectively. The MR decreased monotonically with increasing magnetic field — a trend that contrasted with the magnetization curve, which approached saturation at 2 kOe. This discrepancy indicates that both the bulk magnetic moment of Fe₃O₄ particles and their surface magnetic moment play critical roles in spin transport. Furthermore, the differences in MR among the samples suggested that magneto transport is regulated by the anchoring groups.

Figure 7(b) presents the MR–d curves at 300 K, showing that MR decayed exponentially as the molecular length (d) increased. The decay rate varied with the anchoring group: MR decayed most slowly for carboxylic acid samples, followed by sulfuric acid samples, and most rapidly for sulfonic acid samples. When the spin polarization of interface-injected carriers was P₀, it decayed to P₀·e^−d/λ after tunneling through the molecular layer, where λ was the spin diffusion length. According to the Jullière model, MR can be expressed as [43]

(1)\left|MR\right|=\left|{\displaystyle \frac{R(H)-R(0)}{R(0)}}\right|={\displaystyle \frac{P_0^2{\mathrm{e}}^{-d/\lambda }}{1+P_0^2{\mathrm{e}}^{-d/\lambda }}},

where R(H) and R(0) denote the resistance under an applied magnetic field H and under zero magnetic field, respectively. The Jullière model assumes ideal spin injection and negligible interfacial spin scattering. In our system, considering the influence of orbital hybridization, P₀ refers to the spin polarization of the injected carriers, which not only reflects the intrinsic spin polarization of Fe₃O₄, but also includes the effect of different anchoring groups on interfacial spin injection. Xiong et al. [43] used the same method to fit the spin diffusion length in LSMO/Alq₃/Co devices. The MR−d data for these samples were fitted using Eq. (1), yielding λ_C (300 K) = 42.3 nm, λ_SO (300 K) = 17.8 nm, and λ_S (300 K) = 13.2 nm, with the relationship λ_C > λ_SO > λ_S.

As shown in Figs. 8(a)–(d), the temperature-dependent tunneling magnetoresistance (MR) is plotted for S(Cn), S(Sn), and S(SOn). The MR values decreased linearly with decreasing temperature (T), independent of the type and length of the coated molecules, the nearly identical slopes are likely due to the common constituent material of these samples — Fe₃O₄. Figure 8(e) shows that \left|P_0\right| increased with decreasing T. Previous studies have indicated that spin polarization is related to the saturation magnetization [44, 45], and the same slopes is also observed in the M_S1–T curves of the samples [Fig. 4(b)]. M_S1 decreased monotonically with increasing T for all three coated samples. Moreover, the order of M_S1 is M_S1(C12) > M_S1(S12) > M_S1(SO12), which matches the order of \left|P_0(C)\right|>\left|P_0(S)\right|>\left|P_0(SO)\right|. As discussed earlier, the anchoring groups alter the surface magnetic moment of Fe₃O₄ nanoparticles via p−d orbital hybridization and charge transfer, consequently leading to a change in the intrinsic spin polarization of Fe₃O₄. Because most electrons participating in tunneling transport originate from the particle surface, the surface magnetic moment plays a dominant role in spin transport.

Additionally, orbital hybridization at the Fe₃O₄/molecule interface also influences the spin injection. As evidenced by the ICOHP and PDOS results in Fig. 6, for the spin-up channel, a clear energy gap between the bonding and anti-bonding states is observed across all samples, effectively acting as an additional tunneling barrier. In contrast, the ICOHP values in the spin-down channel are close to zero, specifically −0.62 for −SO₃H, −0.60 for −OSO₃H, and −0.38 for −COOH, indicating weak Fe-O interactions. Meanwhile, for the ICOHP of Fe-O in the spin-down channel, the anti-bonding states are occupied by electrons below the Fermi level, thus it providing a preferential tunneling pathway for spin-down carrier, this is applicable to all samples.

