Spin Polarization Inversion at Benzene-Absorbed Fe4N Surface

We report a first-principle study on electronic structure and simulation of the spin-polarized scanning tunneling microscopy graphic of a benzene/Fe4N interface. Fe4N is a compound ferromagnet suitable for many spintronic applications. We found that, depending on the particular termination schemes and interface configurations, the spin polarization on the benzene surface shows a rich variety of properties ranging from cosine-type oscillation to polarization inversion. Spin-polarization inversion above benzene is resulting from the hybridizations between C pz and the out-of-plane d orbitals of Fe atom.

A major topic in organic spintronics is the spin related properties at the interface between a ferromagnetic substrate and organic material, i.e. the spinterface 22 . Much effort has been made to clarify the underlying mechanisms that drive the peculiarities, such as spin polarization inversion, at various spinterfaces 21,[23][24][25][26] . For the interfaces between Fe and benzene molecule (as well as C 5 H 5 and C 8 H 8 ), Atodiresei et al. argue that it is the p z -d Zener exchange-type mechanism that leads to the spin-polarization inversion 24 . In another study on the thiophene/cobalt(001) interface 25 , the strong spatial dependence of the spin polarization at the interface is attributed to the reduced molecular symmetry. The azobenzene isomer adsorbed on Fe surface has been reported recently, where the switch between two types of azobenzenes takes place by applying light and/or heat 21 . On the other hand, studies are extended to systems consisting of AFM substrates including benzene adsorbed on monolayer AFM Mn 26 or metal phthalocyanine 4,[27][28][29] , where the spin polarization modification has often been reported.
But, we are not aware of any investigations into the interfaces between an organic molecule and a compound ferromagnet, such as iron nitride (Fe 4 N). Fe 4 N carries a high spin polarization of nearly ~100% 30 as well as a large saturation magnetization of 1200 emu/cm 3 31 . Its Curie temperature is about 760 K. Together with its high chemical stability 32 and low coercivity 33 , Fe 4 N is a promising candidate for, among other, spin injection source 34 . In this work, we scrutinize the spinterface between a benzene molecule and Fe 4 N substrate. In particular, we will show that different termination schemes and adsorption configurations unique to the benzene/Fe 4 N interface enrich the properties of spin polarization.
Calculation details. Our first principles calculations are based on the density-functional theory (DFT) and the projector augmented wave method as implemented in the Vienna Ab initio Simulation Package code 35,36 . For the exchange and correlation functional, we use the Perdew-Burke-Ernzerhof spin-polarized generalized gradient approximation (PBE-GGA) 37 . The plane-wave basis set is converged Scientific RepoRts | 5:10602 | DOi: 10.1038/srep10602 using a 500 eV energy cutoff. A Γ -centered 3 × 3 × 1 k-mesh is used for the Brillouin-zone integrations. A Gaussian smearing of 0.02 eV is used for the initial occupations. It is worth pointing out that van der Waals force is excluded from our calculation. We do so not only because strong bonding exits between benzene molecule and Fe 4 N (as shown in the due discussion), but also recent studies suggest that it has a negligible effect on GGA optimized structure in, for example, azobenzene/Fe(110) 21 .
Bulk Fe 4 N has a cubic perovskite-type structure (Pm3m) with a lattice constant of 3.795 Ǻ 34 . Fe occupies the corner (Fe I ) or face-centered (Fe II ) position labeled structure graphic of bulk Fe 4 N, whereas N locates at the body-centered site 34 , as shown in Fig. 1(a). Our calculations give a lattice constant of 3.789 Ǻ, in agreement with the experimental value 34 . The Fe 4 N substrate is modeled by slabs of three atomic layers with a (3 × 3) flat surface. We concentrate, in this work, on the effect of different adsorption schemes on the spatial spin-polarization distribution. The subtleties due to the number of atomic layers will be reported in upcoming studies.
Termination schemes and interface models. The benzene/Fe 4 N interfaces are modeled by placing benzene on top of the Fe 4 N(001) surface. The lattice structure of Fe 4 N allows us to have the interfaces with two types of terminations, namely, Fe II N and Fe I Fe II . For Fe II N termination, Fe 4 N surface is the plane across the body-centered site parallel to Fe 4 N(001). For Fe I Fe II termination, Fe 4 N surface refers to the plane across the face-centered site. For each termination scheme, we further consider two stacking models based on whether N or Fe atom, in the first layer, is right beneath the center of benzene molecule: models Fe II N-C and Fe I Fe II -C are named after the terminations with N or Fe atom in the Fe 4 N surface, locating right beneath the center of benzene molecule, whereas models Fe II N-NC and Fe I Fe II -NC are referring to the ones without, see Fig. 1. During the lattice structure relaxation, the atoms in the bottom layer of slab are fixed at their bulk positions, whereas other atoms are fully relaxed until the force is weaker than 0.03 eV/Å. In order to decouple adjacent slabs, a thick vacuum layer of 15 Ǻ is included in the direction perpendicular to the surface. To illustrate the nature of the spin-polarization inversion in the real space, we calculate the spin-polarization distribution by the constant-height spin-polarized scanning tunneling microscopy (SP-STM) simulation 38 .

