Giant spin signals in chemically functionalized multiwall carbon nanotubes

Electronic impact of the chemical functionalization of the outershell of the MWCNT

In this work, nitrobenzene (NB) diazonium (NBD) molecules, one of the simplest diazonium compound, are used to functionalize the surface of large-diameter (>60 nm) MWCNTs. The experimental details of the chemical functionalization are fully described and presented in Materials and Methods and also in (34). Upon functionalization, the NBD molecule loses its N₂ tail to form a highly reactive NB radical, as depicted in fig. S1C. As revealed by a representative high-resolution transmission electron microscopy image presented in Fig. 1A, the NB radicals are only reacting with the outershell of the MWCNT in the experimental conditions. This peculiar reactivity was also previously demonstrated for double-wall CNTs (DWCNTs) (37). To get a better overall view, the expected functionalization is also schematized in Fig. 1B for the case of a small-diameter DWCNT for clarity reason. The estimated grafting surface density is in the range of 10⁻¹⁰ to 10⁻⁹ mol cm⁻² (38). The systems illustrated in Fig. 1D are therefore representative of the experimental molecular surface density. To understand the impact of the chemical functionalization on the electronic properties of MWCNTs, we performed first-principles calculations using ab initio density functional theory (DFT; see Materials and Methods for technical details). Although H-saturated NB does not exhibit any magnetic moment (see fig. S1B), its radical develops a magnetic moment of 1 bohr magneton (μ_B) with ~93% located on the dangling bond (see fig. S1C). This radical moiety can be stabilized by the formation of dimers in the solution, or it can react and can be grafted onto the outershell of the large-diameter MWCNT, the latter being modeled by a graphene monolayer in the DFT calculations as shown in Fig. 1 (C and D). At the end of this functionalization process, the NB molecule is stabilized over the MWCNT outershell forming a saturated chemical bond with a C atom from the outershell.

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As a physical consequence, upon functionalization, each affected C atom of the outershell of the MWCNT modifies its electronic configuration from a conducting sp² to an insulating sp³ hybridization, which should render the outershell of the MWCNT quite insulating. Pristine graphene is nonmagnetic (as calculated in fig. S1D), but upon functionalization by one NB molecule on a given sublattice, the system could acquire a net magnetic moment (see Fig. 1C) (39). In contrast to physisorption where the magnetic moment stays fully localized on the π-π stacked molecule (see fig. S1F), in the case of NB chemisorption, the magnetic moment is well transferred into graphene, though slightly reduced to 0.96 μ_B (see Fig. 1C). As illustrated in Fig. 1C, two spin-split almost-flat bands are located close to the Fermi level in a range of ~200 meV with ideal spin polarization P passing from −100% to +100%. However, as this magnetization propagates into graphene from a given NB molecule, it is important to check how it will interact with the nearest-neighbor molecule. As demonstrated in literature, for instance, in case of hydrogen (40, 41), the choice of the sublattice as anchoring site and the distance between two grafted molecules is a key parameter for determining these interactions. As expected, when restoring the balance between the two sublattices, the magnetic moment vanishes as observed in Fig. 1D for the case of two NB molecules on sublattice “A” and two others on sublattice “B” (see also fig. S2). Experimentally, as the density of anchoring A and B sites for NB molecules in the outershell of the MWCNT is identical and that NB radicals react randomly with both sites during the functionalization process (34, 37, 42), a globally vanishing total magnetic moment is expected. Residual but very localized paramagnetic states cannot be fully excluded, but no proof of their existence is directly measured in this study. Also, the influence of those residual magnetic moments on the spin transport is not described here in this article. As discussed below, the spin signal transport is believed to occur mostly in the next inner shells free of functionalization for which the impact of those hypothetical paramagnetic states should thus be anyway limited. Last, this optimized functionalization process has also been experimentally demonstrated in a previous study (34) to increase the injection resistance above the 10⁶ ohm range within the ideal window for an efficient spin injection in MWCNTs (20) and SiC graphene (12).

