Surface electronic structure of the Fe 3 O 4 „ 100 ... : Evidence of a half-metal to metal transition

M. Fonin,1,* R. Pentcheva,2 Yu. S. Dedkov,3 M. Sperlich,4 D. V. Vyalikh,3 M. Scheffler,5 U. Rüdiger,1 and G. Güntherodt4 1Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany 2Department of Earth and Environmental Sciences, University of Munich, Theresienstr. 41, 80333 Munich, Germany 3Institut für Festkörperphysik, Technische Universität Dresden, 01062 Dresden, Germany 4II. Physikalisches Institut, Rheinisch-Westfälische Technische Hochschule Aachen, 52056 Aachen, Germany 5Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany Received 27 June 2005; published 29 September 2005


I. INTRODUCTION
5][6] Among them magnetite ͑Fe 3 O 4 ͒, a ferrimagnet with T C = 851 K, is an important material owing to its technological applications in catalysis and magnetic recording media.Moreover, Fe 3 O 4 has been theoretically predicted to be a half-metallic ferrimagnetic material with a conductive minority spin channel and semiconducting majority spin channel, 7,8 which results in a 100% spin polarization at E F .][11] Fe 3 O 4 crystallizes in the cubic inverse spinel structure ͑space group Fd3m, a = 8.396 Å͒ where the oxygen anions ͑O 2− ͒ form a close-packed face-centered-cubic ͑fcc͒ sublattice with Fe 2+ and Fe 3+ cations located in interstitial sites. 1 Two different kinds of cation sites exist in the magnetite crystal: tetrahedrally coordinated A sites occupied by Fe A ͑typically assigned with a charge state 3+͒, and octahedrally coordinated B sites occupied by Fe B ͑typically assigned with charge states 2+ and 3+ in equal numbers͒.The bulk crystallographic structure of magnetite can be represented as a stack of ͑100͒ layers containing either iron atoms in tetrahedral A sites or oxygen and iron ions in octahedral B sites ͓Fig.1͑a͔͒.In the B layers, only half of the octahedral sites are occupied and Fe ions form close-packed rows along the ͓011͔ direction.In successive B planes these rows are arranged perpendicular to each other.
The two different bulk truncations of Fe 3 O 4 ͑100͒ either with an A layer containing Fe A ions or with a B layer consisting of oxygen and Fe B ions ͓see Fig. 1͑b͔͒ are considered to be polar according to the classification given by Tasker. 12he previous understanding was that such surfaces must reconstruct to minimize the electrostatic energy.4][15][16][17][18][19][20][21] During the last decade, several possible structural models were proposed for the ͑ ͱ 2 ϫ ͱ 2͒R45°reconstruction [13][14][15][17][18][19][20][21][22] but the atomic arrange- ment of the Fe 3 O 4 ͑100͒ surface has been a matter of discussion.
Chambers et al. 18 investigated the Fe 3 O 4 ͑100͒ surface using x-ray photoelectron spectroscopy ͑XPS͒ and x-ray photoelectron diffraction ͑XPD͒.Applying the autocompensation rule, 23 the authors concluded that the surface structure is a half-filled A layer with strong inward relaxations of the surface layer.More recently, low energy ion scattering ͑LEIS͒ experiments 26 also favored this termination.In a molecular dynamics calculation with classical potentials Rustad et al. 22 proposed a 0.5 ML A termination where the surface and half of the subsurface Fe A relax towards octahedral positions in the surface B layer.
