Noncontact atomic force microscopy imaging of atomic structure and cation defects of the polar MgAl${}_2$O${}_4$ (100) surface: Experiments and first-principles simulations

Atom-resolved noncontact atomic force microscopy (NC-AFM) was recently used to reveal that the insulating spinel MgAl${}_2$O${}_4$(100) surface, when prepared under vacuum conditions, adopts a structurally well-defined Al and O-rich structure (Al${}_4$-O${}_4$-Al${}_4$ termination) consisting of alternating Al and double-O rows, which are, however, interrupted by defects identified as interchanged Mg in the surface layers (so-called antisite defects). From an interplay of futher NC-AFM experiments and first-principles NC-AFM image simulations, we present here a detailed analysis of the NC-AFM contrast on the MgAl${}_2$O${}_4$(100) surface. Experiments show that the contrast on MgAl${}_2$O${}_4$(100) in atom-resolved NC-AFM is dominated by two distinctly different types of contrast modes, reflecting two oppositely charged tip-apex terminations. In this paper, we analyze the contrast associated with these imaging modes and show that a positively charged tip-apex (presumably Mg${}^{2+}$) interacts most strongly with the oxygen atoms, thus imaging the oxygen lattice, whereas a negatively charged tip-apex (O${}^{2-}$) will reveal the cation sublattice on MgAl${}_2$O${}_4$. The analysis of force-vs-distance calculations for the two tips shows that this qualitative picture, developed in our previous study, holds for all realistic tip-surface imaging parameters, but the detailed resolution on the O double rows and Al rows changes as a function of tip-surface distance, which is also observed experimentally. We also provide an analysis of the tip dependency and tip-surface distance dependency for the NC-AFM contrast associated with single Al vacancies and Mg-Al antisite defects on the MgAl${}_2$O${}_4$(100) surface and show that it is possible on the basis of NC-AFM image simulations to discriminate between the Al${}^{3+}$ and Mg${}^{2+}$ species in antisite defects and hypothetical Al vacancies.

Figure 1

(a) Side view of a ball model showing the bulk structure of MgAl${}_2$O${}_4$ spinel. (b) The stoichiometric 50% Mg-terminated surface. (c) Nonstoichiometric surface terminated by an O${}_4$-Al${}_4$-O${}_4$ layer formed by removing the Mg atoms from the bottom and top layers. (d) and (e) Same O${}_4$-Al${}_4$-O${}_4$ surface termination as in (c), however, with a surface incorporated antisite (d) and an Al vacancy (e).

Figure 2

Tip-surface unit cell used in simulations. The upper part reflects the tip apex model as an MgO cube, which in this situation is oriented to expose an O-terminated tip. The lower part shows the O${}_4$-Al${}_4$-O${}_4$ surface of MgAl${}_2$O${}_4$(100).

Figure 3

Experimental NC-AFM images of the (a) oxygen and (b) aluminum lattice obtained with a positive and a negative tip apex, respectively. Line scans (c) and (d) illustrate the periodicities measured on the oxygen lattice (a) with a positive tip. Line scans (e) and (f) illustrate the periodicities measured on the Al lattice (b) with a negative tip. In both lattices, the distances $d_{\parallel }$ and $d_1$ $+$ $d_2$ match the values from the structural model in Fig. 1(c). NC-AFM parameters: (a) $d{f}_{\mathrm{set}}$ $=$ −126 Hz, $A_{p-p}$ $=$ 10 nm, $U_{\mathrm{bias}}$ $=$ 1.0 V (b) $d{f}_{\mathrm{set}}$ $=$ −30 Hz, $A_{p-p}$ $=$ 10 nm, $U_{\mathrm{bias}}$ $=$ 3.0 V.

Figure 4

(a) NC-AFM simulations of the O${}_4$-Al${}_4$-O${}_4$-terminated surface utilizing a positively charged tip apex. Images are shown as the tip-surface distance $Z$ is varied from 2.5 to 4.0 Å. (b) Spectroscopy curves showing the detuning as a function of tip-surface distance at four different surface sites. (c) Line scan perpendicular to the oxygen rows (marked in the images with dashed lines) at $Z$ $=$ 3.0 Å shows how the distance between two oxygen atoms ($d_1$) is clearly resolved; however, at $Z$ $=$ 4.0 Å, this distance is no longer well defined. (d) Line scans along the rows (marked with solid lines) show how the corrugation of the oxygen atoms decreases when going from $Z$ $=$ 3.0 to 4.0 Å. At $Z$ $=$ 4.0 Å, the periodicity doubles (2 × $d_{\parallel }$, quadratic unit cell indicated in $Z$ $=$ 3.5 Å image), however, the corrugation is 0.1 Hz, which is approximately the resolution limit in our NC-AFM setup.

