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Here Γ is the width at half maximum of the resonance produced by the hybridization with the conduction electrons in the right and left lead and ǫ 0 is the energy of the local state. The value of Γ depends on the height and width of the barrier potential between the central region and the leads.

We present theoretical studies based on the use of realistic electronic structures, which conclude that in the spin polarized electron energy loss spectrum of Fe and of ultrathin Fe films a strong signature of spin waves should appear for energy losses in the range of 250 meV and below. New experimental data we present show that indeed the spin asymmetry in the loss spectrum increases dramatically in this regime, as expected from its presence. [S0031-9007(99)08710-4] PACS numbers: 75.30.Ds, 75.50.Bb Currently there is great interest in ultrathin ferromagnetic films and, more generally, in the outer surface layers of magnetic materials. Through their study, we may test our ability to predict electronic structures and magnetic properties of new, artificially synthesized materials and to extend our knowledge of bulk magnetism to the very different surface environment. One may also explore magnetism in two dimensions and the transition to three. With ultrathin films incorporated into multilayers, exciting applications in magnetic recording have been realized, and new applications to magnetic storage are envisioned. Such applications require full knowledge of the response characteristics of ultrathin ferromagnetic films. Finally, while the remarks above and the present paper place their primary focus on ultrathin ferromagnetic films, we note that in many other systems of current interest magnetism in reduced dimensionality plays a key role. The high temperature superconductors provide an example. Thus, new experimental methods which explore the magnetism of ultrathin films and surfaces are of fundamental interest. In this paper, we present theoretical calculations and the first data which show that electron energy loss spectroscopy in its spin polarized version (SPEELS) can probe short wavelength spin waves in ultrathin magnetic films. This is thus a new technique which may be employed to probe the nature of spin fluctuations at the surface of diverse magnetic materials, and in thin films of such materials.Theory in the area of ultrathin film and surface magnetism has focused almost entirely on ground state properties of the ultrathin films [1]. Electronic band structures from such studies do approximate the quasiparticle energies; these can be compared with data taken by techniques such as inverse photoemission [2].In addition, such films possess a spectrum of spin excitations which control their dynamic response. Also, these enter importantly into the analysis of other phenomena. For instance, the spin dependence of the inelastic mean free path of excited electrons is controlled by their scattering from spin excitations. This enters centrally into the analysis of diverse spin polarized electron spectros-copies and also transport in such materials. Low lying spin waves in ultrathin films have been studied both by ferromagnetic resonance [3] and by Brillouin light scattering [4]. Both methods excite only modes with very long wavelengths compared to a lattice constant. Thus, they probe only properties of the film th...

Using the time-dependent non-crossing approximation, we calculate the transient response of the current through a quantum dot subject to a finite bias when the dot level is moved suddenly into a regime where the Kondo effect is present. After an initial small but rapid response, the time-dependent conductance is a universal function of the temperature, bias, and inverse time, all expressed in units of the Kondo temperature. Two timescales emerge: the first is the time to reach a quasi-metastable point where the Kondo resonance is formed as a broad structure of half-width of the order of the bias; the second is the longer time required for the narrower split peak structure to emerge from the previous structure and to become fully formed. The first time can be measured by the gross rise time of the conductance, which does not substantially change later while the split peaks are forming. The second time characterizes the decay rate of the small split Kondo peak (SKP) oscillations in the conductance, which may provide a method of experimental access to it. This latter timescale is accessible via linear response from the steady state and appears to be related to the scale identified in that manner [A. Rosch, J. Kroha, and P. Wölfle, Phys. Rev. Lett. 87, 156802 (2001)].

The response of a quantum dot in the Kondo regime to rectangular pulsed bias potentials of various strengths and durations is studied theoretically. It is found that the rise time is faster than the fall time, and also faster than time scales normally associated with the Kondo problem. For larger values of the pulsed bias, one can induce dramatic oscillations in the induced current with a frequency approximating the splitting between the Kondo peaks that would be present in steady state. The effect persists in the total charge transported per pulse, which should facilitate the experimental observation of the phenomenon.The theoretical predictions 1 of consequences of the Kondo effect for the steady state conduction through quantum dots began a decade ago. At low temperatures, a narrow resonance in the dot density of states can form at the Fermi level, leading to a large enhancement of the dot's conductance, which is strongly dependent on temperature, bias, and magnetic field. Many of these effects have been recently observed by a set of experiments by several groups. 2 These successes, supplemented by the anticipation that time dependent experiments 3 are not far behind, have spurred a number of theoretical groups 4 to consider the effects expected when sinusoidal biases or gate potentials are applied. Surprisingly, the application of steps or pulses, which can provide a less ambiguous measure of time scales, have not been considered until very recently; 5 the latter work considered the time dependent change in linear response conductance when a stepped potential was applied to a gate, thereby shifting the dot into the Kondo regime. In the present work we consider the response of a dot already in the Kondo regime to a sudden change of the bias potential across the dot. We show that the physics is qualitatively different from the latter case, 5 leading to a different range of characteristic times and physical phenomena.While Ref. 5 studied the time scale for the system to go from one equilibrium configuration to another, we study here the time scale to go from an equilibrium configuration to a nonequilibrium one; and then back to equilibrium again. We find that these latter two times scales are very different from each other, the first being much shorter-and also much shorter than the time scale of Ref. 5. Furthermore, if one applies a rectangular bias pulse large enough to split the Kondo resonance, then there appear current oscillations 6 at a frequency characterizing the splitting between the Kondo peaks. We show that these current oscillations cause oscillations in the charge transported through the dot as a function of pulse length, thus providing a clear experimental signature. The damping of the oscillations provides an additional time scale which also can be measured directly.We model the quantum dot by a single spin degenerate level of energy ⑀ dot coupled to leads through tunnel barriers, as illustrated schematically in the inset to Fig. 1. The Coulomb charging energy U prevents the level from being doub...

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Polarized reflection spectra between 4.000 and 20 cm -1 and absorption spectra (at temperatures of liquid helium) between 2.000 and 650 cm -1 have been measured of the isomorphous crystals NaNO3, CaCOa, MgCO 3 (D~a) and of CaMg (CO3) 2 (C32i). The wavenumbers of the fundamental infrared transitions and of the twophonon-combinations have been determined. The combinationbands show a structure, which allows some insight into the wavevector dispersion of the phonon branches of these crystals. Selection rules have been worked out for several points in the interior and on the border of the Brillouin zone. By comparison with the spectra they give evidence for the presence of critical points of the phonon-branches for wavevectors parallel to the trigonal axis of the crystal.

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