Significant variation of surface spin polarization through group IV atom (C, Si, Ge, Sn) adsorption on Fe₃O₄(100)

Abstract

The adsorption of group IV atoms (C, Si, Ge, Sn) on the magnetite Fe₃O₄(100) surface is investigated by density functional theory calculations. All these atoms prefer to bond to the surface oxygen atom which has no tetrahedral Fe(A) neighbor. The spin-up surface states of clean Fe₃O₄(100) are completely removed and half-metallicity is recovered by C adsorption. The spin-up band gap of the C-adsorbed Fe₃O₄(100) surface is wider than that of the H-adsorbed one and closer to the value of bulk Fe₃O₄. For the adsorption of other group IV atoms, the adsorbate–substrate interaction decreases and the adsorbate–adsorbate interaction increases with the increase of atomic number Z. As a consequence, the spin polarization varies from −99.4% (C adsorption) to +44.2% (Sn adsorption) for the electronic states of the adsorbed atom integrated from −0.5 eV to the Fermi level. The ability to tune the surface spin polarization by the choice of adsorbate is of significance for magnetite-based spintronic devices.

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I. Introduction

Organic spintronics continues to attract significant attention, in part due to the weak spin–orbit and hyperfine interactions in organic materials and the associated spin relaxation times which are much longer than in conventional metals and semiconductors.^1–7 It has been reported that the spin relaxation time can exceed 1 second in an organic nanowire spin valve of Co/Alq₃/Ni.¹ A spin diffusion length as long as 13.3 nm has also been measured in junctions with amorphous rubrene and is predicted to reach millimeters in single-crystalline rubrene.² Beside spin transport, spin injection is a crucial premise to organic spintronics. Spin-polarized currents have been successfully injected into organic materials by contact with conventional ferromagnetic metals such as Fe, Co and Ni.^1–5 Recently, special interest^6–10 has been shown in magnetite Fe₃O₄, which has the inverse spinel structure, due to predicted half-metallicity in the bulk and a high Curie temperature.^11–13 The half-metallicity of Fe₃O₄ is characterized by a long demagnetization time, which is two orders of magnitude higher than for Ni, through femtosecond spin excitation.¹⁴ However, a significant reduction in the spin polarization at around the Fermi level is observed because of the inevitable presence of a surface or interface. Values of −(55 ± 10)% (Fonin et al.¹⁵) and −40% (Tobin et al.¹⁶) have been observed for the Fe₃O₄(100) surface at room temperature using spin-resolved photoemission spectroscopy (SPPES). Theoretical calculations with density functional theory (DFT)^17,18 suggest that this reduced surface spin polarization is mainly caused by surface electronic states arising due to O and Fe atoms at the topmost surface layer.

To improve the efficiency of spin injection from Fe₃O₄, it is necessary to enhance the spin polarization at the corresponding surface or interface. Some efforts have been made to achieve this through structural and electronic modifications of the surface by adsorption of hydrogen atoms or molecules.^17–24 Among these attempts, the adsorption of hydrogen atoms was found to be an effective way to enhance the surface spin polarization using spin-polarized metastable deexcitation spectroscopy (SPMDS) and SPPES.^19,20 DFT calculations confirmed that the half-metallicity can be recovered through atomic hydrogen adsorption at the Fe₃O₄(100) surface.^17,20 However, the −100% spin-polarized electronic states are localized to surface Fe atoms and do not extend to surface O atoms or adsorbed H atoms.¹⁷ In order to seek a magnetite surface with a high spin polarization at around the Fermi level not only at Fe atoms but also elsewhere on the surface, we have investigated the adsorption of group IV atoms (C, Si, Ge, Sn) on the Fe₃O₄(100) surface through DFT calculations. Group IV atoms were chosen because they can easily bond with O atoms and may have a significant effect on the spin polarization of the Fe₃O₄(100) surface, as for H adsorption. Another reason is that C is one of the main components of most organic materials employed in organic spintronics research. The carbonyl group (C=O) is commonly formed as a reactive intermediate and widely exists in many organic compounds such as ketones, esters, carboxylic acids, etc. Understanding of the nature of the interaction between C and the Fe₃O₄(100) surface will be helpful for a study of more advanced, functional organic materials with the same substrate. As for Si, Ge and Sn, they are widely-used semiconductor materials for integrated circuit fabrication. The study of spin injection to these materials is significant for spintronics based on present electronic devices. Our calculations predict that the C-adsorbed Fe₃O₄(100) surface not only has a wider spin-up band gap than the H-adsorbed one, but also that it has the ability to provide a −100% spin-polarized current. Calculations for the adsorption of Si, Ge or Sn atoms are also presented revealing quite different results, even though they belong to the same group.

