First Principles Study of Cu-Embedded Ni ( 110 ) Surfaces

The atomic geometries and electronic band structures of Cu-embedded Ni(110) surfaces were studied theoretically. First principles calculation with spin-resolved local density functional theory was applied to the Ni(110) surface, and one to four Cu-embedded Ni(110) surfaces in the 2×2 surface unit cell. The optimized structures for the Ni(110) surface showed that interlayer spacing between the first and the second layer shrunk 11.1% of the bulk distance, but the second and third layer spacing expanded by 2.9% in agreement with previous studies. For the Cu-embedded surfaces, embedded Cu atoms are 11-14 pm higher than the top Ni atoms, which is about four times larger than the difference of the atomic radii. The detailed band structures and corresponding local density of states (LDOS) were calculated. At the embedded Cu atom sites, the surface LDOS near the Fermi level was reduced in agreement with previous scanning tunneling microscopy observation. In addition, by increasing the number of Cu atoms in the top layer, magnetic moments were decreased near the surface regions. [DOI: 10.1380/ejssnt.2009.681]


I. INTRODUCTION
Surface metal alloys have drawn a great deal of attention for decades due to such potential new functions as catalytic reactions, corrosion resistance, and novel magnetic properties.Among such alloys, Cu-Ni alloys are one of the most studied materials since the beginning of surface science, particularly in terms of Cu segregation on alloy surfaces.Bulk Cu-Ni alloys have no miscibility gap at high temperatures and form uniform solid solutions for all fractions, but Cu is known to be segregated on the alloy surface by heat treatment since its surface energy is lower than that of Ni [1].Therefore, Cu overlayers on Ni and Cu-Ni alloy surfaces are thought to be energetically stable.However, our recent scanning tunneling microscopy (STM) study [2] showed that, for such relatively open surface structures as the (110) face, deposited Cu displaces surface Ni, and Cu is embedded into the topmost layer rather than forming two-dimensional Cu islands on top of the Ni surface.As a result, even for one monolayer Cu deposition the surface is not fully covered by the Cu overlayer, but the Cu/Ni mixed layers are stabilized.For other faces such as Ni(100) [3] and Ni(111) [4], no such intermixing was reported, at least at room temperature.This Cu incorporation into the top Ni(110) surface layer is due to the marginal mixing enthalpy of Cu into Ni [5] as well as the open nature of the fcc(110) surface structure that enables a three-body cyclic exchange with an adsorbed atom [6].

II. CALCULATION SCHEME
We employed the first principles calculation code based on density functional theory [7].The projectoraugmented wave method (PAW) was used for the Ni and Cu pseudopotentials, and the spin-resolved local density functional was amended by generalized gradient approximation (GGA).Calculation for bulk Ni showed that lattice constant and cohesive energy were reproduced respectively within 0.2 and 2.0% of the experimental values with energy cut off of 24.77 Ry.Obtained magnetic moment 0.62 µ B /atom was in fairly good agreement with the experimental value in the literature [8].With this lattice constant, we constructed a (110) oriented slab structure with a 2×2 surface unit cell, and a 11-layer thick with 0.5-nm vacuum gap on both sides.The middle layer was fixed to be the calculated bulk lattice constant.The following Schoenflies point group symbols referred to as this slab geometry.The top view of the atomic geometry of the Ni(110) surface and the unit cell employed in this calculation are schematically illustrated in Fig. 1.We used the Methfessel-Paxton method to evaluate partially filled bands [9] and optimized the smearing energy width to be σ=0.12eV.By compromising the number of k -points in the reciprocal lattice and the acceptable calculation time, we chose a two-dimensional k -mesh of (k x , k y )=12×10, which corresponds to 0.526 nm −1 and 0.446 nm −1 along [ 110] (denoted as x) and [001] (y) directions, respectively.This corresponds to 42 irreducible k points with the D h 2 point group.Except for the middle layer, all atoms were fully relaxed until the force reduced below 0.1 eV/nm, and the wavefunction and the charge density were both iterated until the total electron energy converged to 10 µeV in the unt cell.We carefully verified that this kmesh was sufficient to converge the atomic geometry and the electron energy by changing the number of k points.

