Marta Brajczewska

Ionization energy and electron affinity of a metal cluster in the stabilized jellium model: Size effect and charging limit

We report the first reliable theoretical calculation of the quantum size correction c which yields the asymptotic ionization energy I(R)=W+(12+c)/R+O(R−2) of a simple-metal cluster of radius R. Restricted-variational electronic density profiles are used to evaluate two sets of expressions for the bulk work function W and quantum size correction c: the Koopmans expressions, and the more accurate and profile-insensitive ΔSCF expressions. We find c≈−0.08 for stabilized (as for ordinary) jellium, and thus for real simple metals. We present parameters from which the density profiles may be reconstructed for a wide range of cluster sizes, including the planar surface. We also discuss how many excess electrons can be bound by a neutral cluster of given size. Within a continuum picture, the criterion for total-energy stability of a negatively charged cluster is less stringent than that for existence of a self-consistent solution.

Self-compression of metallic clusters under surface tension

Abstract The stabilized jellium model is used to explore the physics of self-compression for spherical clusters of simple-metal atoms. Within the continuum or liquid drop model, strong compression of the interior ionic density of a small cluster (with respect to the bulk density) results from cooperation between surface tension and surface suppression of the elastic stiffness. The latter effect is due to the large negative value of σ″, the second derivative of surface tension with respect to uniform strain. Self-compression also renormalizes the effective curvature-energy coefficient, and contributes to the asymptotic (large-radius) size effect on the ionization energy. A quantum-mechanical calculation of interior density as a function of electron number displays small shell-structure oscillations around the average behavior predicted by the liquid drop model. Numerical results are presented for clusters of Al, Na, and Cs. For compact 6-atom clusters of these metals, predicted bond lengths are smaller than their bulk values by 10%, 6%, and 4%, respectively.

Dependence of metal surface properties on the valence-electron density in the stabilized jellium model

Abstract The stabilized jellium model is the simplest model which yields realistic results for the physical properties of simple metals. For the surface properties, its single input is the valence-electron density, which is described by the density parameter r s . We remark that the surface energy and the work function as a function of r s , within that model, are reasonably approximated by power laws and compare that behaviour with similar descriptions found in the literature and with experiment. We also present a simple relationship between the surface energy and the bulk modulus, which is well fitted by the power − 7 2 of the density parameter (when the effective valence is taken to be z ∗ =1 ). Another simple relationship between the work function and the bulk modulus is shown.

Volume shift and charge instability of simple-metal clusters

Abstract Experiment indicates that small clusters show changes (mostly contractions) of the bond lengths with respect to bulk values. We use the stabilized jellium model to study the self-expansion and self-compression of spherical clusters (neutral or ionized) of simple metals. Results from Kohn — Sham density functional theory are presented for small clusters of Al and Na, including negatively-charged ones. We also examine the stability of clusters with respect to charging.

Thermal boson expansion for the Heisenberg ferromagnet

A boson expansion, which takes into account fluctuations around a mean-field description at finite temperatures, is applied to the Heisenberg model of S=12 ferromagnet. The approach incorporates the T3/2-law for the magnetization at low temperatures and, without considering dynamical interactions, provides a better estimate of the critical temperature than the conventional energy renormalized magnon theory and the random-phase approximation.

Application of the thermal boson expansion to the Heisenberg ferromagnets EuO and EuS

Abstract The method of thermal boson expansion [1] is extended to the Heisenberg model with spins S ⩾ 1 and applied to the ferromagnetic insulators EuO and EuS. Taking in the momentum space an adequate cut-off, which is almost independent of the spin, a good guess of the critical temperature is made. The temperature dependent renormalization factor for spin waves and the reduced magnetization are calculated for a fcc lattice with S = 7/2, providing a reasonable agreement with the experimental data available on EuO and EuS.

The 1D Heisenberg antiferromagnet model by the variation after projection method

The four site and eight site 1D anti-ferromagnetic Heisenberg chains in the Jordan–Wigner representation are investigated within the standard Hartree–Fock and random phase approximation (RPA) approaches, both in the symmetry unbroken and in the symmetry broken phases. A translation invariant groundstate, obtained by the projection method as a linear combination of a symmetry-broken HF state and its image under reflection, is also considered, for each chain type. It is found that the projection method considerably improves the HF treatment for instance as far as the groundstate energy is concerned, but also with respect to the RPA energies. The results are furthermore confronted with the ones obtained within so-called SCRPA scheme.

The Heisenberg Antiferromagnet— An Explicitly Rotational Invariant Formulation —

A simple derivation of an explicitly rotation invariant Lagrangian describing the dynamics of an antiferromagnetic spin system is presented. The scope of the derived Lagrangian is analysed in the context of schematic models. It is shown that the Lagrangian describes the behaviour of spin systems from the anti-ferromagnetic to the ferromagnetic regimes.

Self-expansion and compression of charged clusters of stabilized jellium

In a positively charged metallic cluster, surface tension tends to enhance the ionic density with respect to its bulk value, while surface-charge repulsion tends to reduce it. Using the stabilized jellium model, we examine the self-expansion and compression of positively charged clusters of simply metals. Quantal results from the Kohn-Sham equations using the local density approximation are compared with continuous results from the liquid drop model. The positive background is constrained to a spherical shape. Numerical results for the equilibrium radius and the elastic stiffness are presented for singly and doubly positively charged aluminum, sodium, and cesium clusters of 1–20 atoms. Self-expansion occurs for small charged clusters of sodium and cesium, but not of aluminum. The effect of the expansion or compression on the ionization energies is analyzed. For Al6, we also consider net charges greater than 2+. The results of the stabilized jellium model for self-compression are compared with those of other models, including the SAPS (spherical averaged pseudopotential model).

Application of the thermal boson expansion to the Heisenberg antiferromagnet MnF2

Abstract We apply the thermal boson expansion which has been presented in refs. [1–3] to the Heisenberg isotropic antiferromagnet, submitted to an external field. Considering only spin waves with wave vectors up to a certain cut-off, the magnetization and the principal susceptibilities are calculated. The results are compared with the experimental data on MnF2.