Transition between tetramer and monomer phases driven by vacancy configuration entropy onBi∕Ag(001)

Abstract

A phase transition between low-temperature $c(4\ifmmode\times\else\texttimes\fi{}4)$ and high-temperature $c(2\ifmmode\times\else\texttimes\fi{}2)$ phases on $\mathrm{Bi}∕\mathrm{Ag}(001)$ has been investigated using low energy electron diffraction, scanning tunneling microscopy (STM), and angle resolved ultraviolet photoelectron spectroscopy (ARUPS). STM experiments show that the $c(4\ifmmode\times\else\texttimes\fi{}4)$ surface is composed of Bi tetramers arrayed on a square lattice, while the tetramers are decomposed to monomers in the $c(2\ifmmode\times\else\texttimes\fi{}2)$ phase. ARUPS shows an upward shift of a Bi-induced surface resonance band around $\overline{\ensuremath{\Gamma}}$ upon the transition from $c(4\ifmmode\times\else\texttimes\fi{}4)$ to $c(2\ifmmode\times\else\texttimes\fi{}2)$, which suggests that the Bi tetramer is stabilized by local, covalent bonding between Bi atoms constituting a tetramer. ARUPS also indicates large Rashba spin-orbit splitting of the Bi-induced surface resonance band. The phase transition is associated with an intermediate temperature region in which the two phases coexist on the surface with their area changing gradually with changing temperature. The transition temperature is lowered for surface with higher vacancy density. A model is presented to show that vacancy configuration entropy drives the phase transition. Larger vacancy configuration entropy in the $c(2\ifmmode\times\else\texttimes\fi{}2)$ phase, due to the decomposition of tetramers, accounts for the behavior of the phase transition via the two-phase coexisting region.