As illustrated in Fig. 8(a), for n = 4, |MR(C4)| > |MR(S4)| > |MR(SO4)|. With increasing molecular length (d), the MR–T curve of S(Sn) gradually approached that of S(SOn) [Figs. 8(b) and (c)], whereas the difference between these two curves and that of S(Cn) became increasingly pronounced. At n = 16, the MR curves of S(S16) and S(SO16) nearly overlapped [Fig. 8(d)], differing by approximately 1.3% from S(C18). These observations indicated that MR decayed with d at different rates across the three categories sample, implying that their spin diffusion lengths (λ) differed.

Figure 8(f) shows λ as a function of temperature (T) in the range 150–300 K. Interestingly, λ is T-independent, indicating that the decrease in MR with T was not caused by intramolecular spin relaxation. A similar T-independent λ was reported by Jiang et al. [46], who studied exchange interaction-dominated spin current transport through Alq₃ molecules in Y₃Fe₅O₁₂/Alq₃/Pd heterostructures. At 5.5 kOe, the intramolecular spin diffusion lengths for sulfonic acid, sulfuric acid, and carboxylic acid were λ_S = 12.8 ± 0.8 nm, λ_SO = 18.1 ± 0.7 nm, and λ_C = 41.5 ± 1.3 nm, respectively. These results demonstrate that −COOH provides superior spin injection efficiency and transport properties at the Fe₃O₄/molecule interface compared with other anchoring groups.

Therefore, we examined whether the T-independent properties of λ persisted under different magnetic fields. Figures 9(a), (b), and (c) list the λ–T curves of sulfonic acid, sulfuric acid, and carboxylic acid samples at different magnetic fields, respectively. Notably, λ remained essentially T-independent across all measured fields, indicating that phonon scattering exerted a negligible influence on spin relaxation during tunneling transport. This behavior contrasted sharply with temperature-dependent spin relaxation mechanisms observed in carrier hopping [47], where spin relaxation was predominantly governed by spin–orbit coupling (SOC) [26] or hyperfine interactions (HFI) [48]. Due to the T-dependent hopping rate, the spin diffusion length in the HFI-dominated spin relaxation increase with T. For SOC-dominated hopping transport, λ decreases with increasing T. Therefore, the disparate T-dependences between SOC- and HFI-induced spin relaxation allow an experimental determination of spin relaxation mechanisms in individual organic solids. However, in our study, it was the intramolecular tunneling between Fe₃O₄ particles that was nearly T-independent; thus, spin relaxation caused by SOC or HFI was similarly unaffected by temperature. Although the electron density near the fermi level of Fe₃O₄ increased with T, this primarily influenced the number of carriers participating in tunneling [49], rather than the barrier height, width, or tunneling probability.

We further investigated the effect of applied magnetic fields (H) on spin relaxation in organic molecules. As shown in Fig. 10, λ_S and λ_SO increased monotonically with H in the range of 200–300 K. Specifically, λs increased by 1.2–3.2 nm, whereas λ_SO increased by 1.9–2.4 nm. Then whether this change related to a non-intrinsic effect associated with differences in magnetic interactions between adjacent Fe₃O₄ particles? Specifically, to stabilize the system, the magnetic moments of adjacent Fe₃O₄ particles tend to be antiparallel, exhibiting a certain degree of anti-ferromagnetism. Compared to S(S16), S(S4) exhibits stronger inter-particle magnetic interactions and a more significant resistivity increase due to its shorter molecule length. When a magnetic field was applied, the magnetic moments gradually aligned with the field direction, increasing |ρ(H)−ρ(0)| and consequently enhancing MR in the absence of interparticle magnetic interactions. Then, as d increased and the distance between adjacent Fe₃O₄ nanoparticles grew, both the magnetic interaction and the resistivity ρ(0) changed — the former decayed, and the latter increased — thereby reducing the net contribution to |ρ(H)−ρ(0)|. Thus, long-chain molecular samples exhibited smaller MR changes than short-chain counterparts, leading to shorter λ. With increasing H, |ρ(H)−ρ(0)| continued to grow, whereas the contribution from magnetic interactions to |ρ(H)−ρ(0)| and MR became progressively weaker; thus, λ obtained from MR–d fitting increased with H.

