Role of Metal Lattice Expansion and Molecular π-Conjugation for the Magnetic Hardening at Cu-Organics Interfaces.

Magnetic hardening and generation of room-temperature ferromagnetism at the interface between originally nonmagnetic transition metals and π-conjugated organics is understood to be promoted by interplay between interfacial charge transfer and relaxation-induced distortion of the metal lattice. The relative importance of the two contributions for magnetic hardening of the metal remains unquantified. Here, we disentangle their role via density functional theory simulation of several models of interfaces between Cu and polymers of different steric hindrance, π-conjugation, and electron-accepting properties: polyethylene, polyacetylene, polyethylene terephthalate, and polyurethane. In the absence of charge transfer, expansion and compression of the Cu face-centered cubic lattice is computed to lead to magnetic hardening and softening, respectively. Contrary to expectations based on the extent of π-conjugation on the organic and resulting charge transfer, the computed magnetic hardening is largest for Cu interfaced with polyethylene and smallest for the Cu-polyacetylene systems as a result of a differently favorable rehybridization leading to different enhancement of exchange interactions and density of states at the Fermi level. It thus transpires that neither the presence of molecular π-conjugation nor substantial charge transfer may be strictly needed for magnetic hardening of Cu-substrates, widening the range of organics of potential interest for enhancement of emergent magnetism at metal-organic interfaces.

Introduction

Electronic hybridization at the interface between metal substrates and organic materials and the ensuing emergence of electronic states and pron class="Chemical">perties different from the interface constituents has long attracted the interest of the scientific community.[1−6] Understanding hybridization at metal–organic interfaces holds the key to controlling and fine tuning the emerging electronic and spin properties (injection, storage, and transfer) with potential benefits for the miniaturization and energy efficiency of sensing, information storage, and classical or quantum computing.[1−24]

As recently observed, hybridization between a n class="Chemical">metal substrate and an organic material can be used also to promote magnetism and ferromagnetic ordering between originally nonmagnetic components.[25−32] The phenomenon is appealing because control and enhancement of emergent magnetism between cheap and nontoxic materials such as light transition metals and organic semiconductors may provide more eco-friendly and sustainable alternatives to conventional magnetic materials and devices.[30−32]

Following earlier generation of molecular-localized magnetism in originally diamagnetic molen class="Chemical">cular adlayer adsorbed on diamagnetic substrates,[25−29] recent experimental characterization of the interfaces between paramagnetic (Sc, Mn, Pt) or diamagnetic (Cu) transition-metal layers and differently π-conjugated organic substrates (fullerene C60 and amorphous carbon, aC, films of different density) has provided evidence of a second type of emergent magnetism with room-temperature ferromagnetic ordering being mostly localized either on the metal substrate[30] or at the intimate metal–organic interface.[31] The compelling experimental evidence on the emergence of ferromagnetic ordering has been complemented by density functional theory (DFT) modeling of some of the interfaces considered. The available DFT modeling points to both charge transfer between the metal and the organics and interface-relaxation-induced distortions at the metal substrates as the two key drivers for the magnetic hardening of the metal substrate and consequent emergence of magnetic ordering.[31] To date, the relative importance of charge transfer between the metal and the (π-conjugated) organic and distortion of the metal lattice for the emergence of interfacial magnetic ordering remains unquantified with the immediate consequence of interfaces between metal and non-π-conjugated molecules having being overlooked in recent investigations of emergent magnetism.[30−32]

However, recent spin-resolved photoemission sn class="Chemical">pectroscopy measurements on a linear alkane, pentacontane C50H102, on Co(001) have unambiguously shown that π-conjugation on the organic is not necessary for emergence of strongly spin-polarized interface states between ferromagnetic metals such as Co and an adsorbed organic molecule or layer.[20] These results inevitably raise the question as to whether π-conjugation is actually necessary (or not) also for the magnetic hardening and emergence of magnetism at the interface between originally nonmagnetic transition metals and molecular systems.

To answer this question, in this work we disentangle the role of metal distortion, n class="Chemical">metal–organics charge transfer, and organic π-conjugation for the magnetic hardening at metal–organic interfaces. Specifically, we screen via DFT the electronic and magnetic properties of several models of interfaces between Cu (known to originate ferromagnetic ordering when contacted with C60 and aC films[30,31]) and four polymeric systems of different steric hindrance, π-conjugation, and electron-accepting properties, disentangling the relative importance and interplay between these factors and the resultant interface magnetic hardening or softening.

Methods

Computational Details

Following refs (30 and 31), standard and fixed spin moment,[33] van der Waals (vdW) corrected,[34] density functional theory (DFT) simulations were exen class="Chemical">cuted via the projected augmented wave (PAW) method as implemented in the VASP program[35] with the PBE exchange-correlation (XC) functional,[36] a 400 eV plane-wave energy cutoff, and (0.2 eV, first order) Methfessel–Paxton electronic smearing.[37] The grids for k-point sampling were defined on the basis of convergence tests on the magnetic properties of bulk Cu in the face-centered cubic (FCC) structure (see Figure S1 in the Supporting Information) and scaled according to the size of the reciprocal lattice of the system under consideration. The atomic-force threshold for geometry optimization was 0.02 eV Å–1. All atoms in the Cu slabs and in the polymers were fully relaxed in all directions. A vacuum separation of at least 15 Å was present between replicated images of the 5-layer Cu(111) slab models for the in-plane interface models (Figure ). Bader charge analyses[38] were computed on the total charge density, i.e., accounting for both the electronic and the ionic core charges.