II. Calculation methods

All calculations were performed within the framework of DFT using a plane-wave basis set, as implemented in the Vienna ab initio simulation package (VASP).^25,26 The calculation model and parameters are similar to those in our previous study of H adsorption on the Fe₃O₄(100) surface.¹⁷ Exchange–correlation interactions are described by the Perdew–Burke–Ernzerhof-generalized gradient approximation (GGA).²⁷ The projector-augmented wave method is used to represent the electron–ion interaction.^28,29 The Brillouin-zone integration is calculated with a 4 × 4 × 1 k-point grid using the Monkhorst–Pack method.³⁰ All calculations are spin-polarized with a 400 eV plane-wave energy cutoff.

A reconstructed substrate is used with a unit cell, which has been observed by low energy electron diffraction (LEED)^15,18 as well as scanning tunneling microscopy (STM)³¹ and reproduced by DFT calculations.^15,18,32 The surface is represented by a 13-layer slab with both sides terminated by octahedral Fe(B) atoms, which is energetically more favorable than a surface terminated by tetrahedral Fe(A) atoms.^33,34 The vacuum region is as large as 17.5 Å. Group IV atoms are adsorbed on the topmost and bottom-most surfaces. All adsorbed and substrate atoms are relaxed until the force on each atom is less than 0.01 eV Å⁻¹.

III. Results and discussion

A. Adsorption of C

For the Fe(B)-terminated Fe₃O₄(100) surface, there are two kinds of surface O atom (inset of Fig. 1), denoted as O1 (without an Fe(A) neighbor) and O2 (with an Fe(A) neighbor) in the following text. We investigated the coverage with four adsorbed atoms per unit cell. For C adsorption, the O1 site is the most energetically favorable among the six computed sites shown in Fig. 1. The adsorption energy (5.509 eV) is much larger than for H adsorption (3.096 eV).¹⁷ Here, the adsorption energy is defined as E_ads = (E_Fe3O4 + nE_C − E_C/Fe3O4)/n, where E_Fe3O4, E_C and E_C/Fe3O4 are the total energies of the clean Fe₃O₄(100) surface, a free C atom and the C-adsorbed surface, respectively. The tilting angle of C–O1 bonds from the surface normal (18.1°) is smaller than that of H–O1 bonds (56.3°). The C–O1 bond length (1.21 Å) is very close to that of C=O bonds (1.23 Å) in carbonyl compounds, indicating strong adsorption of C atoms on the Fe₃O₄(100) surface.

Fig. 1 The adsorption energy of a C atom at different sites on the Fe₃O₄(100) surface. The inset shows atoms at the top two layers of the substrate and labels of possible adsorption sites. A1 and A2 are the midpoints of the most and second nearest O1 atoms. B1 and B2 are the midpoints of the most and second nearest O2 atoms.