In contrast, Voogt et al. 17 suggested a structure consisting of a B-terminated surface with oxygen vacancies.The possibility of ordered hydroxyl groups was also discussed in this work. 17The former model of the B-terminated Fe surface with oxygen vacancies has been supported in a STM study by Stanka et al. 19 The STM images show rows of octahedral iron atoms exhibiting a wavelike structure which was attributed to relaxations away from the missing oxygen atoms in the B layer. 19Also, a noncompensated termination with charge ordered B layer was suggested from STM measurements performed using ferro- 27 or antiferromagnetic tips. 20,21owever, the observed magnetic contrast alone cannot provide a clue on the stabilization mechanism of the surface.Bipolaronic effects in the B termination have also been discussed as a possible interpretation of the magnetic contrast obtained with an antiferromagnetic STM tip. 21ecently, using ab initio atomistic thermodynamics Pentcheva et al. 24 compiled a surface phase diagram for a variety of stoichiometric and nonstoichiometric configurations and found that the lowest energy configuration is a modified bulk termination with a ͑ ͱ 2 ϫ ͱ 2͒R45°periodicity which does not fulfill the autocompensation rule. 24The ideal ͑1 ϫ 1͒ termination was found to be Jahn-Teller instable.The theoretical results are confirmed by qualitative x-ray diffraction 24 ͑XRD͒ and low-energy electron diffraction ͑LEED͒ analyses. 255][36] Recent investigations, 30,36 however, showed that band dispersions 7,8 must be taken into account for the interpretation of photoelecton spectra of Fe 3 O 4 .
4][35] The spin polarization P͑h͒ of the photoelectrons with energies up to 11.2 eV was measured by a Mott scattering detector.A maximum value of −60% near the Fermi energy ͑E F ͒ was measured at around 5 eV photon energy at 10 K. 34 From a single-ion-in-a-crystal-field ͑SICF͒ model a maximum value of the spin polarization at T =0 K is P = −66.6%͑Refs.34 and 35͒ which was considered to be in agreement with the measured value of −60%.
Recently, spin polarization measured on the Fe 3 O 4 ͑111͒ surface at E F at room temperature ͑RT͒ by means of spinpolarized angle-resolved photoemission spectroscopy ͑SPARPES͒ was reported to be as high as −͑80± 5͒% which can be an evidence of the half-metallic nature of the magnetite in ͓111͔ direction. 36However, for the ͑100͒-oriented Fe 3 O 4 thin films the spin-resolved photoelectron spectroscopy measurements of thin epitaxial films grown on MgO͑100͒ substrates yielded spin polarization values of only −͑40-55͒% near E F . 38,39These values are significantly lower than the −100% predicted by local spin density approximation ͑LSDA͒ calculations for the bulk material 8 as well as the −͑80± 5͒% measured on the ͑111͒-oriented Fe 3 O 4 surface at E F at RT. 36 The low value for the ͑100͒ surface was ascribed either to surface imperfection 38 or to strong electron correlation effects. 39 the present paper we report a combined experimental and theoretical study of the crystallographic as well as electronic surface structure of epitaxial Fe 3 O 4 ͑100͒ thin films.Experimentally, in situ prepared, well-characterized Fe 3 O 4 ͑100͒ films were studied by means of LEED, STM, and SP-PES.On the theoretical side, DFT calculations are performed to investigate the surface atomic arrangement as well as the electronic structure of Fe 3 O 4 ͑100͒.The contrast in measured STM images is interpreted on the basis of STM simulations.The work-function value of the Fe 3 O 4 ͑100͒ surface extracted from the cutoff of the photoelectron spectra is compared to the value predicted for the lowest energy configuration by the DFT calculations.Furthermore, the spin polarization at the Fermi energy is measured via SP-PES and compared to the value obtained from the DFT calculations.Finally, based on the DFT calculations, we analyze how the symmetry breaking at the surface as well as of the surface reconstruction alter the electronic properties.

A. Experimental setups
The STM experiments were carried out in an ultra-high vacuum ͑UHV͒ system with a base pressure of 8 ϫ 10 −11 mbar equipped with LEED optics, a gas inlet, e-beam evaporation cells, and an Omicron UHV AFM/STM.All STM measurements were carried out at RT using electrochemically etched polycrystalline tungsten tips cleaned in UHV by Ar + sputtering.The presented STM images were taken in the constant-current mode.
The SP-PES measurements were carried out at U125/1-PGM beamline at the BESSY II storage ring.The UHV system for SP-PES ͑base pressure 8 ϫ 10 −11 mbar͒ consists of a UHV chamber equipped with LEED optics, a gas inlet, e-beam evaporation cells, and an Omicron SPLEED spin analyzer.The SP-PES spectra were recorded in normal emission.The total energy resolution and the acceptance angle were set to 100 meV and 6°, respectively.