Spin transport measurements at cryogenic temperatures

The experimental details related to both the nanofabrication procedures and the magnetotransport measurements can be found in Materials and Methods. Two samples named A and B are presented in the following. Sample A is fabricated with Ni contacts, and sample B is fabricated with Co contacts. Those two FM metals were chosen to probe different interfacial spin polarization and coupling with the molecules as widely studied before (36, 43). The selective switching of their magnetizations is obtained by tuning the shape anisotropy with different electrode widths (500 and 200 nm). Because the length of the large-diameter MWCNTs is quite limited (few micrometers), the electrode separation is 900 nm for sample A and 800 nm for sample B.

Figure 2A depicts a schematic of the magnetoresistive devices studied here supported by a scanning electron microscopy image of sample B shown in Fig. 2B. The local MR signal defined as MR=RAP−RPRP=IP−IAPIAP measured at cryogenic temperatures and at −140 mV in sample A between two nickel (Ni) electrodes is plotted in Fig. 2C. R_AP is the electrical resistance measured in the antiparallel configuration of the magnetizations, and R_P is the resistance measured at H = 0 T in the parallel configuration of the magnetizations. The low-temperature resistance reaches 10⁹ to 10¹⁰ ohms for this first sample. It is only due to the presence of the molecular injection barrier as demonstrated in (34). The blue (black) dots are measured while sweeping the magnetic field toward positive (negative) values. This measurement exhibits important variations of the device’s MR including negative values going at maximum down to −40%. This negative sign of the MR might be unexpected as both interfaces are supposed to be the same, but it will be explained in the next part. It also reveals some interesting magnetoresistive features that can be identified and classified into three categories. First, a progressive decrease of the resistance at high magnetic fields (> 50 mT) is reported. This high-field MR has already been observed in MWCNTs in the case of applied transverse magnetic fields and was attributed to weak localization effects (44). In fig. S3, a high-field MR plot up to 1 T is also shown, in perfect agreement with those reported in (44). Second, the two regions with very large and sharp variations of resistances around ±40 mT display similar amplitudes and, respectively, appear at positive (negative) magnetic field when the magnetic field is swept toward positive (negative) values. This behavior is typically the signature of spin transport in a spin-valve configuration (20). It allows us to identify the coercive fields corresponding to both electrodes. The largest coercive field is attributed to the narrowest magnetic electrode. The lowest state of resistance located in between −40 and −50 mT corresponds to the antiparallel configurations of the magnetizations (represented by yellow arrows in Fig. 2C). Last, weak positive MR (<5%) can be observed at low magnetic field (|H| < 30 mT). In opposition to the spin-valve effect, this magnetoresistive effect persists and could even reverse its sign when the magnetic field is rotated away from the electrodes’ magnetization easy axis (see the angular dependence presented in fig. S5). The results presented in fig. S5 strongly indicate a tunneling anisotropic MR (TAMR) effect associated to the FM electrode/molecule interfaces (45, 46). TAMR effects of similar intensity have previously been reported also at polycrystalline FM metal/molecule interfaces (45, 47, 48). Strongly supported by the angular dependence, all those arguments combined together demonstrate that the magnetoresistive effect of −40% can be unambiguously attributed to spin transport through the device. Those spin-dependent transport effects have also been reproduced in a second sample named sample B with cobalt (Co) electrodes, revealing the robust nature of the MR (see fig. S6). The local MR measurements reported in fig. S6C also present important MR effects down to −20%. The low-temperature resistance reaches 10⁷ ohms for this second sample. However, the coercive fields are less defined, in particular for the sweep toward the negative values of the magnetic field. It is possible to identify in fig. S6C two regions corresponding to an antiparallel configuration of the magnetizations, which again indicate spin transport between the two magnetic electrodes.

