Modern nanotechnology allows one to scale down various important devices (sensors, chips, fibers, etc.) and thus opens up new horizons for their applications. The efficiency of most of them is based on fundamental physical phenomena, such as transport of wave excitations and resonances. Short propagation distances make phase-coherent processes of waves important. Often the scattering of waves involves propagation along different paths and, as a consequence, results in interference phenomena, where constructive interference corresponds to resonant enhancement and destructive interference to resonant suppression of the transmission. Recently, a variety of experimental and theoretical work has revealed such patterns in different physical settings. The purpose of this review is to relate resonant scattering to Fano resonances, known from atomic physics. One of the main features of the Fano resonance is its asymmetric line profile. The asymmetry originates from a close coexistence of resonant transmission and resonant reflection and can be reduced to the interaction of a discrete (localized) state with a continuum of propagation modes. The basic concepts of Fano resonances are introduced, their geometrical and/or dynamical origin are explained, and theoretical and experimental studies of light propagation in photonic devices, charge transport through quantum dots, plasmon scattering in Josephson-junction networks, and matter-wave scattering in ultracold atom systems, among others are reviewed.

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Fano resonances in nanoscale structures

Spin-polarized electron tunneling

Recently it has been shown that many traditional models used for a description of dilute magnetic alloys are completely integrable and may be solved exactly without any approximation. In this article we summarize the results which have been obtained in this way. The main part of the article is devoted to the consistent and detailed account of the Bethe-Ansatz technique for the s-d exchange (Kondo) model with arbitrary impurity spin, s-d model with anisotropic exchange, degenerate exchange model and for the canonical Anderson model. The thermodynamic properties of a magnetic impurity in a non-magnetic metal host obtained by the Bethe method are considered in detail. Mainly attention is paid to the analysis of singularities associated with the formation of a localized moment, Kondo effect and mixedvalence phenomenon, which can be treated analytically. In the introductory part of the article we discuss the applicability of the models which we study in the paper to the real alloys and consider some m...

Exact results in the theory of magnetic alloys

Valence fluctuation phenomena occur in rare-earth compounds in which the proximity of the 4f level to the Fermi energy leads to instabilities of the charge configuration (valence) and/or of the magnetic moment. The authors review the experimental results observed in the subset of such systems for which the 4f ions form a lattice with identical valence on each site. The discussion includes key thermodynamic experiments, such as susceptibility and lattice constant, and spectroscopic experiments such as XPS and neutron scattering. This is followed by a review of existing theoretical work concerning both the ground states and the isomorphic phase transitions which occur in such compounds; the emphasis is on those aspects which make valence fluctuation phenomena such a challenging many-body problem.

https://iopscience.iop.org/article/10.1088/0034-4885/44/1/001/pdf

Valence fluctuation phenomena

In this paper, we review some of the key concepts in ultrathin film magnetism which underpin nanomagnetism. We survey the results of recent experimental and theoretical studies of well characterized epitaxial structures based on Fe, Co and Ni to illustrate how intrinsic fundamental properties such as the magnetic exchange interactions, magnetic moment and magnetic anisotropies change markedly in ultrathin films as compared with their bulk counterparts, and to emphasize the role of atomic scale structure, strain and crystallinity in determining the magnetic properties. After introducing the key length scales in magnetism, we describe the 2D magnetic phase transition and survey studies of the thickness dependent Curie temperature and the critical exponents which characterize the paramagnetic–ferromagnetic phase transition. We next discuss recent experimental and theoretical results on the determination of the exchange constant, followed by an overview of measurements of the magnetic moment in the elemental 3d transition metal thin films in the various crystal phases that have been successfully stabilized, thereby illustrating the sensitivity of the magnetic moment to the local symmetry and to the atomic environment. Finally, we discuss briefly the magnetic anisotropies of Fe, Co and Ni in the fcc crystalline phase, to emphasize the role of structure and the details of the interface in influencing the magnetic properties. The dramatic effect that adsorbates can have on the magnetic anisotropies of thin magnetic films is also discussed. Our survey demonstrates that the fundamental properties, namely, the magnetic moment and magnetic anisotropies of ultrathin films have dramatically different behaviour compared with those of the bulk while the comparable size of the structural and magnetic contributions to the total energy of ultrathin structures results in an exquisitely sensitive dependence of the magnetic properties on the film structure.