Figure 1

Monomer atomic structure for the polymers considered: (a) polyethylene (PE), (b) polyacetylene (PAC), (c) polyethylene terephthalate (PET), and (d) polyurethane (PUR). Schematic representation of the two interface models used: (e) in-plane (∥) geometry with the polymer chain inserted parallel to the Cu(111) plane and (f) perpendicular (⊥) geometry with the polymer chain inserted perpendicular to the Cu(111) plane.

Monomer atomic structure for the polymers considered: (a) n class="Chemical">polyethylene (PE), (b) polyacetylene (PAC), (c) polyethylene terephthalate (PET), and (d) polyurethane (PUR). Schematic representation of the two interface models used: (e) in-plane (∥) geometry with the polymer chain inserted parallel to the Cu(111) plane and (f) perpendicular (⊥) geometry with the polymer chain inserted perpendicular to the Cu(111) plane.

Due to the computed nonmagnetic ground state for all models studied, atom-resolved approximations to the Stoner exchange integral (IS) were calculated by enforcing a magnetic moment of 0.1 μB/n class="Chemical">Cu-atom via fixed spin moment DFT.[33] Following refs (39) and (30 and 31) and owing to the weak wave-vector (k) dependence of the energy difference between spin-up and spin-down bands (band splitting, ΔE),[39] atom-resolved values of IS were computed from the (PAW-core-projected) ΔE values integrated over the Brillouin zone and the (PAW-core-projected) atomic magnetic moment (m) asOwing to the dependence of ΔE on the energy of the Kohn–Sham states,[39] the error for the computed IS was quantified by calculating the standard deviation between the ΔE values at the stationary points (maxima and minima) of the PAW-core projected PDOS in the energy interval between the Fermi energy (E) and EF – 3 eV. This interval was chosen following numerical tests in order to have at least three stationary points of the PDOS used in the computation of the average IS value and its standard deviation (see Figure S2 in the Supporting Information). Following refs (11, 13, 30, and 31) an increase (decrease) of IS with respect to the reference bulk value is taken as an indication of magnetic hardening (softening) for a given substrate.

Being based on a mean-field approximation to exchange interactions (n class="Chemical">as approximately parametrized in the adopted semilocal PBE XC-functional) the procedure cannot intrinsically account for spin fluctuations that may be responsible for the measured ferromagnetic ordering at the interfaces between originally nonmagnetic systems.[30−32] Quantitative description of these effects would require more sophisticated (and computationally demanding) methods capable of describing dynamical aspects of local magnetic susceptibilities.[23,40,41] In spite of these intrinsic limitations, the approach is nevertheless capable of producing trends in magnetic hardening that semiquantitatively match the measured magnetization of Cu–C60 and Cu–aC interfaces.[30,31] These considerations and the overall very light computational cost of the approach enable fast and convenient simulation of systems up to over 200 atoms as considered in this study in our view justify its use for exploratory screening of novel strategies toward molecule-induced magnetic hardening and possible emergent magnetism.

Magnetocrystalline anisotropy energies (MAEs) were computed via fixed-spin moment (0.1 μB/n class="Chemical">Cu-atom), noncollinear DFT simulations with inclusion of spin–orbit coupling as available in VASP.[35] The simulations were carried out non-self-consistently, that is, keeping the charge density (from a collinear run) fixed. The magnetic field was selectively oriented perpendicular to the high-symmetry directions of the considered system and the corresponding energy subtracted to quantify the MAEs. These noncollinear DFT simulations were performed with the same number of symmetry irreducible k points tested to yield PAW-integrated IS values (Figure S1 in the Supporting Information and section below) and total DFT energies converged to within 2 and <1 meV, respectively, for bulk FCC Cu. After the scaling due to the larger simulation cell for the Cu–polyethylene models (section ), this accounts for 8436 and 25 (symmetry irreducible) k points for bulk FCC Cu and the Cu–polyethylene interfaces, respectively.

Interface Models

To disentangle the role of Cu–lattice expansion and charge depletion for the observed magnetic hardening of n class="Chemical">Cu at molecular interfaces,[30,31] we study several models of interfaces between FCC Cu and organic systems with different electron-accepting properties, steric hindrance, or excluded volume and owing to a different extent of π-conjugation, conformational flexibility and relaxation possibilities when interfaced with the Cu–substrate. We focus on four different polymeric systems, namely polyethylene (PE), polyacetylene (PAC), polyethylene terephthalate (PET), and polyurethane (PUR) whose monomeric units are shown in Figure . These systems have been chosen on the basis of their different electron affinities (EA) and hence expected electron-accepting properties neglecting interface-relaxation effects to be quantified in the following. The measured or computed EA for the considered systems range from negative for PE (experimentally derived value −0.5 ± 0.5 eV[42−46]) to increasingly positive values going from PUR (B3LYP-computed vertical value, neglecting electronic and atomic relaxation 0.63 eV[47]) to PET (experimental value 2.85 ± 0.05 eV[48]) and PAC (extrapolated adiabatic value for infinite chain at the B3LYP level 5.5 eV[49]). On the basis of these values, the expectation, to be verified against the results for the relaxed interface models, is that the charge transfer from Cu to the polymer should increase following the series PE < PUR < PET < PAC.

