Kardar-Parisi-Zhang roughening associated with nucleation-limited steady crystal growth.

The roughness of crystal surfaces and the shape of crystals play important roles in multiscale phenomena. For example, the roughness of the crystal surface affects the frictional and optical properties of materials such as ice or silica. Theoretical studies on crystal surfaces based on the symmetry principle proposed that the growing surfaces of crystal growth could be classified in the universal class of Kardar-Parisi-Zhang (KPZ), but experiments rarely observe KPZ properties. To fill this the gap, extensive numerical calculations of the crystal growth rates and the surface roughness (surface width) have been performed for a nanoscale lattice model using the Monte Carlo method. The results indicate that a (001) surface is smooth within the single nucleation growth region. In contrast, the same surface is atomically smooth but thermodynamically rough in the poly-nucleation growth region in conjunction with a KPZ roughness exponent. Inclined surfaces are known to become Berezinskii-Kosterlitz-Thouless (BKT) rough surfaces both at and near equilibrium. The two types of steps associated with the (001) and (111) terraces were found to induce KPZ surface roughness, while the interplay between steps and multilayered islands promoted BKT roughness.

Slope-temperature faceting diagram for macrosteps at equilibrium.

Faceting diagrams between surface slope and temperature are calculated numerically based on statistical mechanics for inclined surfaces between (001) and (111) surfaces at equilibrium. A lattice model is employed that includes point-contact-type step-step attractions from the quantum mechanical couplings between neighbouring steps. Comparing the obtained faceting diagrams with the phase diagram for step bunching proposed by Song and Mochrie for Si(113), the effective step-step attraction energy for Si(113) is approximately estimated to be 123 meV. The slope dependences of the mean height of the faceted macrosteps with a (111) side surface and that with a (001) side surface are calculated using the Monte Carlo method. The faceting diagrams can be used as a guide for controlling the assembling/disassembling of faceted macrosteps for designing new surface arrangements.

Faceted-rough surface with disassembling of macrosteps in nucleation-limited crystal growth.

To clarify whether a surface can be rough with faceted macrosteps that maintain their shape on the surface, crystal surface roughness is studied by a Monte Carlo method for a nucleation-limited crystal-growth process. As a surface model, the restricted solid-on-solid (RSOS) model with point-contact-type step-step attraction (p-RSOS model) is adopted. At equilibrium and at sufficiently low temperatures, the vicinal surface of the p-RSOS model consists of faceted macrosteps with (111) side surfaces and smooth terraces with (001) surfaces (the step-faceting zone). We found that a surface with faceted macrosteps has an approximately self-affine-rough structure on a 'faceted-rough surface'; the surface width is strongly divergent at the step-disassembling point, which is a characteristic driving force for crystal growth. A 'faceted-rough surface' is realized in the region between the step-disassembling point and a crossover point where the single nucleation growth changes to poly-nucleation growth.

Crossover from BKT-rough to KPZ-rough surfaces for interface-limited crystal growth/recession.

The crossover from a Berezinskii-Kosterlitz-Thouless (BKT) rough surface to a Kardar-Parisi-Zhang (KPZ) rough surface on a vicinal surface is studied using the Monte Carlo method in the non-equilibrium steady state in order to address discrepancies between theoretical results and experiments. The model used is a restricted solid-on-solid model with a discrete Hamiltonian without surface or volume diffusion (interface limited growth/recession). The temperature, driving force for growth, system size, and surface slope dependences of the surface width are calculated for vicinal surfaces tilted between the (001) and (111) surfaces. The surface velocity, kinetic coefficient of the surface, and mean height of the locally merged steps are also calculated. In contrast to the accepted theory for (2 + 1) surfaces, we found that the crossover point from a BKT (logarithmic) rough surface to a KPZ (algebraic) rough surface is different from the kinetic roughening point for the (001) surface. The driving force for crystal growth was found to be a relevant parameter for determining whether the system is in the BKT class or the KPZ class. It was also determined that ad-atoms, ad-holes, islands, and negative-islands block surface fluctuations, which contributes to making a BKT-rough surface.