https://iopscience.iop.org/article/10.1088/0034-4885/71/5/056501/pdf

Magnetism in ultrathin film structures

Many rare-earth compounds (e.g., Sm chalcogenides, ${\mathrm{YbAl}}_{3}$) exhibit temperature-independent magnetic susceptibility at low temperatures in their mixed valence phase despite the fact that the ionic configuration in at least one of the valences is such as to lead to a Curie-Weiss behavior. An essential feature of these compounds is that the Fermi level is pinned to the $f$ levels. We first examine the effect of this feature in the Anderson model for an isolated impurity and find through a strong-coupling variational wave function as well as through a simple Green's-function treatment that the susceptibility is finite at $T\ensuremath{\rightarrow}0$\ifmmode^\circ\else\textdegree\fi{}K and of order $\frac{{\ensuremath{\mu}}^{2}}{\ensuremath{\Gamma}}$ where $\ensuremath{\Gamma}$ is the virtual width of the $f$ level corrected for correlation effects. For the compounds, a two-band ("$f$" and "$d$" with orbital degeneracies neglected) Hubbard-like model leads in the same treatment to a finite susceptibility at $T=0$, where now $\ensuremath{\Gamma}$ is essentially the $f\ensuremath{-}d$ hybridization energy. Order-of-magnitude agreement with experiments is obtained with a reasonable value of the $f\ensuremath{-}d$ mixing interaction. The physics of the finite susceptibility at $T=0$ is the renormalization of the local moments by the conduction electrons which is strongest when the $f$ levels are at the Fermi level.

Magnetic susceptibility of mixed-valence rare-earth compounds

The dependence of the calculated Ruderman-Kittel-Kasuya-Yosida range function of a one-dimensional free-electron metal on the order of the integrations over the occupied states, and over the Fourier components of the perturbation is discussed and clarified. The correct result is derived. The range function of a magnetized layer (e.g., a magnetic layer in a multilayer material) is also calculated and compared with the range functions of point sources in the one-dimensional and in the three-dimensional cases.

Ruderman-Kittel-Kasuya-Yosida range function of a one-dimensional free-electron gas.

We determine the range of values of the uniaxial surface anisotropy ${K}_{s}$ that leads to the formation of domains in an atomic monolayer of ferromagnetically coupled spins. If the ratio f of ${K}_{s}$ to the dipolar energy is larger than a minimum value ${f}_{\mathrm{min}}$ determined by the ratio of exchange to dipolar energies, and if the easy direction is normal to the layer plane, then a domain pattern is energetically favorable compared to any uniformly magnetized configuration. The maximum component of magnetization normal to the layer, ${M}_{\ensuremath{\perp}}$, increases continuously from zero as f increases from its threshold ${f}_{\mathrm{min}}$ and tends to the saturation magnetization value for large f. Above threshold (f=${f}_{\mathrm{min}}$), the width of the domains is very sensitive to the value of f, increasing very rapidly with f and reaching the macroscopic value of the order of 1 cm for a value f=1.4. Contrary to the usual assumption of thin domain walls determined by the ratio of exchange to anisotropy energy, in monolayers it is necessary to treat the domain structure as a whole and to include explicitly the dipolar energy. A variational treatment gives, at the threshold of ${K}_{s}$, a simple cosine dependence on distance for the magnetization normal to the layer. The calculation is extended to layers consisting of a few atomic planes.

Ferromagnetic strip domains in an atomic monolayer.

Dipole-dipole interactions and two-dimensional magnetism

As a model for mixed-valence thulium which fluctuates between the configurations ${f}^{13}$, S=(1/2), and ${f}^{12}$, S=1, we consider an ion with orbital degeneracy embedded in a free-electron continuum. We construct variational states of different total-spin multiplicity, namely singlet, doublet, and triplet. We find that the ground state is a singlet, with the triplet and doublet lying higher in energy and in that order. If we confine ourselves to the simplest variational functions, i.e., those that do not include electron-hole excitations of the Fermi sea, then the splitting between singlet and triplet is very small, of the order of a few percent of the mixing width. (Under the same approximation, this splitting for the case where one of the valence states is nonmagnetic, is of the order of the mixing width.) When excited states of the Fermi sea are included, we find that the 1/N expansion, which shows that in ${f}^{0}$ to ${f}^{1}$ fluctuating valence the corrections due to these states are small for large N, is not applicable to the present case because the degeneracies of ${f}^{1}$ and ${f}^{2}$ are comparable, and so N is of order unity. We do a perturbation calculation to all orders, keeping only the dominant logarithmic terms. This has the effect of enhancing the energy separation between singlet and magnetic states by a factor of order 3. This separation is still very small however; we conclude that the magnetism of TmSe is probably caused by interactions between ions.

Y. Yafet

Papers

Magnetic susceptibility of mixed-valence rare-earth compounds

Ruderman-Kittel-Kasuya-Yosida range function of a one-dimensional free-electron gas.

Ferromagnetic strip domains in an atomic monolayer.

Dipole-dipole interactions and two-dimensional magnetism

Ground state of an ion fluctuating between two magnetic valence states.