Fig. 2 shows the band structure and total density of states (DOS) of clean¹⁷ and the C-adsorbed Fe₃O₄(100) surface. An obvious band gap appears in the spin-up electronic band structure (left panel of Fig. 2(b)). Consequently, there are no spin-up electronic states at the Fermi level (right panel of Fig. 2(b)), which means half-metallicity is recovered by C adsorption. The recovery of half-metallicity has been theoretically and experimentally reported for the H-adsorbed Fe₃O₄(100) surface^17,19 and, as discussed in our previous paper,¹⁷ the low spin polarization at around the Fermi level on the clean Fe₃O₄(100) surface is caused by eight spin-up surface state bands (SSB) (Fig. 2(a)). For the H-adsorbed surface, only half of the SSB disappear due to O–H bonding, with the other half remaining but with slightly larger binding energies than those at clean surface. In contrast, no residual SSB are observed in the spin-up band structure in the C-adsorbed surface (Fig. 2(b)). The band gap (Δ_spin-up) of spin-up electronic states (0.73 eV) is wider than that of the H-adsorbed surface (0.65 eV) and closer to that of the bulk (0.87 eV).¹⁷ The energy interval (Δ_EF-VBM) from the Fermi level to the valence band maximum (VBM) of C/Fe₃O₄ is larger than that for H/Fe₃O₄ by 0.15 eV (Table 1). These larger values for Δ_spin-up and Δ_EF-VBM means they will be more easily resolved in experimental measurements and will be preferable for spintronic device applications. It should be mentioned that the number of adsorbed C atoms is equal to that of available O1 atoms. With a less coverage, the half-metallicity can't be completely recovered since there are still some dangling bonds at the surface. With a more coverage, the adsorbed C atoms assemble with each other, resulting in a stronger adsorbate–adsorbate interaction and a much weaker adsorbate–substrate interaction. The electronic structure of the adsorbed C atom is fairly different from that in Fig. 3.

Fig. 2 Band structure (left and middle panels) and total density of states (right panel) for a clean¹⁷ (a) and C-adsorbed Fe₃O₄(100) surface (b). Black and red lines represent spin-up and spin-down electronic states, respectively. The spin-down bands which have a strong contribution of C are highlighted with blue lines.

Fig. 3 Total and partial DOS of Fe(B), O2, O1 and the adsorbed C atoms. Positive and negative values represent spin-up and spin-down electronic states, respectively.

Table 1 Adsorption energy (E_ads), adsorbate–adsorbate interaction energy (E_M–M), bond lengths between neighboring atoms and tilting angle of adsorbate–O1 bonds from the surface normal (θ)

	H	C	Si	Ge	Sn	Clean surface
E ads (eV)	3.096	5.509	4.575	3.629	3.144
E M–M (eV)	0.293	1.081	1.676	1.621	1.786	—
d M–O1 (Å)	0.970	1.210	1.648	1.851	2.078	—
d M–FeB (Å)	2.762	2.479	2.729	2.823	3.047	—
d O1–FeB (Å)	2.116	2.327	2.185	2.109	2.094
d M–M (Å)	1.836/4.118	2.292/3.661	2.693/3.261	2.821/3.133	2.948/3.006	—
d O1–O1 (Å)	2.503/3.450	2.912/3.042	2.770/3.184	2.738/3.216	2.705/3.249	2.457/3.503
d O2–O2 (Å)	2.861/3.093	2.946/3.008	2.879/3.075	2.761/3.193	2.755/3.198	2.600/3.354
d FeB–FeB (Å)	2.560/3.394	2.451/3.503	2.574/3.380	2.745/3.209	2.759/3.195	2.917/3.037
θ (°)	56.3	18.1	1.4	1.3	3.3	—

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A magnetite thin film is a potential candidate for the magnetic electrodes of a spintronics device and is expected to inject spin-polarized current into organic materials. At the H/Fe₃O₄(100) surface, the adsorbed H atoms cannot allow current flow to other molecules at the interface since there are no electronic states around the Fermi level. Conversely, as shown by the local DOS of surface atoms (Fig. 3), significant spin-down peaks at −0.48 eV and −0.96 eV can be observed for C adsorption and an obvious change occurs to the surface O1 and O2 atoms. The corresponding bands which have a strong contribution of the adsorbed C atom are highlighted with blue lines in Fig. 2(b). Additionally, the density of electronic states around the Fermi level becomes considerable (Fig. 3) in contrast to the H/Fe₃O₄(100) surface where they may be neglected.¹⁷ Even the DOS of bare Fe(B) atoms at the C/Fe₃O₄ surface are much larger than those at the H/Fe₃O₄ surface. Furthermore, the spin polarization integrated from −0.5 eV to the Fermi level is −97.2%, −86.4%, −97.0% and −99.4%, respectively, for Fe(B), O1, O2 and C atoms at the topmost C/Fe₃O₄(100) surface. Therefore, in comparison with the H-adsorbed Fe₃O₄(100) surface, the C-adsorbed Fe₃O₄(100) surface would be favorable for spintronic devices since it has a much greater ability to create spin-polarized electron densities for organic materials.