Magnetic domain patterns on strong perpendicular magnetization of Co/Ni multilayers as spintronics materials: I. Dynamic observations.

Materials with perpendicular magnetic anisotropy can reduce the threshold current density of the current-induced domain wall motion. Co/Ni multilayers show strong perpendicular magnetic anisotropy and therefore it has become a highly potential candidate of current-induced domain wall motion memories. However, the details of the mechanism which stabilizes the strong perpendicular magnetization in Co/Ni multilayers have not yet been understood. In the present work, the evolution of the magnetic domain structure of multilayers consisting of pairs of 2 or 3 monolayers (ML) of Ni and 1 ML of Co on W(110) was investigated during growth with spin-polarized low-energy electron microscopy. An interesting phenomenon, that the magnetic domain structure changed drastically during growth, was revealed. In the early stages of the growth the magnetization alternated between in-plane upon Co deposition and out-of-plane upon Ni deposition. The change of the magnetization direction occurred within a range of less than 0.2 ML during Ni or Co deposition, with break-up of the existing domains followed by growth of new domains. The Ni and Co thickness at which the magnetization direction switched shifted gradually with the number of Co/Ni pairs. Above 3-4 Co/Ni pairs it stayed out-of-plane. The results indicate clearly that the Co-Ni interfaces play the important role of enhancing the perpendicular magnetic anisotropy.

Magnetic domain patterns on strong perpendicular magnetization of Co/Ni multilayers as spintronics materials: II. Numerical simulations.

Magnetic domains in ultrathin films form domain patterns, which strongly depend on the magnetic anisotropy. The magnetic anisotropy in Co/Ni multilayers changes with the number of layers. We provide a model to simulate the experimentally observed domain patterns. The model assumes a layer-dependent magnetic anisotropy. With the anisotropy parameter estimated from experimental data, we reproduce the magnetic domain patterns.

Sticky steps inhibit step motions near equilibrium.

Using a Monte Carlo method on a lattice model of a vicinal surface with a point-contact-type step-step attraction, we show that, at low temperature and near equilibrium, there is an inhibition of the motion of macrosteps. This inhibition leads to a pinning of steps without defects, adsorbates, or impurities (self-pinning of steps). We show that this inhibition of the macrostep motion is caused by faceted steps, which are macrosteps that have a smooth side surface. The faceted steps result from discontinuities in the anisotropic surface tension (the surface free energy per area). The discontinuities are brought into the surface tension by the point-contact-type step-step attraction. The point-contact-type step-step attraction also originates "step droplets," which are locally merged steps, at higher temperatures. We derive an analytic equation of the surface stiffness tensor for the vicinal surface around the (001) surface. Using the surface stiffness tensor, we show that step droplets roughen the vicinal surface. Contrary to what we expected, the step droplets slow down the step velocity due to the diminishment of kinks in the merged steps (smoothing of the merged steps).

Non-universal equilibrium crystal shape results from sticky steps.

The anisotropic surface free energy, Andreev surface free energy and equilibrium crystal shape (ECS) z = z(x,y) are calculated numerically using a transfer matrix approach with the density matrix renormalization group (DMRG) method. The adopted surface model is a restricted solid-on-solid (RSOS) model with 'sticky' steps, i.e. steps with a point-contact-type attraction between them (p-RSOS model). By analyzing the results, we obtain a first-order shape transition on the ECS profile around the (111) facet; and on the curved surface near the (001) facet edge, we obtain shape exponents having values different from those of the universal Gruber-Mullins-Pokrovsky-Talapov (GMPT) class. In order to elucidate the origin of the non-universal shape exponents, we calculate the slope dependence of the mean step height of 'step droplets' (bound states of steps) (n(p)) using the Monte Carlo method, where p = (∂z/∂x,∂z/∂y) and (·) represents the thermal average. Using the result of the |p| dependence of (n(p)), we derive a |p|-expanded expression for the non-universal surface free energy f(eff)(p), which contains quadratic terms with respect to |p|. The first-order shape transition and the non-universal shape exponents obtained by the DMRG calculations are reproduced thermodynamically from the non-universal surface free energy f(eff)(p).