In addition, the systems examined have different torsional flexibility owing to either the lack (PE) or different extent of π-conjugation (n class="Chemical">PET ≈ PUR< PAC) and different steric hindrance due to the presence (PET and PUR) or absence (PE and PAC) of bulkier phenyl groups. Both these elements are anticipated to affect the relaxation at the interface with Cu, enabling quantification of the role of both the polymer-induced distortion of the Cu lattice and the polymer relaxation for the emerging magnetic properties at the interfaces.

Before proceeding we recall that all Cu–organics interfaces capable of emergent magnetism men class="Chemical">asured to date have been prepared by alternated magnetron sputtering deposition of Cu (metal) and organics (C60 molecules or C atoms) films. The sample preparation protocol leads to creation of films with nanometer range roughness.[30,31] Since, in principle, alternative routes to preparation of single Cu–organics interfaces could be realized via chemical or electrochemical deposition of Cu on a polymeric film, practical creation of the Cu–polymer interfaces studied below cannot be excluded a priori, motivating our interest in exploring computationally emergent magnetism at suitably treated interfaces of polymer substrates.

In analogy to the molecular films in refs (30 and 31), ordinary noncrystalline films of the n class="Chemical">polymers considered are not atomically flat, with roughness in the nanometer range[46] or above. Since such molecular roughness would inevitably result in growth of the deposited Cu inside pits of the polymer film or around “self-passivating” protruding polymer loops present at the surfaces of polymer films,[50] we bracket the possible interface geometries by the two extreme cases shown in Figure : in the first one, the polymer chain is placed parallel to the Cu(111) planes of a five-layer slab (in-plane model); in the second one, the polymer chain is perpendicular to the slab plane (perpendicular model).

Here, it is worth noting that magnetron sputtering preparation of the n class="Chemical">metal–organic interfaces is not a thermodynamic-driven process based on chemical equilibrium. Metastable systems can be initially formed. Indeed, the magnetron-sputtering-prepared metal–molecule interfaces are experimentally observed to relax, following thermal treatment or aging, into lower (free) energy systems of partially or strongly modified magnetic properties.[30,31] These considerations motivate the neglect of thermodynamics-related parameters such as the formation energy (always positive for the considered interface models and progressively less favorable as the number of Cu atoms in the models increases) in favor of an exploratory focus on screening the electronic and magnetic properties of a model Cu–polymer interface forcing different degrees of interface geometric relaxation. As in ref (30), to include the effects of differently constrained optimization of the Cu–polymer interface on the emerging magnetic properties, different models were prepared for each interface geometry and polymer using several cutoffs on the initial Cu–polymer distance (dCu–pol = 1.5, 2.0, 2.5, and 3.0 Å). The Supporting Information (Figure S3) contains images of a selection of the initial geometries prepared with dCu–pol = 1.5 Å. The values of dCu–pol were chosen in order to start the interface structural relaxation both in repulsive and in attractive regimes, as estimated from the shortest Cu–C distances measured by I–V LEED for an archetypal interface between Cu and a π-conjugated system: the 7-vacancy C60/Cu(111)-4 × 4 reconstruction (shortest interfacial Cu–C distance 1.98 Å, longest interfacial Cu–C distance 2.20 Å).[51] Since the interface properties depend on the details of the electronic rehybridization, which may change depending on the relaxation freedom available in the system, this strategy offers the possibility to quantify the role of differently constrained relaxations, as likely present in real samples of limited crystallinity,[30,31] on the emerging electronic and magnetic properties of the models studied.

For the in-plane (∥) interface models, commensurability between the Cu(111) slab and the n class="Chemical">polymer chains was achieved by modeling the smallest Cu(111) slab in either a hexagonal or an orthorhombic cell, capable of minimizing the lattice mismatch with the given periodic polymer chain. Compromising between reduction of the periodicity mismatch and size of the simulation cell, we settled for lattice mismatches < 1.2% for PE, PAC, and PUR and roughly 3% for PET. The positive lattice mismatch values indicate that the polymer chain was stretched to match the Cu(111) slab one. Table S1 in the Supporting Information reports a summary of the geometric parameters for the simulation cells used for the different Cu–polymer interface models. For the perpendicular (⊥) interface models, the size of the simulation cell along the direction perpendicular to the Cu(111) was based on the optimized period of the given polymer chain.

Results and Discussion

Magnetic Properties of Isotropically Distorted Bulk FCC Cu

With the final aim of disentangling the role of charge transfer and lattice distortion for the magnetic hardening of Cu, we start our investigation by considering the den class="Chemical">pendence of the magnetic properties on the local geometry and coordination of Cu atoms in the bulk phase. To quantify the relative importance of both the Cu–Cu distance and the coordination symmetry for the magnetic properties of bulk Cu, we focus initially on the effect of isotropic expansion and compression of bulk FCC Cu, i.e., distortions altering the Cu–Cu distance without affecting the local coordination symmetry of the Cu atoms.