The strong bonding of C–O1 causes significant electron donation and redistribution. To visualize the charge flow, differential charge densities (Fig. 4) are calculated according to the following formula for spin-up and spin-down electronic states, respectively:

Δρ_spin-up = ρ(C/Fe₃O₄)_spin-up − ρ(C)_spin-up − ρ(Fe₃O₄)_spin-up

Δρ_spin-down = ρ(C/Fe₃O₄)_spin-down − ρ(C)_spin-down − ρ(Fe₃O₄)_spin-down

where ρ(C/Fe₃O₄), ρ(C) and ρ(Fe₃O₄) are the charge densities of the C-adsorbed Fe₃O₄ surface, the C atoms, and the Fe₃O₄ substrate, respectively. The latter two have the same geometric structure as the adsorbed system. The yellow or blue color indicates the gain or loss of electrons. The spin-up differential charge density map (top panel of Fig. 4) indicates that spin-up electrons are transferred from the adsorbate to the substrate mostly through the p_x(p_y) orbital of C atoms. The surface atoms of the substrate gain electrons in the horizontal plane through the p_x(p_y) orbital of O1 atoms and the d_x2–y2 orbital of Fe(B) atoms. This electron donation process induces the saturation of the dangling bond of the surface O1 atoms and causes the disappearance of the spin-up SSB. In the spin-down differential charge density map (bottom panel of Fig. 4), the electron loss in the p_x(p_y) orbital of C atoms is much less than that in the spin-up case, whereas the electron gain in the p_z orbital is more prominent. A similar phenomenon occurs in the O1 atoms. Such an electron redistribution process is caused by the bonding of C–O1, which is contributed more by the p_z orbital and less by the p_x(p_y) orbital. The dominant loss of spin-up (p_x/p_y) and gain of spin-down (p_z) electrons in the C atom induces a small magnetic moment (−0.1 μ_B).

Fig. 4 Iso-surface of differential charge densities (0.01e Å⁻³) for spin-up and spin-down electronic states. Yellow: gained electrons. Blue: lost electrons. Only densities around half of the adsorbed C, surface O1, and FeB atoms are shown.

Now we turn to discuss the differences in the adsorbate–substrate interaction mechanism for H- and C-adsorbed Fe₃O₄(100) surfaces. It is clear that hybridization mainly occurs through orbitals of H-1s and O1-2p for H/Fe₃O₄. In contrast, except for s–p hybridization, there is significant p–p hybridization for C/Fe₃O₄ since the electronic states of C-2p and O1-2p overlap over a wide energy range (two bottom panels of Fig. 3). On the other hand, the interaction between H and Fe(B) is negligible for H/Fe₃O₄ because the bond length of H–Fe(B) (2.762 Å) is much longer than that of O1–Fe(B) (2.116 Å) and the electronic states of H-1s hardly overlap with those of Fe(B)-3d. In comparison, the bond length of C–Fe(B) (2.479 Å) in C/Fe₃O₄ is close to that of O1–Fe(B) (2.327 Å) and the overlap between C-2p and Fe(B)-3d is considerable (top and bottom panels of Fig. 3). Therefore, except for the strong interaction with O1 atoms, the adsorbed C atoms also interact with the surface Fe(B) atoms. The direct interaction between C and Fe(B) atoms can be observed in the spin-down differential charge density map (bottom panel of Fig. 4), in which electrons are gained via the d_xz(d_yz) orbital of Fe(B) atoms, shown in yellow. The s–p and p–p hybridization between C–O1 as well as the p–d hybridization between C–Fe(B) suggest that the interaction of the Fe₃O₄(100) surface with C atoms is much stronger than that with H atoms. This is consistent with the larger adsorption energy of C atoms (Table 2).