The work function as well as x-ray absorption spectroscopy measurements ͑XAS͒ were performed in an UHV system located at the Russian-German Laboratory at the BESSY II storage ring.An UHV chamber ͑base pressure 1 ϫ 10 −10 mbar͒ equipped with LEED optics, a gas inlet, e-beam evaporation cells, and a 127°CLAM4 analyzer was used for these measurements.XAS spectra have been collected in the total electron yield mode and normalized to the maximum intensity.

B. Sample preparation
The epitaxial Fe 3 O 4 ͑100͒ films used for STM and SP-PES measurements were prepared on MgO͑100͒ single crystals.The epitaxial Fe 3 O 4 ͑100͒ films for the work-function measurements were prepared on a W͑100͒ single crystal.The MgO͑100͒ substrates were cleaned in acetone, isopropanol, and methanol before the introduction into UHV and finally annealed in situ in 5 ϫ 10 −6 mbar O 2 for 2 h at about 600 °C.The W͑100͒ single crystal was cleaned in situ by using standard cleaning procedure: heating in O 2 at 1800 K followed by flashing up to 2300 K. Fe was evaporated from high purity rods heated by electron bombardment.High quality 150-300 Å thick Fe 3 O 4 ͑100͒ films were prepared in situ by Fe evaporation on MgO͑100͒ or W͑100͒ substrates in O 2 atmosphere.During the growth, the O 2 pressure was maintained at 2 ϫ 10 −6 mbar and moderate substrate temperatures of about 300 °C were used to prevent magnesium interdiffusion in case of MgO͑100͒ substrates.The high degree of crystalline order of the epitaxial Fe 3 O 4 ͑100͒ films obtained in our experiments has been checked by LEED and STM.The surface cleanliness has been monitored by valence-band as well as core-level photoemission.Figure 2 presents the Fe L 2,3 edge XAS spectrum of the epitaxial Fe 3 O 4 ͑100͒ film in comparison with that of the epitaxial Fe͑100͒ film.The characteristic multiplet structure of the XAS spectrum at the Fe L 2,3 and the O K absorption edges ͑not shown here͒ of Fe 3 O 4 agree with earlier experiments, 28,29 confirming good bulk quality of the prepared samples.

C. Theoretical methods
The DFT calculations were performed using the fullpotential augmented plane waves ͑FP-APW͒ method in the WIEN2K implementation 40 within the generalized gradient approximation ͑GGA͒ 41 of the exchange-correlation functional.The Fe 3 O 4 ͑100͒ surface was modeled in the supercell geometry where the slab for, e.g., the B termination, consists of seven B layers and six A layers.The vacuum between the repeated slabs amounts to 10 Å.The lateral parameter of the supercell is set to the GGA bulk lattice constant, 8.42 Å, which is in good agreement with the experimental value of A STM overview of a ͑ ͱ 2 ϫ ͱ 2͒R45°reconstructed Fe 3 O 4 ͑100͒ surface is shown in Fig. 4. Atomically flat terraces with the step edges of nondefined shape can be clearly seen, revealing a layer-by-layer growth.The average step height was found to be about 2.1 Å ͑see height profile in Fig. 4͒, which corresponds to the distance between adjacent A-A or B-B planes of the bulk Fe 3 O 4 structure.Atomically resolved rows running along the ͓011͔ and ͓01 ¯1͔ directions are clearly visible in this STM image ͑Fig.4͒.The rows on neighboring terraces are oriented in a perpendicular fashion.A change of the row direction can be also observed within a terrace with the transition regions appearing as lines along the ͓001͔ or ͓010͔ directions ͑marked by black lines in Fig. 4͒.
In the high-resolution STM image of a typical terrace ͑Fig.5͒, rows consisting of bright protrusions are imaged.The distance between two bright protrusions within the same row was measured to be about 3 Å, and the distance between two rows is about 6 Å. Alternating pairs of bright protrusions within each row are shifted into the same direction perpendicular to the rows, resulting in a wavelike surface structure.Regularly ordered large dark depressions appear at the wide openings of the waves.The centers of these depressions are separated by 8.4 Å and have a ͑ ͱ 2 ϫ ͱ 2͒R45°symmetry.