We first quantify the convergence of the computed atomic magnetic moments (m) and band splittings (Δ) (hence, IS in eq ) for bulk Cu in the FCC structure n class="Chemical">as a function of both the k-point grid sampling and the volume of the FCC cell, varied between compressions of 15% and expansion of 20% around the computed energy minimum (3.649 Å lattice parameter, see Figure S1 in the Supporting Information). It is found that a spacing of at least 0.0079 Å–1 between k points is sufficiently dense to yield computed values of m, Δ, and IS converged, over the range of volume changes considered, to within <10–3 μB, 6 and 2 meV, respectively. On the basis of these results, a spacing of at least 0.0079 Å–1 was used for all simulations of bulk FCC Cu, and the k-point sampling for the Cu–polymer interface models was scaled according to the size of the reciprocal lattice to maintain this level of convergence for the magnetic properties.

For the range of volumes considered, the computed PDOS-averaged (see Figure S2 in the Supporting Information) values of IS for bulk FCC Cu n class="Chemical">as a function of the lattice parameter (Figure a) reveal a small variation (<0.05 eV or, equivalently, <6%) from the optimized reference value. Compression (expansion) of the Cu FCC lattice results in a decrease (increase) of IS, with slightly larger changes (up to 6%, that is, 0.05 eV) upon compression. The computed magnetic hardening for expanded Cu lattices agrees qualitatively, but not quantitatively, with results for C60-perturbed FCC Cu substrates, where increases up to a factor of over three in IS were computed for 15% expansion of the local Cu FCC coordination.[30] This result provides a first indication that an increase of Cu–Cu distances without changes of the local coordination symmetry for Cu–atoms and depletion of the electronic charge by the organics is not exceedingly effective in inducing magnetic hardening of Cu substrates. The similarity between the maximum change of IS as a function of the volume change (<0.07 eV) and its computed error (up to nearly 0.06 eV for the most deformed cases in Figure a) strengthens this conclusion.

Figure 2

Computed (a) Stoner exchange integral (IS) and (b) density of states at the Fermi level [DOS(EF)] as a function of both the lattice parameter for bulk FCC Cu and the sum of the 12 shortest nearest-neighbor (NN) Cu–Cu distances. (c) Computed IS as a function of DOS(EF). (d) Change of IS × DOS(EF) as a function of the lattice parameter. Vertical red line marks the values for the optimized lattice parameter (3.649 Å). Horizontal continuous (0.15 spin–1 atom–1) and dashed (0.19 spin–1 atom–1) magenta lines in d mark the largest computed IS × DOS(EF) product at the same level of theory for the interfaces between Cu and as-deposited (1.7 g/cm3) and annealed (2.3 g/cm3) amorphous carbon measured to be ferromagnetic in ref (31).

Computed (a) Stoner exchange integral (IS) and (b) density of states at the Fermi level [DOS(EF)] as a function of both the lattice parameter for bulk FCC n class="Chemical">Cu and the sum of the 12 shortest nearest-neighbor (NN) Cu–Cu distances. (c) Computed IS as a function of DOS(EF). (d) Change of IS × DOS(EF) as a function of the lattice parameter. Vertical red line marks the values for the optimized lattice parameter (3.649 Å). Horizontal continuous (0.15 spin–1 atom–1) and dashed (0.19 spin–1 atom–1) magenta lines in d mark the largest computed IS × DOS(EF) product at the same level of theory for the interfaces between Cu and as-deposited (1.7 g/cm3) and annealed (2.3 g/cm3) amorphous carbon measured to be ferromagnetic in ref (31).

However, the increase of IS with the lattice parameter is accompanied by a parallel rise in the density of states at the Fermi energy [DOS(EF), Figure b and 2c], leading to up to 30% larger IS × DOS(EF) products (Figure d), closer to comply with the Stoner criterion for spontaneous onset of ferromagnetic ordering in 3d n class="Chemical">metals (IS × DOS(EF) > 1).[52,53] Conversely, compression of bulk FCC Cu and the ensuing reduction in both IS and DOS(EF) leads to up to over 30% reduction of IS × DOS(EF). These results indicate that volume expansion is more effective than compression in inducing magnetic hardening of bulk FCC Cu. Notably, the largest increase in of IS × DOS(EF) for 20% expanded bulk Cu FCC leading to a value of roughly 0.16 spin–1 atom–1 is substantially smaller (−30%) than what is computed, at the same level of theory, for Cu–C60 interfaces (up to 0.23 spin–1 atom–1),[30] confirming that isotropic FCC expansion may not be the most effective strategy toward magnetic hardening of Cu substrates. However, it also worth noting that for the as-prepared Cu–aC interfaces measured to develop ferromagnetic ordering,[31] the computed IS × DOS(EF) products are close to 0.15 spin–1 atom–1, which ultimately points to the exploration of Cu FCC lattice expansion, possibly by epitaxial growth of ultrathin films on suitable substrates, as a potentially alternative route toward magnetic hardening of Cu and ensuing emergence of ferromagnetic ordering without the use of molecular interfaces. This aspect will be the subject of a forthcoming study.

Noncollinear fixed-n class="Gene">spin DFT simulations for all compressed and expanded bulk FCC systems indicate minimal changes (<10–7 eV/atom) in the MAEs that remain consistently in the order of 10–6 eV/atom, in line with the weak shape anisotropies measured for ferromagnetic Cu–C60 interfaces (∼10–6 eV/Cu-atom).[30] Although the computed differences in MAEs are clearly orders of magnitude below the (meV range, see Methods section) convergence of the simulations, the computed MAE values can be nevertheless taken as an indication that the isotropic deformations studied are not capable of substantially increasing MAEs for Cu–substrates to the meV range, as desirable for practical applications.[13]

Cu–Polymer Interfaces

Geometric Relaxation of the Interface Models

Depending on the n class="Chemical">polymer and in-plane or perpendicular interface, geometry optimization of the Cu–polymer models (Figure ) leads to different relaxation of the Cu slab and loosening of the Cu lattice as quantified by the average cumulative 12 nearest-neighbor (NN) Cu–Cu distances for the Cu atoms in the slab (Figure ). In all cases, no barrierless breaking of the bonds of the polymer chain and atom transfer to the interface Cu atom during the geometry optimization was observed.