Table 2 The band gap Δ_spin-up and the energy interval from the Fermi level to the valence band maximum Δ_EF-VBM of spin-up electronic states

	Bulk Fe3O4	H/Fe3O4(100)	C/Fe3O4(100)
Δ spin-up (eV)	0.87	0.65	0.73
Δ EF-VBM (eV)	0.52	0.25	0.40

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B. Adsorption of Si, Ge and Sn

We also investigated the adsorption of other group IV elements such as Si, Ge and Sn on the Fe₃O₄(100) surface, since they have the same structure of outermost valence electrons and are more easily experimentally realized than C deposition due to lower evaporation temperatures. Si, Ge and Sn atoms adsorb almost vertically on O1 atoms with tilting angles less than 5° (Table 2). The adsorption energy is considerably smaller than that of the C atom and decreases with the increase of the atomic number Z. The bond length of M–O1 (M = Si, Ge and Sn) is longer than that of C–O1 and increases with Z due to the weaker adsorption energy and the larger atomic radius. It is known that the distribution of surface atoms is nonuniform due to surface reconstruction indicated by two values of bond lengths in Table 2. Atomic adsorption can induce variations in the geometric structure of surface atoms. As indicated by the bond lengths of O1–O1, O2–O2 and Fe(B)–Fe(B), the arrangements of the O1 and O2 atoms are more uniform for the adsorption of the low-Z element (C) than for high-Z ones (Si, Ge and Sn). Conversely, the distribution of Fe(B) atoms is more uniform in the adsorption of high Z elements. Thus, compared to the clean substrate, surface modification is largest for C adsorption and smallest for Sn adsorption. Another noticeable feature in the geometric structure is that the bond length of M–Fe(B) is much longer than that of O1–Fe(B) when Si, Ge or Sn atoms are adsorbed, indicating that the interaction between the adsorbate and surface Fe(B) atoms is negligible for high-Z element adsorption.

Compared to C adsorption, the Si-, Ge- or Sn-adsorbed Fe₃O₄(100) surfaces show clear variations in the band structure (Fig. 5). Several spin-up SSB appear with some of them crossing the Fermi level, eliminating half-metallicity. The appearance of spin-up SSB at the clean Fe₃O₄(100) surface (Fig. 2(a)) can be dominantly attributed to the contributions of surface O1, O2 and Fe(B) atoms.¹⁷ For Si-, Ge-, Sn-adsorbed Fe₃O₄(100) surfaces, the band-decomposed charge density (not shown) indicates that the SSB not only contains contributions from surface O1, O2 and Fe(B) atoms, but also from the adsorbed Si, Ge or Sn atoms. Some bands which have a strong contribution of adsorbate are highlighted with blue lines in Fig. 5. The substantial contribution of the adsorbates can also be observed in the local DOS. There are significant spin-up states around the Fermi level in the adsorbed Si, Ge and Sn atoms (Fig. 6). These states are caused by the adsorbate–adsorbate (M–M) interaction but not the adsorbate–substrate interaction because they mainly consist of p_x(p_y) orbitals and not p_z orbitals (Fig. 6). We also calculated the adsorbate–adsorbate (M–M) interaction energy (Table 2), which is defined as: E_M–M = (nE_M − E_nM)/n, where E_M and E_nM are the total energies of a free M (M = Si, Ge, or Sn) atom and a set of n-adsorbed M atoms with the same geometric structure of the adsorption system. The M–M interaction energy of Si, Ge and Sn is larger than that of C by 0.595, 0.540 and 0.705 eV per atom, respectively. Thus, both the weakening of the adsorbate–substrate interaction and the enhancement of the adsorbate–adsorbate interaction are responsible for the appearance of SSB as well as disappearance of the half-metallicity.

Fig. 5 Band structures of (a) Si/Fe₃O₄(100), (b) Ge/Fe₃O₄(100) and (c) Sn/Fe₃O₄(100) surfaces. Black and red lines represent spin-up and spin-down electronic states, respectively. Some bands which have a strong contribution of the adsorbate are highlighted with blue lines.

Fig. 6 Total DOS and partial DOS of the adsorbed C, Si, Ge and Sn atoms.

The surface electron spin polarization is one of the most important indices in spintronic devices and, since it is located at the surface, the spin polarization of the adsorbate is essential for the operation of a device. Of relevance to the limited energy resolution typical of experiments, the spin polarization integrated from −0.5 eV to the Fermi level is −99.4% for the C adsorption surface and +44.2% for Sn adsorption. This means that the polarity of surface spin polarization may be tuned by the choice of adsorbate, offering an additional advantage in using group IV elements to modify the surface properties of magnetite Fe₃O₄.