A. Ni(110) surface
Before calculating the Cu/Ni surface, we studied the Ni(110) surface with the same unit cell.The optimized interlayer spacings are shown in Table I with many previous experimental values and a theoretical prediction employing the equivalent-crystal theory.Experimentally, there is general agreement that first to second layer spacing d 12 shrinks 8 to 9%, but second to third layer spacing d 23 expands 3% comparing with the bulk value.Our calculated d 12 is somewhat overestimated, but d 23 is correctly predicted.The spin-resolved band structure and the local density of states (LDOS) are represented in Fig. 2. We referred to ref. 26 for the two-dimensional Brilliouin zone of the Ni(110) surface.The first Brilliouin zone for the Ni(110)2×2 unit cell is half of the original 1×1 unit cell for both X and Ȳ directions.Therefore, we denoted the midpoints of Γ − X and Γ − Ȳ lines as 1 2 X and 1 2 Ȳ, respectively, and the center of the original 1×1 Brilliouin zone as 1  2 S. In Fig. 2, most parts of the bands near and below E F come from Ni 3d -derived bands, and the majority (denoted as up, blue lines) and the minority (down, red lines) spin bands are split across E F .The value of exchange splitting ∆E ex is 0.75 eV, which is more than three times larger than the photoelectron spectroscopy [27].The discrepancy, however, reflects the inherent nature of photoelectron spectroscopy and is well documented [28,29].
The layer-resolved LDOS for the top and bottom layers is presented in Fig. 3.Each LDOS is decomposed into spherical harmonics for each spin, and each component is color coded.For both the top and bottom Ni atoms, most parts of the LDOS come from the Ni 3dderived bands, and the exchange splitting between the majority and minority spins again resembles that of the total density of states shown in Fig. 2.More importantly, the exchange splitting at the bottom atom (Fig. 3  (upper panel) does not significantly change.This is because the lower coordination of the top Ni atom and thus narrower d -bands [28,30,31] is almost compensated by the smaller d 12 compared to the bulk, although slight reduction of d -derived LDOS is seen below -3.5 eV.The spectral similarity between the bulk and surface Ni atoms near E F indicates no magnetic dead layer in agreement with experimental observations [32].Indeed, the theoretical magnetic moment at the top Ni atom is 0.75 µ B /atom, which is slightly enhanced compared to the bulk moment [28,30].Thus the pinning of the minority spin subband is almost restored at the surface layer, and the surface LDOS as well as the magnetic moment are not significantly altered by the surface formation.Finally, we obtained the surface energy of 2.219 J/m 2 or 1.214 eV/1×1 unit for the structure optimized Ni(110) surface. of the Ni(110) surface, we calculated these Cu-embedded Ni(110) surfaces.
When one of the four Ni atoms in the top layer is replaced with Cu (denoted as Cu 1 Ni 3 /Ni(110) hereafter), the optimized atom heights measured from the middle layer are listed in Table II.The symbols of the atoms in Table II correspond to the geometry indicated in Fig. 4. The embedded Cu protrudes 11.8 pm into the vacuum against the average height of the top Ni atoms, as schematically drawn in the bottom panel in Fig. 4. The amount of protrusion is smaller than the simple steric hindrance of 38 pm, assuming hard spheres with the bulk atomic radii, but it is significantly larger than the 3.2 pm difference of the atomic radii between Cu and Ni.The corrugation can be compared to some substitutional surface alloys with c(2×2) reconstruction, such as Ni(110)c(2×2)Sn [33], Cu(110)c(2×2)Mn [34], and Ni(110)c(2×2)Mn [25], where corrugations of the embedded atoms are larger than the difference of the atomic radii.Although corrugation of the Cu-embedded Ni surface is fairly small compared to those alloys, enhanced corrugation is due to the depletion of the electron density at the surface layer [33].The average interlayer spacing between the top three Ni atoms and the second Ni layer is shrunk by 10.5% from the bulk value, which is slightly smaller than the d 12 of the Ni(110) surface.d 23 also has a somewhat smaller value of 2.2%.Within the D h 2 point group, the second layer is allowed to move laterally, but the stable position for the a' atom (see Fig. 4(a)) is only 0.09% of the atomic distance, or a 0.2 pm shift toward the +x direction and virtually no shift in the y direction from the bulk position.Even by lowering the symmetry such as C h 1 , displacements still converge to virtually the same geometry.Therefore, the underneath layers are almost intact even if the surface atom is replaced with Cu.The embedded Cu indeed occupies a quite similar position to the Ni atom except for marginal protrusion into the vacuum, which is reflected by smoothing surface elec- tron distribution [35].As shown in Fig. 5, partial waves around Cu in the top layer have an asymmetric d component between the major and minor spins, indicating that in addition to sp conduction bands, 3d -derived bands are affected by the surrounding Ni atoms.As clearly seen in the top panel of Fig. 5, the Cu LDOS at E F is smaller than that of Ni, which is consistent with scanning tunneling microscopy observations where clear depression was seen at the Cu sites in the topographic images and the calculated charge density maps [2].The suppression indicates that adjacent Ni atoms do not significantly contribute to Cu LDOS at the Cu site.