Figure 3

Optimized geometries for the considered in-plane (left subpanels, side view) and perpendicular (right subpanels, top view) models of the interface between Cu and (a) PE, (b) PAC, (c) PET, and (d) PUR. Cu–polymer cutoff (dCu–pol, Å) used to prepare the initial geometry is reported in the insets. C, cyan; O, red; N, blue; H, silver; Cu, brown.

Figure 4

Polymer-induced loosening of the Cu lattice for the Cu–polymer interfaces considered as quantified by the average sum of the 12 NN Cu–Cu distances in the optimized slabs. Horizontal red line marks the value of the cumulative 12 NN Cu–Cu distance (30.962 Å) for optimized bulk FCC Cu (lattice parameter 3.649 Å).

Optimized geometries for the considered in-plane (left subpanels, side view) and pern class="Chemical">pendicular (right subpanels, top view) models of the interface between Cu and (a) PE, (b) PAC, (c) PET, and (d) PUR. Cu–polymer cutoff (dCu–pol, Å) used to prepare the initial geometry is reported in the insets. C, cyan; O, red; N, blue; H, silver; Cu, brown.

Polymer-induced loosening of the n class="Chemical">Cu lattice for the Cu–polymer interfaces considered as quantified by the average sum of the 12 NN Cu–Cu distances in the optimized slabs. Horizontal red line marks the value of the cumulative 12 NN Cu–Cu distance (30.962 Å) for optimized bulk FCC Cu (lattice parameter 3.649 Å).

In general, all interface models considered induce loosening of the FCC Cu lattice. n class="Chemical">Not unexpectedly, the distortions for the in-plane models are larger than for the perpendicular ones. In line with expectations based on the larger hindrance of the phenyl group (in PUR and PET) with respect to −CH2–CH2– (PE) and −CH=CH– (PAC) fragments, the computed loosening of the Cu lattice is largest for PUR and PET. Interestingly, the PAC-induced loosening of the Cu lattice is closer to PUR values than PE results. This result suggests a predominant role of the presence (or absence) of molecular π-conjugation (and ensuing Cu–organics charge transfer) for the relaxation of the metal substrate. In the following we quantify the extent to which such an enhanced geometric relaxation directly correlates (or not) with the interface electronic and magnetic properties.

Electronic Properties of the Interface Models

In spite of the substantial relaxation induced on the Cu–substrate by the n class="Chemical">polymer chain, all interfaces are computed to be metallic and characterized by a well-defined 3d band with an absolute density of states (DOS) maximum at about 1.5 eV below EF, as present for bulk FCC Cu (Figure ). Comparison between Cu and polymer-resolved PAW-projected DOS (PDOS), shown in Figures S4 and S5 in the Supporting Information, indicates that the DOS at EF [DOS(EF)] is dominated by Cu states and that the interface relaxation leads to metallization (nonzero PDOS at EF) for all polymers. These findings are in qualitative agreement with the results for other interfaces between Cu and differently conjugated systems such as C60,[30] aC,[31] and linear alkanes,[54] suggesting that π-conjugation of the organics is not necessary for creation of hybrid Cu–polymer delocalized metallic states at the interface.

Figure 5

Computed density of states (DOS) for the in-plane (∥, continuous lines) and perpendicular (⊥, dotted lines)) models of the interface between Cu and (a) PE, (b) PAC, (c) PET, and (d) PUR: black, dCu–pol = 1.5 Å; yellow, dCu–pol = 2.0 Å; blue, dCu–pol = 2.5 Å; green, dCu–pol = 3.0 Å. Computed DOS for bulk FCC Cu at the optimized lattice parameter is shown in red.

Computed density of states (DOS) for the in-plane (∥, continuous lines) and pern class="Chemical">pendicular (⊥, dotted lines)) models of the interface between Cu and (a) PE, (b) PAC, (c) PET, and (d) PUR: black, dCu–pol = 1.5 Å; yellow, dCu–pol = 2.0 Å; blue, dCu–pol = 2.5 Å; green, dCu–pol = 3.0 Å. Computed DOS for bulk FCC Cu at the optimized lattice parameter is shown in red.

Consistent with the larger hybridization between the Cu and the n class="Chemical">polymer modeled for PAC, PET, and PUR by comparison to PE, leading to larger polymer-projected PDOS(EF) for the former systems (Figure S4 in the Supporting Information), Bader charge analysis for the optimized models reveals a larger Cu → polymer electron transfer for the systems with π-conjugation (PAC, PET, and PUR in Figure ).

Figure 6

(a) Computed Cu → polymer Bader charge transferred (Q, e) as a function of dCu–pol, and (b) average cumulative 12 NN Cu–Cu distance in the optimized Cu–polymer interface models.