Similar square-lattice structure types were also observed in STM measurements by Stanka et al. 19 It should be men-  5 are most likely Fe B ions, which is in agreement with other STM studies. 13,15,16,19However, the precise atomic structure of the Fe 3 O 4 ͑100͒ surface remains unclear.
In order to resolve the structure and composition of the surface layer, DFT calculations for a variety of stoichiometric and nonstoichiometric models of Fe 3 O 4 were performed.In the framework of ab initio atomistic thermodynamics, a surface phase diagram of Fe 3 O 4 ͑100͒ as a function of the oxygen pressure was compiled. 24The most striking result is that a modified bulk termination with a B layer showing a wavelike structure has the lowest energy over a broad range of oxygen pressures.Unlike the traditional view of a reconstruction as an ordering of surface defects, in this structure the ͑ ͱ 2 ϫ ͱ 2͒R45°reconstruction emerges as a re- sult of a Jahn-Teller-distortion of the surface layer.
Figure 6 shows the top ͑a͒ and the side ͑b͒ views of the theoretically predicted energetically most favorable surface structure.A strong lateral relaxation of 0.30 Å of the oxygen atoms with a missing Fe A neighbor towards the Fe B row invokes an alternating shift of Fe B pairs by ±0.09 Å perpendicular to the Fe B row.Due to these lateral relaxations a wavelike pattern along the ͓011͔ direction develops on the surface with neighboring B rows running in antiphase to each other.
To interpret the atomically resolved STM images we performed STM simulations of the modified B termination pre- dicted by DFT calculations.The simulated STM image in Fig. 6͑c͒ is obtained in the constant current mode using the Tersoff-Hamann approximation. 42The charge density was integrated from E F to E F + 1.1 eV, which corresponds to the voltage used in the STM measurements presented above.In Fig. 6͑c͒ light protrusions mark the positions of the surface Fe B .As indicated by the arrows, alternating pairs of such protrusions are shifted perpendicular to the ͓011͔ direction giving rise to a wavelike pattern.Although the wavelike structure is clearly visible in the side view of the DFT structure in Fig. 6͑b͒ it is much less pronounced than in the experimentally obtained STM image in Fig. 5.This may be attributed to a softness of the surface with respect to vibrational modes.
Comparison of the measured and calculated work function ͑⌽͒ of the Fe 3 O 4 ͑100͒ surface gives further support for the modified B termination.For this experiment epitaxial Fe 3 O 4 ͑100͒ films were grown on a W͑100͒ single crystal.The work function is determined from the cutoff of the photoelectron spectra.The work-function values of W͑100͒ ͑4.63± 0.15 eV͒ and Fe͑100͒ ͑4.07± 0.15 eV͒ were measured as reference and the latter agrees well the value for an Fe͑100͒ whisker. 43A work function of ͑5.20± 0.15͒ eV is measured for the Fe 3 O 4 ͑100͒ surface.The DFT calculations show that the formation of the modified B termination is connected not only with an energy gain of approximately 20 meV/ Å 2 with respect to the ideal B termination, but also with a reduction of the work function of 0.46 eV from 5.78 eV for the bulk truncated to 5.32 eV for the modified configuration.A reduction of ⌽ indicates a decrease of the dipole moment induced on the surface, i.e., a decrease in polarity.We note that the measured ⌽ = 5.20± 0.15 eV and the calculated value of the modified B termination ⌽ = 5.32 eV are in good agreement, thus giving another proof for the validity of the proposed structural model.
In the bulk, magnetite shows a half-metallic behavior with a band gap in the majority spin channel of approximately 1.5 eV and a 100% spin-polarization due to the t 2g states of Fe B at E F in the minority spin channel. 8As will be discussed, SP-PES measurements and DFT calculations indicate that the stabilization of the Fe 3 O 4 ͑100͒ surface and the unusual lattice distortions are connected with strong changes in the electronic properties.