However, Rackham et al. [50] reported magnetic ordering of nanospins in the system of oleic acid-coated 11 nm Fe₃O₄ particles. The concentrations ferromagnetism and magnetic random nanospins exceed that of anti-ferromagnetism. When H > 1000 Oe, the antiferromagnetic concentration of nanospins tends to saturate and remains constant; similarly, the concentration of ferromagnetic and random nanospins also essentially saturates at ~3000 Oe [50]. Physically, this magnetic interaction defines a finite energy scale for spin alignment; once the external magnetic field overcomes this energy and stabilizes the interparticle magnetic configurations, the non-intrinsic spin scattering arising from magnetic mismatch should reach a limit. For instance, based on the derived magnetic moment μ of per Fe₃O₄ nanoparticle from Table 2 and considering the molecular length d of S12, the estimated interparticle magnetic interaction energy E_dip~μ²/r³ for S(S12) is approximately 1.47×10⁻²¹ J at 300 K. This energy corresponds to an effective magnetic field of ~91.8 Oe, which is ~0.35 times the thermal energy (k_BT) and considerably lower than the Zeeman energy (E_zee~μH=1.60×10⁻²⁰ J) of Fe₃O₄ particles at 1000 Oe. Therefore, the magnetic interaction is likely more than 10 times lower than the Zeeman energy. If our observed λ−H is solely governed by the magnetic dipole interactions, then its curve should likewise plateau alongside the magnetic ordering. Instead, λ increases continuously up to 5500 Oe (Fig. 10), diverging significantly from the saturation of antiferromagnetic and ferromagnetic concentration. Moreover, magnetic interactions are T-dependent, which contradicts the T-independent λ (Fig. 9).

During tunneling transport, external magnetic field-induced energy splitting occurs between the spin-up and spin-down electrons — known as the Zeeman effect. The induced energy difference (ΔE = μ_BgH) could suppress the spin-flip scattering caused by SOC during tunneling. With increasing H, ΔE increases, further lowering the spin-flip probability and resulting in an increased λ despite the presence of thermal disturbances. Such thermal disturbances mainly affect the magnetic order on the surface of the Fe₃O₄ particles rather than affecting the spin relaxation during tunneling, as tunneling is temperature-independent, which is demonstrated by the results shown in Fig. 9. Therefore, this result strongly suggests that the Zeeman effect serves as the principal mechanism for the variation of λ with H [Figs. 10(a1)–(a5) and Figs. 10(b1)–(b5)]. However, this trend is not observed in the carboxylic acid molecules [Figs. 10(c1)–(c5)]. In this case, λ does not show a distinct monotonic dependence on H. This is likely because the carriers experience weaker SOC during tunneling through these molecules—as evidenced by the significantly higher λ and discussed further below—resulting in an extremely low probability of spin flipping. Consequently, the influence of the magnetic field on λ is not significant, and distinguishing it within the experimental error range is challenging.

Most importantly, the magnetic field modulated λ within a range of 1–3 nm, which was smaller than the minimum difference of ~ 6 nm between any two of the three sample categories. Consequently, the relationship λ_C >λ_SO >λ_S still existed, with λ_C/λ_S ≈ 3.2 and λ_C/λ_SO ~ 2.3, indicating that replacing the carbon-centered anchoring group (−COOH) with sulfur-centered groups (−SO₃H, −OSO₃H) enhanced intramolecular spin relaxation during tunneling. In organic semiconductors, SOC or HFI is the primary cause of spin relaxation [51]. For molecules studied in this work, HFI was primarily governed by atoms with half-integer spins, such as H atoms. In all three molecular categories, the H atoms were located along the alkyl chains, and their numbers were comparable. The effective magnetic field generated by HFI was estimated to be on the order of tens of Oe — two orders of magnitude smaller than the applied magnetic field (typically several kOe) — and thus could not account for a more than threefold difference in spin diffusion length. Moreover, HFI became increasingly suppressed at higher magnetic fields [48], confirming that it was not the primary cause of spin relaxation.

