First-Principles Study of the Temperature Dependence of Structural, Electronic, and Hyperfine Properties of the Cu(100) Surface
In this work, we investigate the temperature-dependent behavior of the pure (undoped) Cu(100) surface using first-principles calculations within the Density Functional Theory framework. One of the main objectives is to determine, as a first step, whether the unexpected linear dependence of the electric-field gradient (EFG) tensor observed in TDPAC experiments on $^{111}$Cd probes deposited on Cu(100) surfaces could arise from the surface generation itself or from surface reconstruction. To this end, we perform a comprehensive $\it{ab}$ $\it{initio}$ study of the Cu(100) surface reconstruction and its associated structural, electronic, and hyperfine properties as a function of temperature, not only at the outermost atomic layer (i.e., the topmost Cu atom) but also as a function of atomic depth relative to the surface. To study the temperature dependence of the EFG, we use experimentally determined temperature-dependent lattice parameters for bulk copper in our calculations. The anisotropic relaxation that arises when bulk symmetry is broken helps unravel the potential sources of EFG temperature dependence at the surface. Studying the electron density of conduction electrons $\rho$($\bf{r}$) at the atomic scale near the Cu nucleus and the atom-resolved partial density of states at the topmost Cu atom allows us to correlate the surface effect on the EFG with respect to the bulk value. Finally, we discuss the linear temperature dependence found for the EFG on the undoped Cu(100) surface in relation to the temperature dependence of the "lattice" contribution to the EFG in the framework of the universal correlation found by Raghavan $\it{et}$ $\it{al.}$ [PRL 34, 1280 (1975)] for noncubic metals, showing that the linear decrease of the EFG as T increases in the $^{111}$Cd-doped Cu(100) surface is probably mostly caused by the generation of the pure Cu(100) surface and its reconstruction.