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We investigate the kinetic roughening of Ar$^+$ ion-sputtered Pd(001) surfaceboth experimentally and theoretically. \textit{In situ} real-time x-rayreflectivity and \textit{in situ} scanning tunneling microscopy show thatnanoscale adatom islands form and grow with increasing sputter time $t$.Surface roughness, $W(t)$, and lateral correlation length, $\xi(t)$, followsthe scaling laws, $W(t)\sim t^{\beta}$ and $\xi(t)\sim t^{1/z}$ with theexponents $\beta\simeq 0.20$ and $1/z\simeq 0.20$, for ion beam energy$\epsilon=0.5$ keV, which is inconsistent with the prediction of theKuramoto-Sivashinsky (KS) model. We thereby extend the KS model by applying theSigmund theory of sputter erosion to the higher order, ${\cal O}(\nabla^4,h^2)$, where $h$ is surface height, and derive a new term of the form$\nabla^2(\nabla h)^2$ which plays an indispensable role in describing theobserved morphological evolution of the sputtered surface.Comment: 4 pages, 6 figure

Kinetic Roughening of Ion-Sputtered Pd(001) Surface: Beyond the Kuramoto-Sivashinsky Model