Figure 5

Experimental NC-AFM images recorded within a short time period with the same positively charged tip. (a) Image recorded with $d{f}_{\mathrm{set}}$ $=$ −72 Hz showing the oxygen atoms fully resolved close to the surface. (b) Far from the surface at $d{f}_{\mathrm{set}}$ $=$ −32 Hz, the oxygen atoms are resolved in pairs. (c) Line scan belonging to the image in (a) illustrating the corrugation of the double-row oxygen atoms. (d) Line scan belonging to the image in (b) illustrating how the corrugation Δ$f_{\mathrm{o}-\mathrm{o}}$ equals zero when scanning at larger $Z$, thereby resolving the oxygen atoms in pairs. NC-AFM parameters for both images: $A_{p-p}$ $=$ 10 nm, $U_{\mathrm{bias}}$ $=$ 2.1 V

Figure 6

(a) NC-AFM simulations of the O${}_4$-Al${}_4$-O${}_4$-terminated surface utilizing a negatively charged tip apex. Images are shown as the tip-surface distance $Z$ is varied from 2.5 to 4.0 Å. (b) Spectroscopy curves showing the detuning as a function of tip-surface distance at four different surface sites. (c) Line scans perpendicular to the Al rows (marked by dashed lines in the images) illustrating how the corrugation decreases as the tip-surface distance is increased from $Z$ $=$ 3.0 to 4.0 Å. (d) Line scans along the Al rows (marked by solid lines in the images) illustrating how the corrugation of the Al atoms along the rows decreases when scanning at large tip-surface distance. At $Z$ $=$ 3.5 Å, a double periodicity starts to arise (marked by black square).

Figure 7

Experimental NC-AFM images recorded within a short time period with the same negatively charged tip. (a) Close to the surface ($d{f}_{\mathrm{set}}$ $=$ −48 Hz), the aluminum atoms are fully resolved. (b) Far from the surface ($d{f}_{\mathrm{set}}$ $=$ −40 Hz), the rows are still resolved; however, the aluminum atoms along the rows are no longer resolved. (c) Line scan illustrating the corrugation of the Al rows in image (a). (d) Line scan showing how the corrugation decreases when scanning at larger tip-surface separation in image (b).

Figure 8

NC-AFM simulations of 50% Mg-terminated surface utilizing (a) a positively and (b) negatively charged tip apex. (a) Close to the surface, only the oxygen lattice is resolved; however, when increasing the tip-surface distance, Mg starts to appear as holes in the oxygen rows giving rise to a quadratic surface unit cell. (b) Close to the surface, both the Al and the Mg cations are resolved; however, with increasing tip-surface distance, only the Mg atoms are visible as protrusions giving rise to a quadratic surface unit cell.

Figure 9

NC-AFM images of the (a) oxygen and (b) aluminum lattice. (c) Line scan across the oxygen rows [indicated by solid and dashed lines in (a)] illustrating the change in corrugation of the oxygen atoms when neighboring an antisite. (d) Line scan across the aluminum rows [indicated by solid and dashed lines in (b)] illustrating the decrease in contrast at antisites.

Figure 10

(a) Calculated frequency detuning-vs-distance curves for the positive tip. (b) Simulated image at $Z$ $=$ 2.75 Å illustrating how the oxygen atoms neighboring the antisite possess the highest contrast. (c) Ball model indicating the coordinates of the contrast curves in (a). (d) Experimental NC-AFM image zoom-in on an antisite with a ball model on top for guidance. (e) Experimental NC-AFM image with the oxygen atoms surrounding the antisite better resolved.

Figure 11

(a) Calculated frequency detuning-vs-distance curves utilizing a negative tip. (b) NC-AFM image zoom-in on an antisite with a ball model on top for guidance. (c) Ball model indicating the coordinates of the contrast curves in (a). (d) Simulated image at $Z$ $=$ 2.4 Å illustrating how the antisite is depicted as a hole on the aluminum row. (e) Simulated image at $Z$ $=$ 2.9 Å illustrating how the antisite, at larger distances, are imaged as a protrusion on the aluminum row.

Figure 12

NC-AFM simulations of the O${}_4$-Al${}_4$-O${}_4$-terminated surface containing an Al vacancy utilizing (a) a positive tip and (b) negative tip. In both tip modes, the vacancy is associated with a contrast increase on the aluminum row.