(a) Computed Cu → n class="Chemical">polymer Bader charge transferred (Q, e) as a function of dCu–pol, and (b) average cumulative 12 NN Cu–Cu distance in the optimized Cu–polymer interface models.

Notably, the interfacial charge transfer turns out to qualitatively correlate with the vertical electron affinity (EA) of the n class="Chemical">polymer chains, as first approximated by the position of the LUMO for the isolated chain with respect to the vacuum level. With the exception of the in-plane (∥) Cu–PUR interface model prepared with the shortest dCu–pol (1.5 Å in Figure d), the trend in Bader charge transfer (PE < PUR < PET < PAC) follows qualitatively what was expected on the basis of the vertical EA as first approximated by minus the energy of the LUMO level with respect to the vacuum (again PE < PUR < PET < PAC from Table S2 in the Supporting Information). These results suggest that, at least for the Cu–polymer interfaces studied, trends in interfacial charge transfer between different molecular systems may be effectively estimated based on the position of the LUMO level for the isolated organic. It consequently follows, again at least for the systems considered, that the different interface relaxation (PE < PAC < PUR ≈ PET in Figure ) plays a secondary role with respect to the organic EA for the overall interface charge transfer: larger interface relaxation (Figure ) does not directly correlate with larger charge transfer at the interface.

Before proceeding it is worth nothing that in spite of the substantial rehybridization leading to metallization of n class="Chemical">PE interfaced to Cu, the overall charge transfer from the Cu substrate to PE in the in-plane models is less than 0.14 e in Figure a (0.07 e per PE unit in the simulation cell). This result stems from the competition between Cu → organic donation and organic → Cu back-donation previously discussed for alkanes on metallic substrates such as Cu[54] or Co.[20] Here, it has to be noted that empty (Kohn–Sham) states for PE chains, as typically other saturated aliphatic molecules (alkanes), tend to be localized mostly outside the molecular backbone, leading to accumulation of excess charge in the interstitial regions around the PE chain,[45,46,55−57] an aspect that may have affected Bader partitioning[38] of the electronic charge at the Cu–PE interfaces.

In line with previous results in the literature,[54] we find that in spite of the minimal net charge transfer and the additional constraints induced by the use of infinitely periodic interface models, the n class="Chemical">Cu–PE rehybridization and ensuing metallization of the organic system is accompanied by an increase of up to 1.5% (decrease up to 4%) of C–H (C–C) bond distances and a parallel increase of up to 3% in the C–C–C bond angles in PE (Table S3 in the Supporting Information). These results are indicative of a partial sp3 → sp2 rehybridization of the aliphatic chain upon interaction with Cu, as also evident by the dramatic change in PE-resolved DOS for all Cu–PE interface models (Figure S5 in the Supporting Information).

Finally, analysis of the computed Bader charge transfer as a function of the loosening of the n class="Chemical">Cu lattice (Figure b) reveals another correlation potentially useful when designing Cu–organic interfaces. For all interface models considered, the Cu → organic charge transfer decreases as the local coordination environment of the Cu atoms is expanded. Thus, contrary to the Cu–C60 case,[30] increased interface relaxation and loosening of the Cu–lattice is found to hinder, rather than enhance, depletion of electronic charge at the Cu–substrate by the considered organics. This result indirectly suggests that strain on the π-system (larger for C60 than the considered, originally planar, PAC, PET, and PUR) may play an important role for the interface relaxation and charge transfer, an aspect worthy of detailed investigation in the future. In the following, we quantify the extent to which such a quantitatively different charge transfer affects the emerging magnetic properties of the Cu–polymer interfaces.

Magnetic Properties of the Interface Models

We find the relaxed Cu–n class="Chemical">polymer interfaces to be characterized by generally smaller band splitting (ΔE) and magnetic moments (m) with respect to bulk FCC Cu (Figure S6 in the Supporting Information). The direct (inverse) contribution of these parameters to the approximated Stoner exchange integral (IS, eq ) leads to scattering of the computed Cu-resolved IS both above and below the bulk FCC Cu value, with the largest values in the 1.1–1.3 eV range for all of the different polymers considered, close and in cases above the largest value computed for as-deposited ferromagnetic Cu–aC systems (IS = 1.25 eV).[31] In line with results for Cu–C60 interfaces,[30] the increase in IS is not localized at the immediate Cu–polymer interface but spread over the whole Cu–substrate (Figure S6 in the Supporting Information). Contrary to results for Cu–C60 hybrids[30] but in agreement with simulations of the Cu–aC interfaces,[31] no immediate correlation is found between the increase in IS and the loosening of the Cu lattice as measured by the sum of the 12 NN Cu–Cu distances in the optimized slabs (Figure S7 in the Supporting Information).

In general, Cu–substrate average Is values turn out to be either minimally larger (less than 0.1 eV incren class="Chemical">ase) or smaller than for bulk FCC Cu (Figure a). An exception to this trend is the parallel Cu–PE interface with dCu–pol = 2.0 Å. For this system the average IS value is nearly 0.2 eV higher than bulk FCC Cu, first revealing that, pending favorable interface relaxation, significant increase in IS can be also produced by interfacing Cu with non-π-conjugated organics such as PE. The nonmonotonic, system-dependent change of the computed IS as a function of dCu–pol (Figure a) clearly indicates that relaxation of the interface under different geometrical constraints, as expected for Cu samples of different crystallinity and homogeneity, can majorly affect the interfacial magnetic properties, answering one of the research questions behind the choice of the models.