SOC is a critical factor governing spin relaxation in molecules and is influenced by different parameters such as atomic number (Z) [52], molecular structure [11], and other intrinsic properties. In organic molecules, the SOC strength typically scales with the fourth power of the atomic number (Z⁴) [53]. For the molecules examined in this study, differences in the central atoms of the anchoring groups could affect SOC, potentially explaining the trend λ_C> λ_S. However, the λ_C/λ_S ratio (~3.2) deviates substantially from the theoretical Z⁴(S)/Z⁴(C) ratio, and the fact that λ_SO> λ_S indicated that inserting oxygen atoms into the anchoring group (−SO₃H) increased λ. This finding suggests that, beyond heavy-atom-induced SOC, additional mechanisms influence spin relaxation, possibly related to SOC arising from intrinsic molecular dipole moments. We investigated the correlation between λ and molecular dipole moment across the three sample categories, as shown in Fig. 11, and found that smaller dipole moments corresponded to larger λ values. This behavior was likely attributed to the intrinsic dipole moment generating non-uniform local electric fields within the molecule, which disrupted the system’s structural inversion symmetry and modulated SOC during tunneling. A larger dipole moment probably produces a steeper electric field gradient, enhancing the SOC effect [54], increasing spin scattering, and thereby reducing the spin diffusion length [55, 56]. Additionally, dipole moments could also alter the SOC strength by modifying the intramolecular charge distribution. As mentioned earlier, chemical adsorption induces charge transfer at the Fe₃O₄/molecule interface, where electrons are transferred from Fe₃O₄ to the adsorbed molecules (Part 4 of the Supplementary Materials). This process leads to a high electron density around the oxygen atoms, resulting in the formation of localized charge centers. Such an inhomogeneous charge distribution enhances the intramolecular local electric-field gradient, thereby influencing the SOC. Further studies are necessary to fully elucidate the detailed spin relaxation mechanisms during tunneling.

4 Conclusions

In summary, we fabricated Fe₃O₄/carboxylic acid, Fe₃O₄/sulfonic acid, and Fe₃O₄/sulfuric acid hybrid nanoparticles to experimentally and theoretically investigate the effects of anchoring atoms (S and C) on spin transport at the Fe₃O₄/molecule interface, spin relaxation, and the underlying physical mechanisms. Electrical transport measurements revealed that the contact resistivity at the Fe₃O₄/molecule interface was highly sensitive to the anchoring groups, following the trend ρ_c(−COOH) > ρ_c(−OSO₃H) > ρ_c(−SO₃H). The theoretical calculations indicated that this behavior was primarily determined by the coupling strength between Fe₃O₄ and the molecules. Magneto-transport results further demonstrated that replacing the carbon-centered anchoring group (−COOH) with sulfur-centered groups (−SO₃H, −OSO₃H) reduced the magnetoresistance and decreased the spin diffusion length (λ) by approximately 69%. DFT calculations were performed to clarify the role of orbital hybridization in tuning the interfacial magnetic properties and spin transport. An analysis of λ using the Jullière model allowed us to examine its dependence on magnetic field and temperature, revealing that the temperature-independent behavior of λ originated from tunneling transport, while its field-dependent behavior stemmed from the Zeeman effect. Our findings strongly suggest that the SOC induced by the dipole moments of the molecules is the dominant factor governing the observed variations in spin relaxation during tunneling. This work provides the first experimental verification of spin scattering within an organic molecule during tunneling and demonstrates the feasibility of controlling spin injection and transport by altering the central atom of the anchoring group, offering new strategies for actively tuning spin transport at ferromagnet/molecule interfaces on the molecular scale.

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