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The identification of the parallel and antiparallel configurations of the magnetization allows the proper use of the MR formula MR=IP−IAPIAP (49) to determine the dependence of the MR as a function of the applied bias voltage. The two I-V and G-V characteristics measured in the parallel and antiparallel states of the magnetizations are shown in figs. S4 and S6A for samples A and B, respectively. The bias voltage dependence is reported in Fig. 2D and fig. S6B for samples A and B, respectively. Different MR characteristics for sample A are also shown in fig. S7 (A to C) for V = −120 mV (0%), −200 mV (−20%), and −130 mV (−12%), respectively. The extracted bias dependence of the MR (dark gray dots) is found to be in excellent agreement with the values of MR extracted from the direct measurements of MR characteristics (red dots in Fig. 2D). In both samples, a strong dependence of the MR is observed with respect to the applied bias voltage. In opposition to what is typically presented in the literature for MWCNTs or even standard magnetic tunnel junctions (20, 50), the maximum values of the MR do not appear close to zero bias but rather around specific values of energy [−140 mV for sample A (Ni contacts) and +130 mV for sample B (Co contacts)]. A change of sign of the MR is even measured in sample B. No evidence of gate voltage dependence is reported, as illustrated in fig. S8, for a bare large-diameter MWCNT excluding coulomb blockade effects, as expected due to the metallic nature of these multiwall tubes.

Spin-polarized calculations of interfaces and MR calculations

To better understand the spin injection at the magnetic electrode/functionalized MWCNT interface, we incorporate a Ni (100) slab composed of three atomic layers in the simulation cell above the NB molecules grafted on graphene. Similarly to the situation in Fig. 1D where sublattices were balanced resulting in no magnetic moment in the graphene layer, the case of two NB molecules grafted on each graphene sublattices is considered here (see Fig. 3B). Both the magnetic moment and spin polarization per atomic layer are computed as presented in Fig. 3 (A and B). It is important to note that those results should be considered from a qualitative point of view as they may fluctuate according to computational methods and atomic details of the interface. For instance, in Fig. 3B, the magnetic moment per Ni atom is ~0.88 μ_B in the outer layer and ~0.69 μ_B in the inner layer of the slab. This should be compared to the value of 0.75 μ_B per atom in bulk (see fig. S1A). The specific choice of an ideal Ni (100) surface will eventually not have a strong influence on the simulation of the MR as the key parameter to induce rapid variations around Fermi level of the spin polarization, including sign change, is brought by the spin-dependent local hybridization of the NB molecular orbitals (51). The hybridization of the molecules with the Ni surface induces a spin-dependent shift and broadening of its molecular orbitals (36, 52). Note that in contrast to Fig. 1D, the oxygen atoms of the NB molecules acquire local positive magnetic moment due to the hybridization effects with the Ni surface. As shown in Fig. 3A, the calculated band structures and density of states projected onto each atomic layers allow us to access the energy-resolved spin polarization per atomic layers, labeled from [1] to [6], of the Ni/molecule/outershell of the MWCNT interface. In particular, one observes that the last layer (i.e., layer [6], which corresponds to graphene and is represented by green lines in Fig. 3A) is almost unpolarized over the entire energy window considered here. At the Fermi level, the Ni outer layer has a spin polarization of about −67%. The NO₂ head and the C₆H₄ body of the NB molecules are here analyzed separately (layers [4, 5]) as the coupling with the Ni surface is mainly located in the NO₂ head of the molecule. Both have a similar spin polarization energy profile, although the NB body does not display a substantial magnetic moment. The decay of the spin-dependent hybridization away from the surface was also previously reported (53–55). From this analysis, the last spin-polarized layer is considered to be layer [5], i.e., the body of the NB molecule, except at Fermi level where the spin polarization is vanishing and where the last spin polarized layer is hence the last nickel layer, i.e., layer [3]. The FM electrode plays two major roles highlighted by those calculations. First, it induces a strong spin polarization incoming from the FM metal/molecule interface due to hybridization. Second, it also magnetically couples to spin states to the FM electrode, creating a new effective magnetic electrode with rapidly varying spin polarization around Fermi level including sign change. With the interfacial energy dependence of the spin polarizations discussed above and presented in Fig. 3A, the magnetoresistive signal can be numerically estimated. The formula developed by Seneor et al. [equation 3 in (12)] is used here, though slightly modified. To account for the potential difference across the two electrodes when applying bias voltages, the injection/detection polarizations have to be energy dependentMR=γL(VL)γR(VR)(1−γL(VL)γR(VR)) 22 cosh(Llsf(Vb))+(RbRchs(Vb)+Rchs(Vb)Rb)sinh(Llsf(Vb))(1)where γ_L/R and V_L/R are the spin polarization and bias voltage at the left/right contact interface (V_b = V_R − V_L, and here as the left contact is at the ground, V_L is set to zero, i.e., to the Fermi level in the calculation), L is the device length, R_b is the contact barrier, Rchs is the spin resistance of the channel, and l_sf is the spin diffusion length. The device length L and the contact resistance Rb=Rdevice2 are parameters taken from the experimental measurements, assuming that both interfaces are equivalent in terms of resistance, while spin polarization γ_L/R has been computed in Fig. 3A. Last, Rchs and l_sf can be estimated using a transport model presented in Materials and Methods and the corresponding calculations in fig. S9. The MR as expressed by Eq. 1 is composed of a product of two terms. On the one hand, the first term depends on the interface polarizations, and its value can evolve from [−0.5:+∞]. On the other hand, the second term depends on interface barrier resistance and device’s properties, and its value belongs to the range [0:1]. In case of really long spin lifetime, l_sf becomes very large compared to L such that in Eq. 1, the hyperbolic cosine and sine functions tend to 1 and 0, respectively, which yields the second term to be maximal, i.e., 1, and offers an optimal transport regime for the MR, which reduces to the first term onlyMRideal channel=γL(VL)γR(VR)(1−γL(VL)γR(VR))(2)

