Atomic structure and electronic properties of ${\mathrm{Ni}}_3\mathrm{Al}\left(111\right)$ and (011) surfaces

We present results of theoretical studies of the structural and electronic properties of (111) and (011) surfaces of paramagnetic ${\mathrm{Ni}}_3\mathrm{Al}$ alloy. Atomic and electronic structures of these surfaces have been obtained from the density-functional calculations performed with the use of plane wave basis set. Our ab initio calculations show that for all considered surfaces, the topmost Al atoms are located above Ni atoms, and the structural parameters of relaxed surface systems well correspond to experimental data provided by earlier low-energy electron-diffraction measurements. The details of the calculated electronic structure of ${\mathrm{Ni}}_3\mathrm{Al}\left(111\right)$ in the vicinity of the Fermi level were compared with the results of scanning tunneling spectroscopy (STS) measurements which we have performed for this system, and a good agreement has been found between the calculated local-density-of-states distributions and the shape of obtained STS spectra.

Figure 1

(a) Schematic plot (side and top views) of the supercell used in calculations for the ${\mathrm{Ni}}_3\mathrm{Al}\left(111\right)$ system (the slab with nine atomic layers is presented). (b) The same as in (a) but for the ${\mathrm{Ni}}_3\mathrm{Al}\left(011\right)$ system.

Figure 2

Schematic side view of the relaxed ${\mathrm{Ni}}_3\mathrm{Al}\left(111\right)$ structure. Values of the denoted characteristic interplane distances are given in Table .

Figure 3

Changes of the positions of atomic planes in the ${\mathrm{Ni}}_3\mathrm{Al}\left(111\right)$ slab caused by relaxation, with respect to an ideal (unrelaxed) geometry for the slab with 9 (a) and 11 (b) layers.

Figure 4

(a) Total LDOS distributions at the surface layer of ${\mathrm{Ni}}_3\mathrm{Al}\left(111\right)$ (thick solid line), and the two subsequent subsurface layers (thin dotted and dashed lines, respectively). For comparison, the corresponding distribution at the bulk layer is also shown (thin solid line). All these distributions represent the sum of LDOS contributions connected with one Al atom and three Ni atoms from the $(2\times 2)$ unit cell of the corresponding layer. (b) LDOS distributions connected with three Ni atoms (solid line) and one Al atom (dashed line) from the $(2\times 2)$ unit cell of the surface layer of ${\mathrm{Ni}}_3\mathrm{Al}\left(111\right)$. (c) LDOS contribution connected with Ni atoms from the ${\mathrm{Ni}}_3\mathrm{Al}\left(111\right)$ surface layer (solid line) and its components built up by $s\text{−}p$ and $d$ states of surface Ni atoms (dashed and dotted lines, respectively). (d) The same as in (c) but for the surface Al atom.

Figure 5

(a) STM image $(75\times 75{\mathrm{\AA }}^2)$ of the clean ${\mathrm{Ni}}_3\mathrm{Al}\left(111\right)$ surface, measured at $I_T=260\mathrm{pA}$, $U_{\mathit{\text{bias}}}=50\mathrm{mV}$, and $T_{\mathit{STM}}=23\mathrm{K}$. The $(2\times 2)$ unit cell is indicated. (b) Filtered STM image (a) using Fourier filter. (c) Tunneling spectra measured at the points indicated on the STM image in (a). Curves 1–5 were acquired after the feedback loop was opened at $85\mathrm{mV}$ at a tunneling current of $120\mathrm{pA}$. The corresponding modulation frequency was $5\mathrm{kHz}$ with an amplitude of $20\mathrm{mV}$. Solid line shows the DOS calculated for the ${\mathrm{Ni}}_3\mathrm{Al}\left(111\right)$ surface.

Figure 6

(a) STM image $(71\times 71{\mathrm{\AA }}^2)$ of the ${\mathrm{Al}}_2{\mathrm{O}}_3∕{\mathrm{Ni}}_3\mathrm{Al}\left(111\right)$ system, measured at $I_T=72\mathrm{pA}$, $U_{\mathit{\text{bias}}}=3.21\mathrm{V}$, and $T_{\mathit{STM}}=23\mathrm{K}$. (b) Tunneling spectra measured at the points indicated on the STM image in (a). Curves 1–5 were acquired after the feedback loop was opened at $190\mathrm{mV}$ at a tunneling current of $71\mathrm{pA}$. The corresponding modulation frequency was $5\mathrm{kHz}$ with an amplitude of $20\mathrm{mV}$. Solid line shows the DOS calculated for the ${\mathrm{Ni}}_3\mathrm{Al}\left(111\right)$ surface.

Figure 7

(a) Schematic side view of the relaxed ${\mathrm{Ni}}_3\mathrm{Al}\left(011\right)$ structure. Values of the denoted characteristic interplane distances are given in Table . (b) Top view of the ideal surface and the subsurface layers. Large black and gray circles denote surface Al and Ni atoms, respectively, while small gray circles represent subsurface Ni atoms. Arrows indicate the direction of the horizontal shift of subsurface Ni atoms caused by the relaxation. (c) The same as in (b) but for the third and fourth layers.

Figure 8

(a) Total LDOS distributions at the surface layer of ${\mathrm{Ni}}_3\mathrm{Al}\left(011\right)$ (thick solid line), and the two subsequent subsurface layers (thin dotted and dashed lines, respectively). In the case of the first and third layers (mixed layers), the corresponding dependences represent the sum of LDOS contributions connected with two Al atoms and two Ni atoms from the respective $(2\times 2)$ unit cell, while for the second layer, the LDOS distribution is the sum of the contributions connected with four Ni atoms. (b) LDOS distributions connected with two Ni atoms (solid line) and two Al atoms (dashed line) from the $(2\times 2)$ unit cell of the surface layer of ${\mathrm{Ni}}_3\mathrm{Al}\left(011\right)$. (c) LDOS contribution connected with Ni atoms from the ${\mathrm{Ni}}_3\mathrm{Al}\left(011\right)$ surface layer (solid line) and its components built up by $s\text{−}p$ and $d$ states of surface Ni atoms (dashed and dotted lines, respectively). (d) The same as in (c) but for surface Al atoms.