When two Cu atoms are embedded in the top Ni(110) layer (denoted as Cu 2 Ni 2 /Ni(110)), there are three possible Cu/Ni configurations: (a) aligned, (b) crossed, and (c) staggered structures, as schematically illustrated in Fig. 6.The relative energies for these configurations, referred to as the aligned structure, are also indicated in the vicinity of each configuration.The optimized heights of these structures are shown in Table III.The aligned structure, where Cu atoms are close to each other in the [ 110] row, is the stablest configuration, although it seems sterically unstable.Even in the calculation with lower symmetry such as the C v 2 point group, which allows a zigzag Cu row, the atomic geometry of the convergent structure is almost the same as the D h 2 constraint.The stability of the aligned structure originates from the fact that the cohesive energy between Cu-Cu and Ni-Ni is larger than Cu-Ni [5], and thus Cu and Ni tend to be phase separated.Of course decomposition is hindered by the entropic gain by Cu-Ni mixing for bulk Cu-Ni alloy.The phase separated Cu and Ni rows at the surface will be energetically stabler than the Cu-Ni mixed rows.Staggered and crossed structures have the same sequence within the [ 110] row, but the energy of the staggered structure is lower than that of the crossed structure due to the energy gain by homogeneous charge density via electrostatic coupling between  III.Relative energies referred from aligned structure are indicated near each configuration.
rows [35].Interestingly, the geometrical corrugations between Cu and Ni for the aligned, crossed, and staggered structures are 10.9, 11.1, and 13.6 pm, respectively, quite similar to the single Cu case.For all three structures, the height differences between the top Cu and Ni are remarkably smaller than that expected from the geometrical constraint deduced from bulk Ni and Cu radii, therefore steric hindrance does not significantly contribute to the total energies.Furthermore, the second Ni layer is virtually unaffected by these replacements.
We further studied a three Cu case (Cu 3 Ni 1 /Ni(110)), and the optimized heights are shown in Table IV.The average height of the embedded Cu atoms is 11.5 pm higher than Ni in the top layer, and the second layer is restored again.The spin-resolved LDOS for the top four atoms are depicted in Fig. 7.An interesting feature is an apparent shift of the Cu 3d -derived minority spin DOS peak located at -2.1 eV for a Cu and b Cu toward larger binding energy for c Cu.This chemical shift is caused by the different number of Ni neighbors for each Cu; i.e., c Cu has six Ni neighbors while a Cu and b Cu have only four.A larger number of adjacent Ni leads to larger hybridization between the Cu sp bands and the Ni 3d orbitals, which reduces the Cu core charge screening and increases Cu 3d binding energy.Similar behavior is also seen for the two Cu-embedded cases where the Cu 3d shift toward higher binding energy for crossed and staggered structures.Experimentally, weak shift toward the higher binding energy of the Cu 3d peak was previously seen by Cu alloying into  the Ni rich layer [36].Finally, when the surface is fully covered by one monolayer Cu (Cu 4 /Ni(110)), the average height of the top Cu layer is 621.7 pm measured from the middle layer, which again closely coincides with the previous Cu heights for the one to three embedded Cu cases.No undulation between the top Cu atoms indicates that the steric effect is negligible.
For the top Ni layer, a lack of counterpart reduces the dd interaction and suppresses the sp-d hybridization, narrowing the Ni 3d -derived bands and thus increasing the d component of the wavefunctions.Because the total charge is fixed, the electron occupation of the minority d bands reduces.The magnetic moment, which is the difference of electron occupation between the majority and minority spin subbands, are therefore increased [28,30].For the Cu-embedded surfaces, similar Ni d -band narrowing and the magnetic moment enhancement will be expected because the Cu d -states are well below E F and no dd interaction to the Ni 3d bands will be expected [30].However, by embedding Cu, sp-d hybridization will be enhanced through the interaction of the Ni d bands with conductive Cu sp bands, and thus the magnetic moment of the top Ni layer will be decreased.Therefore, these two effects, the sp-d dehybridization by reducing the dd interaction and increasing the sp-d hybridization with adjacent Cu sp bands, compete with each other.latory behavior of magnetization for the deeper layers is due to Friedel oscillation caused by the slab geometry of the present calculation.By embedding Cu into the top Ni layer, reduction of the magnetic moment at the second layer Ni rather than the top layer is evident in Fig. 8(a).This is simply because the number of Cu neighbors is larger for the second layer than for the first layer.For example, for the Cu 1 Ni 3 /Ni(110) case, only one third of the top Ni atoms have Cu neighbors, but all Ni atoms in the second layer have contact with the embedded Cu (see Fig. 4).The suppressions of the moment at the second layer for Cu-embedded Ni(110) surfaces are due to increasing the sp-d hybridization with the Cu neighbors, which leads to decreasing the d components at the Ni sites [28,30,37].Such Cu-induced magnetic moment reduction near the surface layers was previously reported for Cu/Ni(111) and Cu/Ni(100) surfaces [30].The magnetic moment reduction is also seen for the third layer, but for the deeper layers the moment is recovered due to screening by the sp conduction electrons.Note that for the Cu have only Cu-Ni mixed rows.Therefore, a large magnetic moment is revived for the aligned structure compared to the other two structures.