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It is clear from this formula that the MR can become negative only if γ_L and γ_R have opposite signs and are at maximum −50% when left and right spin polarizations reach exactly −100% and +100%, respectively. Concerning the experimentally reported negative sign of the MR, it can thus be only well explained by a change of sign in spin polarization such as the one obtained in Fig. 3A. Because of the applied bias voltage, the sign of injected spin polarization might be opposite to the interfacial spin polarization for the detection, thus leading to negative MR. It is, for instance, the case in the [−0.3; 0.0] V bias window and, to some extent, in the [+0.1;+0.3] V bias window, as visible in Fig. 3A. The fact that the experimental MR signal reaches −40% and so indicates, first, that the system is in a regime where the distance between two spin flip events is very long compared to the device length and, second, that both left and right polarizations are close to 100% but with opposite signs. Actually, in case of perfect spin polarizations (γ_L = −100% and γ_R = +100%), the first term of Eq. 1 equals −1/2, and the MR formula reduces toMRideal spin polarizations=−12 22 cosh(Llsf)+(RbRchs+RchsRb)sinh(Llsf)(3)for which Rchs and l_sf can be taken as fully free parameters to produce a dimensionless three-dimensional (3D) color plot (see Fig. 3C), which can be useful to analyze parameter regions where MR can be highly negative. Consequently, even in case of perfect polarizations, Eq. 3 suggests that to obtain MR values such as [−50; −40]% (yellow, red color), l_sf needs to be at least 10 times larger than L ideally when Rchs≈Rb [as discussed in (28)] but should be actually 10⁴ times larger than L when RchsRb≈ 10⁻⁴ or 10⁴. As reported in Eq. 4 presented in Materials and Methods, Rchs and l_sf are actually not free parameters but interdependent variables and related to parameters τ_e and τ_sf, the charge and spin mean scattering times, respectively. Moreover, in the present situation, the contact resistance R_b is very high because of the presence of the NB molecular layer at the interface (34), as shown in the left-hand side of Fig. 3C.

