Visualizing anisotropic propagation of stripe domain walls in staircaselike transitions of ${\mathrm{IrTe}}_2$

We present a scanning tunneling microscopy (STM) study of the domain evolution across two first-order phase transitions of stripe modulations in ${\mathrm{IrTe}}_2$ that occur at $T_{\mathrm{C}}\approx 275$ K and $T_{\mathrm{S}}\approx 180$ K, respectively. Phase coexistence of the hexagonal $(1\times 1)$ structure and the $(5\times 1)$ stripe modulation is observed at $T_{\mathrm{C}}$, while various $(p\times 1)$ modulations ($p=3n+2$ with $2\le n\in \mathbb{N}$) are observed below $T_{\mathrm{S}}$. Using STM atomic resolution, we observe anisotropic propagation of domain boundaries along different directions, indicating significantly different kinetic energy barriers. These results are consistently explained by a theoretical analysis of the energy barrier for domain wall propagation as obtained by density functional theory. Individual switching processes observed by STM indicate that the wide temperature range of the transition from the $(5\times 1)$ stripes to the $(6\times 1)$-ordered ground state is probably caused by the numerically limited subset of switching processes that are allowed between a given initial and the final state. The observations on ${\mathrm{IrTe}}_2$ are discussed in terms of a “harmless staircase” with a finite number of first-order transitions between commensurate phases and within a “dynamical freezing” scenario.

Figure 1

(a) Overview STM image of a ${\mathrm{IrTe}}_2$(001) surface at the first phase transition on cooling. A line section taken at the bottom of the STM image reveals a tilt of $0.7^{\circ }$. (b) A zoomed-in image of the transition region (top panel) identifies the position of the kink as the boundary between the $(1\times 1)$ (right) and the $(5\times 1)$ phase (left). The enhanced corrugation of the $(5\times 1)$ phase can be recognized in the line section (bottom panel).

Figure 2

(a) STM topographic image taken at $T_{\mathrm{S}}=180\mathrm{K}$. Different $(p\times 1)$-ordered areas ($p=3n+2$ with $n\in \mathbb{N}$) are color enhanced in the bottom panel. A domain boundary (DB) separates a $(5\times 1)$ domain (right) from a domain dominated by $(8\times 1)$ modulations (left). It consists of two differently oriented straight segments, marked A and B. A circular label marks a defect to provide a reference point. The temporal evolution of the domain structure is shown after (b) 26, (c) 52, and (d) 78 min. The original position of the DB is highlighted by a line in (d).

Figure 3

(a) Series of STM images at $T_{\mathrm{S}}=180\mathrm{K}$ showing the growth of modulation stripes oriented at an angle of about ${60}^{\circ }$ with respect to the DB. Two surface defects are marked to provide a reference point. (b) Image series of the line-by-line domain growth of stripes running parallel to the DB. The arrow indicates the termination point of the same line. The average growth velocity of a single stripe is much higher than in (a).

Figure 4

(a) Schematic representation of the DB between the $(8\times 1)$ (left) and $(5\times 1)$ (right) phases. Two orientations, DB-A and DB-B (emphasized by elongated parentheses) and their broken dimers, labeled “A-blocks” (dotted line) and “B-blocks” (dashed), are marked green. Blue and black/red arrows represent the tunneling processes of “A-blocks” and “B-blocks,” respectively, with their size being inversely proportional to the potential barrier height. Parallelograms represent regions affected by structural changes during the tunneling processes. (b) Snapshot of the DB-B propagation after three tunneling processes (gray arrows). The double black arrow indicates the spatial movement of DB-A within one step. (c) Alternative propagation of DB-B. The double red arrow shows movement of DB-B within one step.

Figure 5

STM data taken on cleaved ${\mathrm{IrTe}}_2$ at the same sample location at $T=180$ K after cooling down from RT. For clarity, the different domains were color enhanced. Initially (a), the surface area marked by a rectangle ($\approx 25\times 12{\mathrm{nm}}^2$) exhibits $(8\times 1)$-, $(11\times 1)$-, and $(5\times 1)$-ordered domains in close proximity. During the time required to complete the scan a switching occurs (b), resulting in the conversion of one $(11\times 1)$- and one $(5\times 1)$-stripe segment into two $(8\times 1)$ stripes. As shown by the following image (c), the $(11\times 1)$ domain in the upper part of the image is eventually annihilated.