Results and discussion
To illustrate the system, we also define the surface (inter layer, fixed layer) of Fe 4 N slab as I (II, III) layer, and the benzene as M layer. We call the zone above benzene as 'benzene surface' , between benzene and Fe 4 N as 'interfaces' , and atoms of I layer, in Fe 4 N slab, as 'Fe 4 N surface' . The sites where the Fe ion located right below the C atom are defined as the top (_t) sites; the ones where the Fe ion located under the C-C bond are defined as the bridge (_b) sites. At the top or bridge sites, we call the Fe (C) atom by Fe_t (C_t) or Fe_b (C_b). The atom located right under the center of benzene is Fe_c or N_c. Figure 1(c-f) show the side and top views of the four optimized stacking models. After the structure relaxation, benzene plane is no longer flat in all models except Fe II N-NC. Especially, the hydrogen atoms in Fe II N-C and Fe I Fe II -NC models lie fairly further away from the slab surface than carbon atoms, agreeing with earlier reports 18,24 . The C-C bonds become longer than those in the isolated benzene ring.
The Fe 4 N slab also experiences the structural changes. In both Fe II N-C and Fe I Fe II -NC models, the Fe_t and Fe_b atoms move out of the Fe plane of the surface, see Fig. 1(c,f). In the Fe I Fe II -C model, Fe_c moves up, as shown in Fig. 1(e). In the exception arises from the Fe II N-NC model, where the benzene plane is still flat, yet the C-C bonds are equal to that in the isolated benzene. The benzene plane is moving away from the Fe 4 N surface, as shown in Fig. 1(d). The data from our calculation is in the Table 1.
The adsorption energy (E abs ) of different models is labeled in Fig. 1(b). According to the adsorption energy, 4 adsorption models fall into two categories: the endothermic adsorption (two Fe II N terminals models) and exothermic adsorption (two Fe I Fe II terminals models). The Fe II N-C model has the maximum adsorption energy (0.74 eV). This implies that, at high temperatures, it is the most easily formed model among the four. On the other hand, Fe I Fe II -NC shows an exothermic adsorption with the minimum adsorption energy (−2.14 eV), implying that its stability favours low temperatures.
The moment and charge are listed in Table 2. The charge value is calculated using Bader analysis [39][40][41] . We note that the Fe II moment in layer II, see the 3 rd row in Table 2, is smaller than 2.29 μ B in bulk Fe 4 N, where μ B is Bohr magneton. This is due to a stronger yet more localized hybridization between N and Fe II in the second layer [42][43][44] . Apart from the exception in the Fe II ions in layer II, in Fe I Fe II terminal, we observe that, while it gains more charge, the Fe II moment tends to be larger than that in bulk Fe 4 N. But in the Fe II N terminal, this relation no longer holds; no prominent relationship between charge and moment is present.
To understand the bonding mechanisms, we analyze the charge density difference defined by are the charge densities of the full system, isolated benzene and Fe 4 N surface, respectively. Charge accumulation (depletion) is in yellow (blue). In the Fe II N-C model, the charge accumulates on the C-Fe bonds, as Fig. 2(a) shows. In Fig. 2(b), the interface has little charge accumulation between C and Fe ions, indicating that C atoms do not form bonds with Fe 4 N slab. This is consistent with the large distance between the benzene and Fe 4 N surface. Figure 2(c) displays a large charge accumulation in the region right below benzene in the Fe I Fe II -C  For the bridge sites, we note that the spin-up and spin-down π orbitals of benzene are mixed with Fe_b d z 2 and d xz + d yz in −4.14~−3.5 eV energy interval, and with Fe_b spin-down d xz + d yz at 2.54 eV. Besides the strong hybridization that mentioned above, a series of hybridizations between the C p z and Fe d states are drawn in Fig. 3(a). For Fe at both the top and bridge sites, its s and d orbitals, for both spin species, hybridize with the N_c p orbitals in the energy interval −7.6~−3.8 eV. In Fig. 3(b) for the Fe II N-NC model, the benzene π orbitals originating from the C p z orbitals do not hybridize with Fe. The slab keeps mostly the properties of a clean surface. The N p x and p y orbitals are degenerate. The DOS of Fe_t is almost the same as that of Fe_b. Meanwhile, the Fe II d xz + d yz orbitals hybridize with the N p z orbitals in the energy interval −4.1~−6.6 eV and at Fermi energy (E F ). The Fe II d d xy x y 2 2 + − and s orbitals are mixed with the degenerate N p x , p y orbitals at −6.6~−7.2 eV. In the Fe I Fe II terminations, the intensity of local benzene π orbitals peak become weak gradually, and the peak becomes wider. Figure 4 shows the DOS of two Fe I Fe II terminations. In the Fe I Fe II -C model, Fe_c d xz + d yz hybridizes with C p z at −5.1 eV, and with C p x , p y at −7.9 eV, as shown in Fig. 4(a). The Fe_c d z 2 orbitals hybridize with C p z in the energy interval −6.7~−6.3 eV. The hybridization between the Fe_c spin-up d d xy x y 2 2 + − and C p z is strengthened in the energy interval of 1.1 ~ 2.1 eV. At the energy level above 2.5 eV, Fe_c spin-down d z 2 weakly hybridizes with C_t p z .
