Orientation dependence of the Cu(001) surface step stiffness:  Failure of solid-on-solid and Ising models to describe experimental data

We have investigated the step stiffness on Cu(001) surfaces as a function of step orientation by two independent methods at several temperatures near 300 K. Both sets of data agree well and show a substantial dependence of the stiffness on the angle of orientation. With the exception of steps oriented along $〈110〉,$ the experimental stiffness is significantly larger than the stiffness calculated within the solid-on-solid model and the Ising model, even if next-nearest-neighbor interactions are taken into account. Our results have considerable consequences for the understanding and for the theoretical modeling of equilibrium and growth phenomena, such as step meandering instabilities.