IV. CONCLUSION
We demonstrated the detailed atomic structures and electronic states for Ni(110) and Cu-embedded Ni(110) surfaces.Cu embedded into the Ni surfaces shows slightly protrusive but nearly similar atomic positions to that of a pure Ni(110) surface, but, it shows distinct electronic states, particularly in terms of LDOS near E F and the surface magnetic moments.Because the Cu 3d states lay well below E F and are fully occupied, embedded Cu has marginal contribution to the d -derived states near E F compared to the unfilled Ni.This is one reason that the Cu overlayer is stable and inert compared to the bare Ni surfaces.In addition, although the magnetic moment of the relaxed Ni(110) surface is not significantly altered, Cu-embedded surfaces exhibit strong suppression of the surface magnetic moments, particularly at the second layer.

FIG. 2 :
FIG. 2: Band structure (left) and spin-resolved density of states (DOS) (right) for structure optimized Ni(110) surface.Blue and red lines are for majority and minority spin bands, respectively.

FIG. 3 :
FIG. 3: Local density of states (LDOS) for top (upper panel) and bottom (lower panel) atoms.LDOS is decomposed with s, p, and d components, indicated as solid lines with colors shown in inset of upper panel.×20 magnified s and p components are shown as broken lines.

FIG. 5 :
FIG. 5: Local density of states (LDOS) for top Cu (upper panel) and Ni (lower panel) atoms.LDOS is decomposed with s, p, and d components, indicated as solid lines with colors shown in inset of upper panel.

FIG. 6 :
FIG. 6: Three different configurations of Cu2Ni2/Ni(110) surfaces.Cu is represented by shaded circles and Ni is represented by open circles.Labels for each atom correspond to atoms in TableIII.Relative energies referred from aligned structure are indicated near each configuration.
FIG. 7: Local density of states (LDOS) for three top Cu atoms and the top Ni atom.Each LDOS is decomposed of s, p, and d components, indicated as solid lines with colors shown in inset of the second panel.Atom configuration is represented at inset of top panel.

Figure 8 (FIG. 8 :
FIG. 8: (a) Magnetic moments of Ni (filled circles) and Cu (open circles) plotted as a function of layer number.Moments are averaged within respective layer for Cu and Ni.Lines are only visual guides.(b) Average magnetic moments of Ni atoms for first (circles), second (squares), and third (triangles) layers for each Cu/Ni configuration plotted as a function of number of Cu atoms embedded in top layer.Lines are only visual guides.

TABLE III :
Atom heights for three different Cu/Ni configurations shown in Fig.6.Heights are measured from the middle layer.Superscripts in vicinity of elements correspond to atoms in Fig.6.