As mentioned above, it is possible using Eq. 1 to numerically evaluate the MR signal using the DFT calculated interface polarizations together with a transport model based on tight-binding simulations and on two freely adjustable parameters τ_e and τ_sf. We performed such numerical estimation of the MR [see Fig. 4 and the dotted lines on top of the 3D colored plot in Fig. 3 (C and D) corresponding to a specific bias voltage of −0.15 V] using four values of charge scattering time, i.e., τ_e=80 fs, 800 fs, 8 ps, and 80 ps, and, for each of them, four values of spin scattering time, i.e., τ_sf = 10, 10², 10³, and 10⁴ times the value of τ_e. The sets of two free parameters that give the largest negative MR are τ_e = 80 ps and τ_sf = 10⁴ τ_e= 800 ns. The corresponding simulated MR curve is presented in Fig. 4 (blue line) together with the experimental data of sample A with Ni electrodes. As mentioned earlier, the corresponding transport properties of the model are displayed in fig. S9, including the bias-dependent mean free path and spin diffusion length (l_e and l_sf), which are found in the range [26 to 42] μm and [4 to 6] mm, respectively. The estimated spin lifetime τ_sf is thus one order of magnitude higher compared with the recent reported values measured for encapsulated graphene (56). Such extremely long spin diffusion lengths could be interpreted as follows: The spin-polarized electrons are transferred from the FM electrode to the inner shells of the MWCNT passing through an efficient spin filtering FM electrode/NB-functionalized outershell interface. Once in the inner shells, the charges and spins are protected and conveniently transported toward the second magnetic electrode, where the spin information is electrically converted because of a magnetoresistive effect. The fact that the spin polarization is rendered bias voltage dependent with such a rapidly varying sign around the Fermi level due to the NB molecule allows us to interpret the change of sign of the measured MR with respect to the applied bias voltage. The simulations performed predict a change of sign for bias voltage windows ~[−300; 0] mV and ~[+100; +300] mV in line with the measurements. One shall also mention that we voluntarily limit ourselves in the values of the free adjustable parameters τ_e and τ_sf (at maximum 80 ps and 800 ns, respectively), which limits the numerical MR to −15% when using DFT-computed polarizations (see blue line in Fig. 4) and up to −30% if one uses ideal polarizations of −100% and 100% as in Eq. 3 (see orange line in Fig. 4). To complete this analysis of the model, we also plot the numerical MR estimated using DFT polarizations but with ideal channel as in Eq. 2 (see purple line in Fig. 4). Obviously, with ideal polarizations and ideal channel, a negative MR of −50% would be obtained for all bias voltages. The analysis provided in Fig. 4 demonstrates that numerical MR strongly depends on interface spin polarization, which, in turn, strongly depends on the precise molecular interaction with the FM surface. Figure S10 illustrates this dependence of the MR on the Ni/NB molecule interaction through an analysis of the spin polarization energy profile and the corresponding MR for each NB molecule individually. For instance, taking only molecules in sublattice A yields a numerical MR almost solely positive (see the blue line with square symbols in fig. S10D). Although the atomic positions of the atoms were relaxed, the starting position was randomly chosen, and one cannot exclude other Ni/NB molecule interface scenarios not investigated here, which could enhance the injection/detection spin polarization. Local A and B sublattice unbalance could also occur a priori in rare cases, yielding possibly to local polarization of the outershell layer as depicted in fig. S11. For the sake of completeness, the case of a direct Ni/graphene interface is also investigated in fig. S13. Again, this scenario should be nondominant, as the molecular covering is sufficiently high such that Ni atoms are normally not in direct contact with the outershell of the MWCNT. As in fig. S11, the graphene layer becomes the last polarized layer due to a small magnetic moment induced in graphene by proximity effect. Nevertheless, no negative MR is reported in the bias windows of interest. The transport properties and the MR equation are obtained from models that have their own limitations concerning absolute values, which prompt us to use not too optimistic values τ_e and τ_sf, although the very generic forms of the models still allow us to demonstrate that spin lifetime should, in any case, be extremely long to reach an MR effect of −40%.

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Last, concerning the temperature dependence of the MR effect, it vanishes rapidly around 30 K as observed in sample A (see fig. S12). It is a quite rapid extinction of the MR even if not completely different compared to more standard MWCNT-based spin-valves (20, 29) or with organic magnetic junctions (36, 57) for which MR effects can subsist at slightly higher temperatures. Because of the high curie temperature of the Co and Ni electrodes, the loss of magnetization is unexpected. Concerning the hybridization and the induced magnetic coupling of the hybridized spin states with the FM surface, it is also expected to survive up to room temperature (58). A temperature-activated spin scattering mechanism during the transport along the inner shells of the MWCNT could be invoked. The physical origin of the strong influence of the temperature in those systems remains an open question. Only the positive part assigned to the TAMR signal remains at 30 K, thus strongly reinforcing the given interpretation of two distinct MR components (TAMR and spin-valve) originating from different phenomena.