The temperature dependence of magnetization in ferromagnetic nanostructures (e.g., nanoparticles or nanoclusters) is usually analyzed by means of an empirical extension of the Bloch law sufficiently flexible for a good fitting to the observed data an
d indicates a strong softening of magnetic coupling compared to the bulk material. We analytically derive a microscopic generalization of the Bloch law for the Heisenberg spin model which takes into account the effects of size, shape and various surface boundary conditions. The result establishes explicit connection to the microscopic parameters and differs significantly from the existing description. In particular, we show with a specific example that the latter may be misleading and grossly overestimates magnetic softening in nanoparticles. It becomes clear why the usual $T^{3/2}$ dependence appears to be valid in some nanostructures, while large deviations are a general rule. We demonstrate that combination of geometrical characteristics and coupling to environment can be used to efficiently control magnetization and, in particular, to reach a magnetization higher than in the bulk material.
We analyse a model where the anomalies of the bond-stretching LO phonon mode are caused by the coupling to electron dynamic response in the form of a damped oscillator and explore the possibility to reconstruct the spectrum of the latter from the pho
non measurements. Preliminary estimates point to its location in the mid infrared region and we show how the required additional information can be extracted from the oxygen isotope effect on the phonon spectrum. The model predicts a significant measurable deviation from the standard value of the isotope effect even if the phonon frequency is far below the electron spectrum, provided the latter is strongly incoherent. In this regime, which corresponds to the mid infrared scenario, the phonon linewidth becomes a sensitive and informative probe of the isotope effect.
It is shown that the Greens function on a finite lattice in arbitrary space dimension can be obtained from that of an infinite lattice by means of translation operator. Explicit examples are given for one- and two-dimensional lattices.
On the basis of a semi-phenomenological model, it is argued that the high energy anomaly observed in recent photoemission experiments on cuprates is caused by interaction with an overdamped bosonic mode in the mid-infrared region of the spectrum. Ana
lysis of optical conductivity allows to connect this excitation to the incoherent charge response reported for the majority of high Tc materials and some other perovskites. We show that its large damping is an essential feature responsible for the waterfall dispersion and linewidth of the spectral weight.
A new expression for the Greens function of a finite one-dimensional lattice with nearest neighbor interaction is derived via discrete Fourier transform. Solution of the Heisenberg spin chain with periodic and open boundary conditions is considered a
s an example. Comparison to Bethe ansatz clarifies the relation between the two approaches.