Figure 7 shows representative spin-polarized photoemission spectra together with total photoemission intensity of the Fe 3 O 4 / MgO͑100͒ system as a function of binding energy.The position of the Fermi energy corresponds to that of a polycrystalline Au foil in the electrical contact with the sample.The spectra were normalized to the current recorded from the last Au-coated mirror of the beamline.The photon energy was tuned in 2-eV steps over the range 40-60 eV, including the Fe 3p-3d excitation threshold at 58 eV, where a strong resonance behavior was observed.In the region between 0 eV and 9 eV of binding energy, considerable changes in intensity as well as in spectral shape of the features derived from the O 2p and Fe 3d states can be observed as a function of the photon energy.Only weak dispersions ͑if any͒ of the photoemission features were observed along the ⌫-X direction of the Fe 3 O 4 Brillouin zone.In comparison to the present study, well-pronounced band dispersions were reported on the Fe 3 O 4 ͑111͒ 30 and Fe 3 O 4 ͑100͒ 44 which can be due to the better angle resolution of ±1°compared to the acceptance angle of 6°used in the present study.In the valence band of Fe 3 O 4 ͑100͒ several photoemission features can be clearly observed: a peak at 0.5 eV, a small shoulder at 2.2 eV, peaks at 3 eV and 5.9 eV, and a shoulder at 7.6 eV.The positions as well as the general trend of the resonant enhancement of these features is very similar to those already reported for the Fe 3 O 4 ͑111͒ thin films. 30However, a more detailed analysis of the origin of the photoemission features and their behavior is beyond the scope of the present paper and will be presented elsewhere. 44igure 8 shows the spin-resolved photoemission spectra together with the total photoemission intensity recorded in normal emission with h =58 eV ͑a͒, the same spectra in the region near E F ͑b͒, and the resulting spin-polarization values ͑c͒ as a function of the binding energy relative to the Fermi level of the Fe 3 O 4 ͑100͒ film.The value of −͑55± 10͒% at E F measured on the Fe 3 O 4 ͑100͒ surface at RT is significantly lower than the one for the ͑111͒ surface ͑−80% ͒ 36 as well as the −100% predicted by LSDA calculations. 8However, these band structure calculations were performed for the bulk material not taking into account surface structure effects, which can prevail in the ultraviolet photoemission spectroscopy measurements.
We have now calculated the surface electronic structure of striking feature of the spin-polarized bands ͑Fig.9͒ are the states that appear in the band gap of the majority subband leading to a reduction of the spin polarization to about −40% at E F and a loss of half-metallicity at the Fe 3 O 4 ͑100͒ surface.The calculated spin-polarization value is somewhat lower than −͑55± 10͒% obtained from the photoemission measurements.A possible reason for the difference between the calculated and the experimentally measured spin-polarization values may be the finite size of the slab used to model the Fe 3 O 4 ͑100͒.As the states at the Fermi level are relevant for the transport properties of the material their character was analyzed in detail.The spatial distribution of the electronic states in the majority spin channel within the surface plane displayed in Fig. 9͑a͒, shows that these are a hybridization of d x 2 −y 2 states of octahedral iron in the surface layer and p x , p y states of the surface oxygen without a subsurface tetrahedral iron neighbor.
In order to gain an understanding of how the electronic structure changes from bulk to the surface as well as to resolve the influence of the surface reconstruction, we have plotted the projected DOS of a Fe B in the bulk ͓Fig.9͑c͔͒ as well as on the surface in the ideal ͓Fig.9͑d͔͒ and modified B termination ͓Fig.9͑e͔͒.In the bulk the crystal field splitting of the e g and t 2g states of the octahedrally coordinated iron amounts to 2.0 eV.In the majority spin channel both the e g and t 2g are occupied while in the minority spin channel the e g states are unoccuppied and lie 2 eV above the Fermi level and E F crosses the t 2g band.On the surface, due to the broken symmetry in the z direction, the degeneracy within the e g doublet and t 2g triplet is lifted.In the majority spin channel d x 2 −y 2͑d z 2͒ states are shifted to higher ͑lower͒ energies and the former cross the Fermi level even in the ideal ͑unrelaxed͒ B termination ͓Fig.3.6 B for the B termination with bulk positions of the atoms to 3 B for the modified B termination.