Figure 7

Average (a) Stoner exchange integral (IS), (b) density of states at the Fermi level [DOS(EF)], and (c) IS × DOS(EF) product for the Cu–polymer interface models as a function of dCu–pol. (d) Average IS × DOS(EF) product as a function of the average cumulative 12 NN Cu–Cu distance in the optimized models. Horizontal red line marks the values for optimized bulk FCC Cu. Horizontal continuous (0.15 spin–1 atom–1) and dashed (0.19 spin–1 atom–1) magenta lines in c and d mark the largest computed IS × DOS(EF) product at the same level of theory for interfaces between Cu and as-deposited (1.7 gr/cm3) and annealed (2.3 gr/cm3) aC measured to be ferromagnetic in ref (31).

Average (a) Stoner exchange integral (IS), (b) density of states at the Fermi level [DOS(EF)], and (c) IS × DOS(EF) product for the Cu–n class="Chemical">polymer interface models as a function of dCu–pol. (d) Average IS × DOS(EF) product as a function of the average cumulative 12 NN Cu–Cu distance in the optimized models. Horizontal red line marks the values for optimized bulk FCC Cu. Horizontal continuous (0.15 spin–1 atom–1) and dashed (0.19 spin–1 atom–1) magenta lines in c and d mark the largest computed IS × DOS(EF) product at the same level of theory for interfaces between Cu and as-deposited (1.7 gr/cm3) and annealed (2.3 gr/cm3) aC measured to be ferromagnetic in ref (31).

With the exception of the in-plane (∥) Cu–n class="Chemical">PAC (dCu–pol = 2.0 and 2.5 Å) and Cu–PUR (dCu–pol = 3.0 Å) systems, all other interfaces result in a substantial increase (from over 20% to up to a factor of 2) of the computed DOS(EF) with respect to the bulk FCC value (Figure b). Notably, among the in-plane models, the largest DOS(EF) values are computed for Cu interfaced with PE, which completely lacks π-conjugation. These results clearly demonstrate that the presence of a π-system and ensuing enhancement of the Cu → organics charge transfer (Figure ) is not strictly necessary for enhancing the interfacial DOS(EF): suitable interface relaxation and composition can also be effective to this end. It thus emerges that IS and DOS(EF), key quantities of the Stoner model of ferromagnetism,[52,53] are (i) differently sensitive to the composition and structure of the interface and (ii) not directly correlated at least for the systems considered (see also Figure S8 in the Supporting Information).

Notably, in spite of the reduced interface relaxation (Figure ) and charge transfer (Figure ), the computed DOS(EF) for the n class="Chemical">perpendicular (⊥) interface models turns out to be comparable (or noticeably larger in the case of PAC) with the value obtained for the in-plane (∥) systems. It thus turns out that substantial increase of DOS(EF) can be achieved also by relatively localized contacts between the Cu–substrate and the organic.

As shown in Figure c, the combination of the differently altered IS and DOS(EF) leads to IS × DOS(EF) products generally larger than for bulk FCC n class="Chemical">Cu, indicative of magnetic hardening. The only exception to the trend is represented by the in-plane interface between Cu and PAC, the system with the most extended π-conjugated system and the largest Cu → organic charge transfer (Figure ). Further evidence of the nonimmediate correlation between interface magnetic hardening and charge transfer is provided by the fact that the IS × DOS(EF) products for the Cu–PE interface are comparable to those for π-conjugated polymers such as PET and PUR, in spite of the substantially different interfacial charge transfer (Figure ).

Contrary to what found in ref (30), for Cu–C60 interfaces the largest computed IS × DOS(EF) does not apn class="Chemical">pear to correlate with increased loosening of the Cu–lattice as measured by the cumulative 12 NN Cu–Cu distance (Figure d). Additionally, for the Cu–PUR interface, the computed Is × DOS(EF) is found to actually decrease as the Cu lattice is loosened.

Perhaps surprisingly, due to the simultaneous incren class="Chemical">ase in both IS (Figure a) and DOS(EF) (Figure b), the in-plane Cu–PE interface for dCu–pol = 2.0 Å is found to lead to the largest IS × DOS(EF) product (0.21 spin–1 atom–1), larger than what is computed at the same level of theory for the annealed Cu–aC interface (0.19 spin–1 atom–1) measured to be ferromagnetic in ref (31). Noncollinear fixed-spin DFT simulations of this Cu–PE interface point out minimal changes (<10–7 eV/atom) in the computed MAEs that remain consistently on the order of 10–6 eV/atom, in line with the weak shape anisotropies measured for ferromagnetic Cu–C60 interfaces (∼10–6 eV/Cu atom).[30] The same considerations as for the sub-meV MAEs computed for bulk FCC Cu (section ) apply also here.

