Paolo Politi

Instabilities in crystal growth by atomic or molecular beams

Abstract When growing a crystal, a planar front is desired for most of the applications. This plane shape is often destroyed by instabilities of various types. In the case of growth from a condensed phase, the most frequent instabilities are diffusion instabilities , which have been studied in detail by many authors but will be briefly discussed in simple terms in Section 2. The present review is mainly devoted to instabilities which arise in ballistic growth, especially molecular beam epitaxy (MBE). The reasons of the instabilities can be geometric, but they are mostly kinetic (when the desired state cannot be reached because of a lack of time) or thermodynamic (when the desired state is unstable). The kinetic instabilities which will be studied in detail in Sections 4 and 5 result from the fact that adatoms diffusing on a surface do not easily cross steps (Ehrlich–Schwoebel or ES effect). When the growth front is a high symmetry surface, the ES effect produces mounds which often coarsen in time according to power laws. When the growth front is a stepped surface, the ES effect initially produces a meandering of the steps, which eventually may also give rise to mounds. Kinetic instabilities can usually be avoided by raising the temperature, but this favours thermodynamic instabilities of the thermodynamically unstable materials (quantum wells, multilayers …) which are usually prepared by MBE or similar techniques. The attention will be focussed on thermodynamic instabilities which result from slightly different lattice constants a and a +δ a of the substrate and the adsorbate. They can take the following forms. (i) Formation of misfit dislocations, whose geometry, mechanics and kinetics are analysed in detail in Section 8. (ii) Formation of isolated epitaxial clusters which, at least in their earliest form, are ‘coherent’ with the substrate, i.e. dislocation-free (Section 10). (iii) Wavy deformation of the surface, which is presumably the incipient stage of (ii) (Section 9). The theories and the experiments are critically reviewed and their comparison is qualitatively satisfactory although some important questions have not yet received a complete answer. Short chapters are devoted to shadowing instabilities, twinning and stacking faults, as well as the effect of surfactants.

Island nucleation in the presence of step-edge barriers: Theory and applications

We develop a theory of nucleation on top of two-dimensional islands bordered by steps with an additional energy barrier

Dipolar interaction between two-dimensional magnetic particles

\ensuremath{\Delta}{E}_{S}

TUNNELING AND MAGNETIC RELAXATION IN MESOSCOPIC MOLECULES

for descending atoms. The theory is based on the concept of the residence time of an adatom on the island, and yields an expression for the nucleation rate which becomes exact in the limit of strong step-edge barriers. This expression differs qualitatively and quantitatively from that obtained using the conventional rate-equation approach to nucleation [J. Tersoff et al., Phys. Rev. Lett.

Vertex dynamics in finite two-dimensional square spin ices.

72,

Disorder Strength and Field-Driven Ground State Domain Formation in Artificial Spin Ice: Experiment, Simulation, and Theory

266 (1994)]. We argue that rate-equation theory fails because nucleation is dominated by the rare instances when two atoms are present on the island simultaneously. The theory is applied to two distinct problems: the onset of second-layer nucleation in submonolayer growth, and the distribution of the sizes of top terraces of multilayer mounds under conditions of strong step-edge barriers. Application to homoepitaxial growth on Pt(111) yields the estimate

When does coarsening occur in the dynamics of one-dimensional fronts?

\ensuremath{\Delta}{E}_{S}g~0.33

Anisotropy effects on the magnetic excitations of a ferromagnetic monolayer below and above the Curie temperature

eV for the additional energy barrier at CO-decorated steps.

Crystal symmetry, step-edge diffusion, and unstable growth

We determine the effective dipolar interaction between single domain two-dimensional ferromagnetic particles (islands or dots), taking into account their finite size. The first correction term decays as 1/D 5 , where D is the distance between particles. If the particles are arranged in a regular two-dimensional array and are magnetized in plane, we show that the correction term reinforces the antiferromagnetic character of the ground state in a square lattice, and the ferromagnetic one in a triangular lattice. We also determine the dipolar spin-wave spectrum and evaluate how the Curie temperature of an ensemble of magnetic particles scales with the parameters defining the particle array: height and size of each particle and interparticle distance. Our results show that dipolar coupling between particles might induce ferromagnetic long range order at experimentally relevant temperatures. However, depending on the size of the particles, such a collective phenomenon may be disguised by superparamagnetism.

Diversity enabling equilibration: disorder and the ground state in artificial spin ice.

The relaxation of the magnetization in big molecular groups embedded in crystals is studied and compared with experimental data on Mn12O12. At sufficiently high temperatures (T > 2 K in Mn12O12) the relaxation is thermally activated, and the exchange of energy with phonons produces relaxation through a cascade of elementary transitions where the component Sz of the spin along the tetragonal axis changes by δm = ±1 or ±2. At lower temperatures, tunneling occurs, but energy conservation requires exchange of energy with nuclear spins in very low magnetic fields (smaller than the hyperfine field), or with phonons in higher field. The phonon assisted tunneling rate 1/τ is proportional to H3 for weak fields H(H < 2 Tesla). A minimum of τ is expected when the field is of the order of magnitude of the maximum hyperfine field. The theoretically predicted minimum is sharper and should occur at a field value four times as small than experimentally observed.