As a result of the spin flip effect in the minority spin channel, d xz and d yz states are partially occupied and shifted to lower energies, while d xy states of the surface iron remain unoccupied at 0.3 eV above E F .The d z 2 states are pulled to lower energies at 1.1 eV above the Fermi level, almost touching the t 2g band and the splitting between d z 2 and d x 2 −y 2 states amounts to 1 eV.We note that the positions of the d orbitals differ from the qualitative picture proposed by Shvets et al. 21which suggests a small and large splitting of the orbitals of Fe 2+ and Fe 3+ , respectively.The authors of Ref. 21 conclude that only Fe 2+ may be subject to a Jahn-Teller distortion.The model of Shvets et al. 21considers the extreme case where the sixth electron is completely localized at Fe 2+ , while the DFT-GGA calculation renders an average occupation of 5.38 d electrons within the muffin tin for both Fe B ions in the surface.Recently, Wright et al. 45 obtained evidence from x-ray and neutron powder diffraction that the charge disproportionation between octahedral B iron below the Verwey temperature is 2.4 and 2.6, which is only 20% of the ideal value for Fe 2+ and Fe 3+ .This suggests that assigning integer charges to the iron ions may not be appropriate.Still, the influence of strong electron correlation effects on the surface electronic structure remains to be investigated. 46

IV. CONCLUSION
The formation of the wavelike pattern along the ͓011͔ direction observed by STM is explained using DFT calculations as a Jahn-Teller distortion in the surface B layer. 24STM simulations indicate that the contrast in the STM images arises from octahedral iron ions shifted pairwise perpendicular to the ͓011͔ direction.The work-function value of the Fe 3 O 4 ͑100͒ surface extracted from the cutoff of the photoelectron spectra are consistent with those predicted on the basis of DFT calculations.Both the spin-resolved photoemission experiments and the DFT-GGA density of states give evidence for a half-metal to metal transition at the Fe 3 O 4 ͑100͒ surface: the measured negative spin polarization of about −͑55± 10͒% at the Fermi level and the theoretical value of −40% are significantly lower than the −100% predicted by LSDA calculations for the bulk magnetite crystal as well as the −͑80± 5͒% obtained for the Fe 3 O 4 ͑111͒ films.The electronic states in the majority spin-channel responsible for the reduction of spin polarization are dominated by d x 2 −y 2 states of surface Fe B .
Figure 3 shows a typical LEED pattern of the ͑100͒oriented surface of an epitaxial Fe 3 O 4 film grown on MgO͑100͒ substrate.A clear ͑ ͱ 2 ϫ ͱ 2͒R45°reconstruction with respect to the ͑100͒-unreconstructed Fe 3 O 4 surface unit cell is visible.A lattice constant of 8.4± 0.15 Å was measured from the observed LEED patterns.

FIG. 4 .
FIG. 4. ͑Color online͒ 50ϫ 50 nm 2 STM image of a ͑ ͱ 2 ϫ ͱ 2͒R45°reconstructed Fe 3 O 4 ͑100͒ surface.Tunneling param- eters: U T = 1.1 V, I T = 1.2 nA.A line profile ͑A͒ corresponds to the STM height profile along the white line shown in the STM image showing step heights of about 2.1 Å.
FIG. 7. ͑Color online͒ Spin-resolved valence band photoemission spectra ͑spin up: blue open up triangle; spin down: red solid down triangle͒ and total intensity ͑black solid circle͒ of a Fe 3 O 4 ͑100͒ thin film on MgO͑100͒ as a function of binding energy recorded at RT in normal emission at 42-60 eV photon energy.
FIG. 8. ͑Color online͒ ͑a͒ Spin-resolved photoemission spectra ͑spin up: blue open up triangles; spin down: red solid down triangles; total photoemission intensity: black solid circles͒ of the Fe 3 O 4 ͑100͒ /MgO͑100͒ system recorded with h = 58 eV in normal emission, ͑b͒ the region near E F , and ͑c͒ the spin polarization as function of binding energy of the Fe 3 O 4 ͑100͒ /MgO͑100͒ system.