Atomic structure of the (111) surface of the antiferromagnetic 1/1 Au-Al-Tb approximant

The recently discovered antiferromagnetic 1/1 Au-Al-Tb approximant exhibits a whirling spin order oriented along the [111] direction. Here we report an investigation of the atomic structure of the (111) surface by scanning tunneling microscopy and density functional theory (DFT) calculations. Scanning tunneling microscopy reveals a Tb-terminated step-terrace morphology, with step heights appearing to minimize the number of broken bulk icosahedra. The atomic structure of the terraces is bias dependent, with Tb atoms imaged under positive bias and Au/Al atoms under negative bias. The surface is found to reconstruct, with the Au/Al atoms producing a linear row structure, an example of a surface reconstruction in a Tsai-type system. These observations are confirmed by DFT calculations.

Figure 1

(a) Tsai-cluster model of hierarchical shells. A tetrahedron (gray) is contained within a dodecahedron (yellow), icosahedron (green), icosidodecahedron (blue), and rhombic triacontahedron (red). (b) Orthographic projection along the [111] direction of the 1/1 Au-Al-Tb unit cell, showing the spins of the origin and body-center icosahedra.

Figure 2

(a) STM image ($V_b=2$ V and $I_t=172$ pA) of the step terrace structure of the (111) surface. Here $\alpha$ indicates the terrace kink angle. White circles mark islands. The scale bar is 30 nm. (b) Histogram taken from (a), showing the step height distribution. The average step height is labeled. (c) Bulk model of Tb planes arranged along the [111] direction. Groups of three planes are separated by 0.43 nm, as labeled. Groups of planes which correspond to the measured step height are also indicated.

Figure 3

(a) STM image ($V_b=1900$ mV and $I_t=175$ pA) showing the atomic structure of a terrace. Bright dimerlike protrusions (highlighted by an oval) form a rhombohedral unit cell or hexagonal structure, both marked. The crystallographic direction is marked. The scale bar is 3 nm. (b) STM image ($V_b=1900$ mV and $I_t=172$ pA) showing additional features which appear dependent on tip condition. Again rhombohedral and hexagonal cells are marked. The crystallographic direction is marked. The scale bar is 3 nm. (c) Model schematic of Tb atoms (green) forming the structure in (a). The corresponding features (oval, rhombohedron, and hexagon) are marked. The scale bar is 3 nm. (d) Model structure used to explain the additional feature in (b). The scale bar is 3 nm. (e) and (f) Resultant spin structures of the hexagon highlighted in (b) and (d) at two different terraces. Arrows denote the spin direction, while the color indicates the type of icosahedron responsible for the spin. Planar views are shown below. Scale bars are 1 nm.

Figure 4

(a) STM image ($V_b=-1000$ mV and $I_t=140$ pA) of the terrace morphology under negative bias. A rhombohedral unit cell is marked, linking $\mathsf{V}$-shaped protrusions, one of which is circled in black. The crystallographic direction is marked. The scale bar is 3 nm. (b) FFT of (a), where spots are highlighted by circles, showing the sixfold symmetry of the distribution of the $\mathsf{V}$-shaped protrusions. The blue circles mark spots of increased intensity, indicating the twofold symmetry of the rows. (c) Model schematic of (a). Red, blue, yellow, and gray circles indicate fifth-, fourth-, second-, and first-shell positions of Au/Al atoms. The bulk truncated model is shown below the dashed line. A set of individual atoms is circled, indicating which atoms are removed under the reconstruction. Above the dashed line, the rhombohedral unit cell and $\mathsf{V}$-shaped protrusions of (a) are marked. The scale bar is 3 nm. (d) Model slab of the surface including Tb atoms. The rhombohedral unit cell and $\mathsf{V}$-shaped protrusions of (a) are again marked. The scale bar is 3 nm.

Figure 5

(a) Simulated STM image at $V_b=+1900$ mV. Bright circles form a hexagonal network matching the STM image of Fig. 3. Overlaid are some of the Tb atoms which form the hexagonal structure. A dim triangle can be seen at the center of the hexagon, i.e., from the lower Tb plane in Fig. 3. The scale bar is 2 nm. (b) Simulated STM image at $V_b=-1900$ mV. The row structure as observed in Fig. 4 can be clearly seen and is indicated by two parallel arrows. Overlaid are sections of the reconstructed model: One section is colored as with the Tsai-type shells and the other is colored to represent its chemistry, i.e., Au is gold and Al is purple. The $\mathsf{V}$-shaped protrusion and bridging feature in Fig. 4 are indicated with a black circle and an arrow, respectively. A dashed circle indicates a protrusion from first-shell atoms. The scale bar is 2 nm.

Figure 6

(a) Bulk model of Tb atoms illustrating where surface terminations would truncate the Tb icosahedra, either at the top (T), bottom (B), or middle (M). Skeletal structures highlight the nature of the truncation. Dashed lines separated by 0.43 nm illustrate the minimum step height for Tb atoms. (b) Same schematic as (a), altered to reflect the measured step height. The visible planes of Tb atoms are those in Fig. 3.