It thus transpires that in spite of the negligible charge transfer (Figure ), the PE chain is nevertheless capable, via interface relaxation and the ensuing rehybridization with the n class="Chemical">metal (Figures S4 and S5 in the Supporting Information), of inducing magnetic hardening of Cu competitive to that observed for interfaces with substantially larger electron depletion of Cu. Analysis of the computed Cu-resolved IS values as a function of the atomic Bader charges (Figure S9 in the Supporting Information) rules out any direct correlation between atomic charges on Cu atoms and ensuing magnetic hardness as quantified by the IS parameter, strengthening the conclusion that rather than charge transfer it is the Cu–organic rehybridization that is crucial for the interface magnetic hardening. As the data for the Cu–PE interface (Figure ) and published result for alkanes on transition metals[20,54] indicate, important interfacial rehybridization, leading to emergence of interface electronic states of desirable properties [in the present case an increased IS × DOS(EF) product due to joint or separate enhancement of IS and DOS(EF)] may take place also without substantial net charge transfer between the metal and the organic. The computed strong magnetic hardening for the planar (dCu–pol = 2.0 Å) and perpendicular (dCu–pol = 3.0 Å) Cu–PE interface models in Figure d together with the presence of empty “surface” states (amenable to PBE simulation[46] as done here) with a typical vacuum decay length of 3.0 Å for periodic PE chains[46,58] altogether suggest that rehybridization of molecular (empty) surface states with a metal can also be effective in tuning the interface magnetic properties.

These results if not in contrast at len class="Chemical">ast significantly add to existing suggestions that charge transfer from the metal to the π-conjugated molecule is necessary for magnetic hardening and the emergence of ferromagnetic ordering at Cu–organics interfaces.[30−32] Although results about the unnecessity of π-conjugation for the creation of highly spin-polarized states at the interface between a ferromagnetic metal and an organic molecule have been previously published,[20] to the best of our knowledge, here we provide the very first insights into (i) negligible magnetic hardening at the interface between Cu and a completely π-conjugated substrate (PAC) and (ii) the possibility of magnetic hardening at the interface between a transition metal and a non-π-conjugated molecule. The comparable magnetic hardening between the Cu–aC (measured to be ferromagnetic in ref (31)) and the Cu–PE interfaces prompts further research in the overlooked possibilities offered by (non-π-conjugated) aliphatic molecules for promoting emergent magnetism at metal–organic interfaces.

The computed decrease in n class="Chemical">Cu magnetic hardening going from C60 to aC[30−32] to the π-conjugated polymers considered here inevitably raises the question as to whether optimal rehybridization between Cu and π-conjugated organics toward enhancement of interfacial magnetism requires fine tuning of the strain of the π-system on the organics. We hope these results will stimulate further experimental and computational research into this aspect.

Finally, the computed substantial increase of the IS × DOS(EF) products for discontinuous contact between the organic and the n class="Chemical">Cu, as present in the perpendicular (⊥) PE and PAC interfaces prepared with dCu–pol ≥ 2.5 Å in Figure c, is also worthy of mention. The results for these systems suggest that depending on the nature of the organic nonhomogenous interfaces (as in the perpendicular models) may also be effective in inducing interface rehybridization and emergence of magnetic hardening, opening up the study of less regular or more complex multilayer depositions than pursued so far.[30,31]

Conclusion

In summary, DFT simulations have been used to investigate the role of lattice expansion and molecular π-conjugation for the magnetic hardening of n class="Chemical">Cu–organics interfaces. Analysis of the simulations for bare bulk FCC Cu and several models of the interfaces between Cu and differently π-conjugated polymers, namely, polyethylene (PE), polyacetylene (PAC), polyethylene terephthalate (PET), and polyurethane (PUR), indicate the following.

Even in the absence of charge transfer, 10–15% expansion of the bulk FCC Cu lattice results in magnetic hardening comparable to what wn class="Chemical">as computed for the interfaces between Cu and amorphous carbon measured to develop room-temperature ferromagnetic ordering.[31] Conversely, compression of the bulk FCC Cu lattice leads to magnetic softening of the metal.

In spite of the substantially different, polymer-den class="Chemical">pendent, geometry relaxation, all interfaces studied lead to metallization of the organic system.

Organics with larger vertical electron affinity (EA) lead to larger charge transfer when interfaced with Cu. This result suggests a secondary role for the interface relaxation and, n class="Chemical">pending further validation on a more extended set of systems, that the EA of the isolated molecule may be conveniently used in designing of charge transfer at Cu–organics interfaces. The Cu → organic charge transfer is found to be consistently suppressed by an increase in the interfacial relaxation or loosening of the Cu lattice.

At least for the systems studied, charge transfer is found not to directly correlate with the interfacial magnetic hardening. The system with the most extended π-conjugation and largest interfacial charge transfer (n class="Chemical">PAC) leads to the smallest magnetic hardening. Magnetic hardening appears to be governed by the details of the electronic rehybridization with the metal. The precise role of strain in the π-system of the organic for such rehybridization remains to be quantified.

Depending on the interfacial relaxation, rehybridization between n class="Chemical">Cu and vacuum-decaying empty states of the organic, as present in PE, are found to be effective in inducing interfacial magnetic hardening comparable to or larger than Cu–amorphous carbon systems recently measured to develop room-temperature ferromagnetic ordering.[31]

It thus transpires the neither the presence of the organic interface, molecular π-conjugation nor substantial charge transfer may be strictly needed for magnetic hardening of n class="Chemical">Cu–substrates, albeit combination of the present results and available experimental data suggests that maximization of the effect does require both (strained) π-conjugation and substantial charge transfer.[30,31] We believe these results prompts for further research in the, to date overlooked, possibilities of non-π-conjugated molecules with empty surface states and maximally strained π-systems for magnetic hardening and emergent magnetism at transition-metal–organic interfaces.