C. Strong electronic correlation effect

Calculations including the on-site Coulomb interaction (U) term for treating the electron-correlation effects have been proved to be successful in giving a reasonably good explanation of experimental optical spectra of Fe₃O₄.^35,36 In this study, we also conducted the calculation with the GGA + U method to investigate the effects of the electron correlation on the surface spin polarization. Coulomb (U) and exchange parameters (J) of 4.5 eV and 0.89 eV were used. The geometric and electronic structures of the clean Fe₃O₄(100) surface by GGA + U calculation have been discussed in ref. 37–40. For C adsorption, compared with GGA calculation, GGA + U yields a slight decrease of the bond length of C–O1 by 0.007 Å and increases of C–Fe(B) and C–C by 0.067 Å and 0.088 Å, respectively. The tilting angle of C–O1 decreases by 3.1°. The above means that the variation of geometric structure related to the adsorbate is insignificant. Geometric variation also occurs at deep layers. For example, the bond length of O–O changes by about 0.041, 0.031 and 0.012 Å for the first, second and third Fe(B)–O layer, respectively. The adsorption energy of C with GGA + U is 4.956 eV, which still indicates a strong chemical adsorption. The effect on the electronic structure and surface spin polarization by the atomic reconstruction is much less than those by the strong electronic correlation effect and the chemical bonding of C–O1 and not discussed here. Fig. 7(a) shows the total and partial DOS of surface atoms and Fe(B) in the second Fe(B)–O layer calculated with GGA + U. Compared with the local DOS in Fig. 3, the gap of spin-up electronic states is obviously enlarged. Furthermore, a gap is opened for the spin-down electronic states of the surface Fe(B) atom (2nd panel). The corresponding 2p states of C, O1 and O2 atoms, which overlap with Fe(B)-3d states, are shifted toward the deep level (3rd–5th panel). Such a deep level shift results in hardly any electronic states around the Fermi level for the adsorbate and all surface atoms. But there are considerable states located from −1.2 eV to −0.4 eV with −100% spin polarization. It should be mentioned that the gap opening is only for the atoms at the topmost surface. There are significant spin-down electronic states around the Fermi level for Fe(B) atoms at the second Fe(B)–O layer (topmost panel) and deeper layers, which indicates the half metallic behavior of the whole system. A similar gap opening of 0.3 eV due to the strong correlation effect has also been observed for surface atoms of clean Fe₃O₄(100).³⁷

Fig. 7 (a) Total and partial DOS of C, O1, O2 atoms and Fe(B) atoms at the topmost and the 2nd layer. (b) Local DOS of the adsorbed Si, Ge and Sn atoms calculated using the GGA + U method.

Similar to C adsorption, the adsorption energy calculated with GGA + U is smaller than that with GGA by 0.353, 0.176 and 0.094 eV, respectively, for Si, Ge and Sn adsorption. The geometric variation related to the adsorbate is minor. Fig. 7(b) shows the total and partial DOS of the adsorbed Si, Ge and Sn atoms with GGA + U calculation. Compared with Fig. 6, both spin-up and spin-down electronic states are shifted to a deep level for all the three adsorbates. Significant spin-up states contributed by p_x(p_y) orbitals can be observed around the Fermi level due to the adsorbate–adsorbate interaction. Consequently, the polarity of the spin polarization around the Fermi level remains positive, which is the same as that by GGA calculation.

IV. Conclusion

The electronic and magnetic properties of C-, Si-, Ge- and Sn-adsorbed Fe₃O₄(100) surfaces were investigated and compared with those of the H-adsorbed Fe₃O₄(100) surface. The adsorption of C is stronger than that of H atoms and can also restore half-metallicity to the surface. The C-modified Fe₃O₄(100) surface could also provide better device performance than for H-adsorption both due to the ability to inject spin-polarized electron density to organic materials and due to the width of the spin-up band gap. In comparison, modification by other group IV elements, such as Si, Ge, and Sn, did not restore the half-metallicity of bulk Fe₃O₄(100). The reason can be attributed to the weakening of the adsorbate–substrate interaction and the strengthening of the adsorbate–adsorbate interaction for the high-Z element adsorption.

Acknowledgements

This work was supported by the National Basic Research Program of China (973 Program) under Grant No. 2012CB933702, and the Natural Science Foundation of China under Grant No. 11179008, 90921013, and 11274284.

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