In the Fe I Fe II -NC model, we see a rather weak mixture between the C_t p z and Fe_t d z 2, d xz + d yz states in the interval −7.4~−6.0 eV. We note that C_t p z orbitals tend to degenerate with the p x orbitals, yet C_b shows no such tendency. In the interval −5.5~  We note a trend from the above hybridization schemes. As the benzene molecule moves towards the Fe 4 N surface, the hybridization of different orbitals depends on the termination schemes. In the Fe II N-C and Fe I Fe II -C models, the Fe d xz + d yz and d z 2 orbitals hybridize strongly with the C p z state, leading to spin-polarization inversion. In the Fe I Fe II -NC model, the hybridization between both spin species of the C p z and Fe s, d d xy x y 2 2 + − orbitals is stronger than that between C p z and Fe (d xz + d yz , d z 2), unable to reverse the spin polarization. This is consistent with the report in Ref. 17. We are thus led to conclude that the spin-polarization inversion at benzene surface is a result of hybridizations between the p z orbital of C and the out-of-plane Fe d orbitals.
We show, in Fig. 5, the spatial distribution of spin-polarization P space , defined as In each energy interval, the spin-polarization is projected onto the plane that is parallel to the Fe 4 N surface, see Fig. 5(b,c); the distance between the plane and benzene surface is labeled in Fig. 5(b). For the 4 models discussed in this work, we plot, in Fig. 5(a,d), the spin polarization along a few selected lines defined in Fig. 5(b,c).
For the Fe II N-C model, the highest spin polarization is ~80%, and the lowest value is ~−60% via line 2 and line 3, see Fig. 5(a). The intensity of inversion is much stronger than benzene adsorbed antiferromagnetic Mn 26 , due to the hybridization between the p z states and d z 2 In the Fe II N-NC model, line 2 exhibits the spin-polarization inversion, as shown in Fig. 5(b). The DOS, in Fig. 3(b), however, points to a weak adsorption. The spin-polarization distribution in this model is thus similar to that in vacuum (above a clean Fe 4 N surface). For the Fe II N-NC model, the spin polarization of line 1 with a cosine-type distribution is shown in Fig. 5(a).
In both Fe I Fe II terminal models, spin-polarization inversion happens, but the strong spin-polarization inversion in the neighbourhood of benzene happens only in Fe I Fe II -C. In Fe I Fe II terminations, Fe 4 N surface distort significantly, Fe II ions are not located right above N atoms, as shown in Figs. 1(e,f). Then positive spin polarization of N atoms extends into benzene surface. In Fe I Fe II -C model, the most interesting feature is that the positive spin-polarization distributes along the C-C bonds, see Fig. 5(b). In Fig. 6, a positive spin polarization of benzene appears at E F in the Fe I Fe II -C model. On the other hand, in the Fe I Fe II -NC model spin polarization is approximate 0%. Meanwhile spatial spin-polarization, for Fe I Fe II -NC, in the neighbourhood of benzene is almost 0%, see Fig. 5(b). So, the atomic scale spin-polarization, at benzene surface, is modulated by N and C atoms.   Figure 7 is the spin-polarization plane of Fe II N-C structure. It's across the top sites and parallel to Fe 4 N(100). From this figure, benzene hampers the extension of N position spin polarization, and realizes the spatial spin polarization inversion. The reason is the overlap of p z and out-of-plane components of d.

Conclusion
In summary, we have shown that at the spinterface formed by benzene adsorbed on Fe 4 N, depending on the specific termination schemes, a variety of spin polarization, including spin polarization inversion, can take place. The spin-polarization inversion finds its origin in the hybridization between the out-of-plane components of Fe d orbitals and the benzene π orbitals (the p z orbital, in particular). The presence of N atoms partition the adsorption into two categories: the endothermic (adsorption) Fe II N terminal models and the exothermic Fe I Fe II terminal ones. With these results, we can see that adsorptions rely on the temperature. The Fe II N-C with the maximum adsorption energy will be easier to be formed than others under high temperature and has significant spin-polarization inversion, which is desired for the spintronic devices.